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There are many game theory algorithms , and many of them are used in the field of image processing. But how can it be used for image enhancement. And which algorithm will be more suitable for this job.
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Image enhancement usually works by modelling some kinds of defects, determining model parameters, and compensating the effect. It normally uses quantitative methods rather than mere decisions.
IMO, it would be quite artificial to "force" Game theory into image processing.
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Do we know theoretical models how to share benefits between a focal company and for instance 3 tier 1 supplier's using a supply chain finance programme?
so what is ‘fair’
for instance there is a net saving of 1.5 euro using a SCF reverse factoring programme. Is the following split up fair or not, and why from a theoretical point of view:
€ 0.3 to the focal company and 3 times € 0.4 to the (3) tier 1 suppliers
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Dear Mr. Jansen!
May I kindly argue that a financial program in a supply chain network evolves via the context, the objectives set for a green supply chain integration. The performance of actors - the focal company and the 3 tiers - can be measured by the social exchange theory:
Taiwen Feng, et al. 2022. Sustainable supply chain finance adoption and firm performance: Is green supply chain integration a missing link? 28 March 2022, Sustainable Development Early View, Available at:
Yours sincerely, Bulcsu Szekely
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Game theory is a very promising technique to achieve optimal outcomes and can be applied to almost all concepts. I am trying to explore game theory for future purposes. However, as a beginner, I couldn't get very good resources regarding game theory.
Please share your resources (i.e., video or blog tutorial, research paper) regarding game theory, which covers the following things.
1. How to apply game theory?
2. How to prove optimal gain after applying game theory, (e.g., proving Nash equilibrium).
3. What are the state-of-the-art game theory techniques?
Thanks in advance.
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Anik Islam Abhi For example forecasting and game theory are both effective tools to support finance-related decision-making and reduce the impact of risk factors.
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Hello, most of variables in a game formulation are matrices , maybe cramer's Rule can solve NE in a linear object. however, i want to know are there some methods in games' solving using matrix theory. Preferably some papers or phrases, and source code.
Thank you.
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(Google )and search the following topics:
(1) Markov Chains.
(2) Game theory. (Pivot Method)
(3) Operation research-matrix approach.
Regards
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Didactic methods based on computer games are included in the new education 4.0. Therefore, education systems should be improved in such a way as to make the most of the techniques known for the current technological progress known as Industry 4.0.
On the other hand, as part of the technological revolution of Industry 4.0, other technologies are also being developed that should be effectively implemented into modern education tools so that education systems can be improved and adapted to new technologies that are currently being dynamically developed and implemented in industry. In addition, these new technologies Industry 4.0 should also enrich the work of scientists in research laboratories of universities and schools. Scientific research conducted in the field of new technologies, innovations, etc. should also be correlated with Industry 4.0.
Apparently, we are now living in the era of the fourth technological revolution, known as Industry 4.0.
The previous three technological revolutions:
1. The industrial revolution of the eighteenth and nineteenth centuries, determined mainly by the industrial application of the invention of a steam engine.
2. Electricity era of the late nineteenth century and early twentieth century.
3. The IT revolution of the second half of the twentieth century determined by computerization, the widespread use of the Internet and the beginning of the development of robotization.
The current fourth technological revelation, known as Industry 4.0, is motivated by the development of the following factors:
- artificial intelligence,
- cloud computing,
- machine learning,
- Big Data database technologies,
- Internet of Things.
On the basis of the development of these IT instruments and technologies, business analytics of companies such as Business Intelligence and the above-mentioned areas have been dynamically developing in recent years.
The technological revolution described as Industry 4.0 is progressing more and more dynamically. The reforms in the school system should follow this progress, so that modern education 4.0 would be fully adapted and correlated with the progress of Industry 4.0.
The technological revolution Industry 4.0 is carried out so quickly that education systems and fields of study, teaching methods are adapted to these changes often with a significant delay.
On the other hand, research conducted in research centers at universities should support the creation of new innovations in technological solutions for the needs of industry 4.0.
Therefore, the education system should be improved in such a way as to create as much synergy and correlation as possible between the current technological revolution of Industry 4.0 and the reformed systems of new education 4.0.
One of these areas of new teaching techniques are the above-mentioned computer games. In many training centers, for example in the field of training pilots, drivers, cosmonauts, aircraft controllers, etc., simulators that technologically use modern computer games are used. Computer games should therefore be used in the process of improving didactic techniques in education systems 4.0.
Therefore, I am asking you with the following query: Can computer games be used in the process of improving teaching techniques in 4.0 education systems?
Please, answer, comments. I invite you to the discussion.
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Yes, the computer games should be used in the education systems.
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There are some methods to get the NE,i have used the backward induction with Fixed point theorem in my paper. Now i wanna know how to get it with DRL.Thanks.
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I am stuck in a problem where there are two firms A and B. Firm A sells two vertically differentiated products, X & Y. Firm B, on the other hand, sells a product Z which is also vertically differentiated with X but is horizontally differentiated with Y. Now, I am looking at references that have modeled such a scenario using utility functions that means something that has combined the works of Hotelling (1929) and Mussa and Rosen (1978).
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Interesting Dilemma.
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Colonel (retired) Oliver G. Haywood suggested in his brilliant 1954 article, “Military
Decisions and Game Theory” that game theory techniques were relevant to preparing the military
commander's estimate of the situation. Colonel Haywood demonstrated the utility of game theory by analyzing two World War II military operations. In each case, he examined the various friendly courses of action and compared them with enemy courses of action to determine the value of the predicted outcome. He concluded that military decision-making doctrine was similar to solving two-person zero-sum games. Colonel Haywood’s assertion encouraged the operations research community to develop quantitative methods to enhance decision-making.
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Game theory enables the analysis of situations involving strategic interaction, e.g., military decision-making at tactical and strategic levels. Hence, using game theory, one can try to predict the actions and reactions of different interests/countries given the structure of incentives and disincentives facing them. Accordingly, one decide on their own strategy and consequent actions.
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what procedure and data should I use ?
how to structure the empirical study ?
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You may find this paper useful:
Stagnaro, M. N., Arechar, A. A., & Rand, D. G. (2017). From good institutions to generous citizens: Top-down incentives to cooperate promote subsequent prosociality but not norm enforcement. Cognition, 167, 212–254.
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Do you think artificial intelligence will be implemented for computer games?
What can be the effects of artificial intelligence implemented for computer games?
Please, answer, comments.
I invite you to the discussion.
Best wishes
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Uses in games beyond NPCs
Georgios N. Yannakakis suggests that academic AI developments may play roles in-game AI beyond the traditional paradigm of AI controlling NPC behavior. He highlights four other potential application areas:
  1. Player-experience modeling: Discerning the ability and emotional state of the player, so as to tailor the game appropriately. This can include dynamic game difficulty balancing, which consists of adjusting the difficulty in a video game in real-time based on the player's ability. Game AI may also help deduce player intent (such as gesture recognition).
  2. Procedural-content generation: Creating elements of the game environment like environmental conditions, levels, and even music in an automated way. AI methods can generate new content or interactive stories.
  3. Data mining on user behavior: This allows game designers to explore how people use the game, what parts they play most, and what causes them to stop playing, allowing developers to tune gameplay or improve monetization.
  4. Alternate approaches to NPCs: These include changing the game set-up to enhance NPC believability and exploring social rather than individual NPC behavior.
Rather than a procedural generation, some researchers have used generative adversarial networks (GANs) to create new content. In 2018 researchers at Cornwall University trained a GAN on a thousand human-created levels for DOOM (1993); following training, the neural net prototype was able to design new playable levels on its own. Similarly, researchers at the University of California prototyped a GAN to generate levels for Super Mario. In 2020 Nvidia displayed a GAN-created clone of Pac-Man; the GAN learned how to recreate the game by watching 50,000 (mostly bot-generated) playthroughs.
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Theoretical physics is very competitive when solutions have commercial value. For example, the race to produce the first solid state transistor or the atomic bomb. Neither application has commercial value outside a laboratory where theoretical models can be tested, effective designs produced, and an effective solution is determined based on cost to benefit analysis.
Can theoretical physics outside commercial value and experimental test be described by cooperative game theory? For example, many Grand Unification Theories if not all have no real commercial value. Because each approach is funded without commercial expectation or testable results, has the survival of these approaches become an exercise in cooperative game theory where preserving ones financial state in public funding has become more important than actually solving the problem the practitioners promote as being critical to our understanding of how the world works.
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This is a non cooperative game. Pursuing individual self interest might put the collective interest in jeopardy. But I feel market share can be gained if cooperative game can be played by all players. What's the strategy? And can the players solve prisoner dilllema game is critical in this respect.
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I am considering as research an estimate of the equilibrium between supply and demand of pedagogical training, considering how the government makes a decision to offer (or not) pedagogical training to teachers, and, concomitantly, how is the decision making of teachers in participate (or not) in pedagogical training. I thought about doing this using game theory, but I'm not sure what kind of model I should use, or what I should consider to determine that model. Has anyone worked with something similar and could give me any suggestions?
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Dear Carmem Fruhauf de Oliveira,
Your research idea is very interesting. I am sharing my thoughts on it. As mentioned in your question, I consider a game between the government and a potential teacher and it proceeds as follows.
Suppose the government arranges for training and the teachers decide to participate. Now the government must choose the amount of investment. This will create a level of teaching skill which, along with teacher's effort, will become input to produce a particular quality of a good, say 'teaching'. This good will have public good characteristics for the students. On the other hand, a teacher will get a fixed income but only after completion of the training period i.e. in future period. So he will discount his future utility to obtain utility in the present period. But if he does not participate in training, he can still get a job (may be as a contractual teacher) instantaneously but at a lower salary and will produce a low quality public good.
If the government does not invest in training then it will spend that amount in some other development projects which will yield some level of social benefits. In that situation, if a teacher opts for teaching job he will get a lower salary (compared to what he would be getting as a trained teacher) and will produce an inferior quality of the public good (teaching service).
The government, being a social planner, will take decision through maximizing social welfare which will include the payoffs of all the agents, whereas, a teacher will decide by maximizing his own utility.
This is merely a draft of what I thought. You can build a model considering suitable functions and solve it.
With regards,
Tilak Sanyal
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Can game theory be applied to human-computer interaction? E. g., by assuming that the computer and the human are trying to fulfill some objects and they compete and co-operate to gain best payoffs. Is there any such research work already?
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Yes it can be used.
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Are there engineering problems which can be modelled as Bi-Matrix Games?
#Matrix Game Theory
#Lemke-Howson Algorithm
#Engineering Applications
#Nash Equilibria
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I am interested
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In economics and biology, the terms "conditional cooperation" and "indirect reciprocity" are used to describe behavior, where subjects condition their behavior in stage t of a repeated game on the opponent's reputation (see Bolton, Katok, Ockenfels / J Pub Econ 2006), or where subjects play a one-shot game and condition their behavior on the opponent's expected behavior (see Fischbacher, Gächter, Fehr / Economic Letters 2001). I’m wondering whether there is a difference between "conditional cooperation" and "indirect reciprocity," or whether these terms are interchangeable?
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Indirect reciprocity is one type of conditional cooperation. Direct reciprocity is also one type of conditional cooperation. Thus, conditional cooperation is more broad than indirect reciprocity.
Indirect reciprocity is to cooperate under the condition that the opponent's reputation is good, roughly speaking. Direct reciprocity is to cooperate under the condition that the opponent cooperated, roughly speaking. Both indirect reciprocity and direct reciprocity are conditional cooperation.
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The use of computer games at work and education is growing and will grow. Computer game technologies are distributed in parallel to applications in simulators of various means of transport and machines.
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Best wishes
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innovating in the railway sector using gaming … van den Hoogen, J. (2019). The Gaming of Systemic Innovations: innovating in the railway sector using gaming simulation (Doctoral dissertation, Delft University of Technology).
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There are many papers, books that say Game Theory can be applied in Business, but I could not find any paper which takes the real data and applied GT models. Of course, there are some examples like Apple Vs Samsung, Intel Vs AMD, but the payoffs are not taken from the company's real data (only assumed numbers). I would be happy if you could suggest papers or case studies that analyzed real data applying the model of Game Theory.
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Dear Jakhongir Kayumbaev,
Could you suggest papers which showed the application of Game Theory in Business? (with real examples and data, I want to learn to apply GT in B)? I recommend you to search in GoogleScholar as it is the best search engine to find papers published in highly ranked journals.
Best Regards
Desalegn Abraha
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"[...] We saw that unacceptability and ties are a major source of intractability when computing Pareto optimal outcomes. In some cases, checking whether a given partition is Pareto optimal can be significantly harder than finding one.[...]" (Aziz et al., 2013)
So now I have a small question. Is it possible to conclude that all coalition games have a Pareto optimal solution, even though it is maybe extremely hard to find that solution, or is it possible that for some coalition games, a Pareto optimal solution may not exist?
Aziz, Haris, Felix Brandt, and Paul Harrenstein. "Pareto optimality in coalition formation." Games and Economic Behavior 82 (2013): 562-581.
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Depends if the solution is on the contract curve or not ...
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Dear colleagues, friends, and professors,
As we know, we have very strong analytical approaches to control theory. Any dynamic decision-making process that its variables change in time could be characterized by state-space and/or state-action representations. However, we see very few control viewpoints for solving electricity market problems. I would like to invite you to share your thoughts about the opportunities, and limitations of such a viewpoint.
Thank you and kind regards,
Reza.
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I'm writing a review article in which I explain the different mechanisms by which M. tuberculosis reaches a persistent infection by establishing a cross-signal homeostasis with its host, in which both organisms modulate their actions and reactions towards the other one, and at some part I came up with this sentence " This thought provoking notion makes me think of its similarity to Newton’s third law of motion; a system reaches a steady state whenever the forces acting upon it are equal and opposite one another". How prudent is that?
What do you think about it? :)
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The two critical words in the Third Law are 'equal' and 'opposite'. The essence of 'Opposite' may be perceived well in various biological systems.
As pieces of exemplary shreds of evidence, in cancer therapeutics, tumor exerts strong pro-tumor response against applied treatment and imposes therapeutic resistance, one of the major problems seen in preclinical and clinical studies. The same goes for the multidrug resistance in various medically relevant bacteria.
However, measuring/gauging the essence of 'equal' may be a bit difficult task in biological systems.
AFTERALL, BIOLOGY IS A SCIENCE OF EXCEPTION. The rules of physics/chemistry may be applied directly in some cases while in others, they might seem to be bit 'diluted' or rather entwined with greater intricacy... reason: living systems are not isolated systems, which are often considered for the derivation of the rules/laws of physics and chemistry. It is not about the violation of the rules/laws... rather a manifestation of the same in different perspectives- unexplored/unexplained milieu...
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What kind of scientific research dominate in the field of Computer games in the education process?
Please, provide your suggestions for a question, problem or research thesis in the issues: Computer games in the education process.
Please reply.
I invite you to the discussion
Thank you very much
Best wishes
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...Nowadays, students are significantly influenced by the digital era and are constantly handling digital information. As a result, they form their personalities in the light of flexible communities, pursue to be directly connected, require prompt responses and social interaction and prefer learning based on experiences. Undoubtedly, modern students are not fully keen on and attracted by conventional education methods and thus they are seeking for more interesting, fun, motivating and engaging learning experiences.... The increasing popularity of digital games has led to their being broadly utilized and applied. In education, digital games are mostly applied in the form of serious games which focus more on primary purposes. Serious games offer motivating and engaging experiences, interactive learning environments and collaborative learning activities. Hence, they are considered as a proper educational tool which enhances learning procedures and satisfies and fulfills students’ needs and requirements. The pedagogical approach of utilizing digital educational games is called digital game-based learning and can be described as the “coming together” of interactive entertainment and serious learning through digital games. Game-based learning is the act of designing interactive learning activities that can gradually convey concepts and guide students towards an end goal. Furthermore, it promotes a student-centered learning environment in which students’ wellbeing and soft skills are cultivated in a dynamic, enjoyable and playful way... Anastasiadis, T., Lampropoulos, G., & Siakas, K. (2018). Digital Game-based Learning and Serious Games in Education. International Journal of Advances in Scientific Research and Engineering, 4(12), 139-144.
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I am looking for a good couple of reads on game theory, maybe with an historical context. Anything like random walks, or Marvok Process is fine or even, Colonel Blotto, and Prisoners Dilemma. I think my hardship is finding the right literature instead of instructional books. Thank you in advanced.
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"Strategies and Games: Theory and Practice" by Prajit Dutta is a good text
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I do not know much about game theory. I am finding a book where different protocols and algorithms of computer science have been analyzed using the concept of game theory.
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John Von Neumann is the father of game theory and he has published a book on game theory. When you go through it, you will understand the subject very well.
THEORY OF GAMES AND ECONOMIC BEHAVIOR
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Imagine a platoon, such as the "peloton" in a cycling competition or cars on a highway, where the players benefit from travelling close to each other due to wind drag reduction. If each speed would be determined by the optimal operating points stemming from their bikes, aerodynamics and body. For example, player 1, might be optimal (in terms of fuel efficiency) at a specific gear and given a specific cadence. Each player will propose changes to each other, such that each one will give a proposal to the player(s) which are obstructing its optimal trajectory. Negotiations, from say player 2 to player 1 (where player 1 is in front of player 2) such as "pedal 1 m/s faster and you'll get 1 buck", where the new speeds and compensations will be calculated individually from each cyclist such that the prize is lower than the potential "fuel cost" that player 2 would experience from operating at non optimal speeds. These proposals are then accepted or denied. I'm thinking that these proposals should then converge to some optimum where no members in the platoon will benefit from changing its strategy, hence a kind of Nash equilibrium.
I'm fairly new to game theory, but I want to formulate this problem as a game theoretical one, to see where these proposals would converge, and how to prove it. How would I begin?
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Given the game theoretical classification of this system, how would I prove if there exists a Nash equilibrium to it?
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dear reasearchers,
any ideas or repos that discuss the implement of NE in python using using nash py for a stackelberg game .
Greetings
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another stuff some predefined solution in python for convex omptimization problems like using KKT conditions method.
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is there a logical approach for an answer to the non-conformance of Pareto optimal to Nash equilibrium ?
in-game theory context answer is: because of double-cross in Nash equilibrium which that not in Pareto optimal .
but can we find a logical language to Answering this question? for example with preferece modality, hybrid logic , epistemic logic,etc...?
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There are some literatures: one approach is to extend the game theoretical background taking role-switching. This approach is formulated in Kaneko-Kline (2015, International Game Theory Review Vo. 17, "Understanding the Other Through Social Roles". The main issue is how to understand the other person's thinking, but the paper shows some cooperative outcome results without assuming cooperation a priori (This is my answer to you question). The concept of role-switching comes from the tradition from Mead (1934, see the reference list in the KK paper). The other approach is found in Bachrach (1999, also in the list in the KK paper). Anyway, some additional assumtion or structure to the purely noncooperative setting is needed to have a cooperative outcome.
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Greetings,
I am trying to calculate the Shapley Value to obtain the fair distribution of value in a two player cooperative game. All the examples I have found describe three or more players. Can I calculate a Shapley value for two players?
The form I have is a little different. In my situation I have player A providing an improved service at a cost to them of $50. Player B benefits from this service to the value of $350. I wish to know what would be the Shapley (fair) value in this situation to each of the players A and B. There are two outcomes to the game:
  1. In the event player A offers the improved service they (player A) will make a loss of $50, and player B will make a saving of $350 - what would be the Shapley value to player A and B in this scenario assuming they shared the $350 saving?
  2. If player A does not offer the improved service they will make no loss ($0), but player B will have lost the opportunity to save $350
Further clarification if required: player A provides a tool at $50 hire rate per day to player B at player B's facility, Player B pays $300 per day to rent their facility. Therefore if player A can reduce the duration of the job by one day player B will save one days tool hire and one days facility rental ($50 + $300 = $350). However Player A will be hiring their tool for one day less than normal and therefore suffer a loss of $50.
Appreciate any guidance on the above.
Scott
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The Shapley value is the average of all marginal payoffs over all the permutations of the players.
With N = {1,2} there are just two permutations. In the permutation (1,2) player 1 receives v{1} and player 2 receives v(N) - v{1}. In the permutation (2,1) player 1 receives v(N)-v{2} and player 2 receives v{2}. Average each player's payoffs to obtain the Shapley value for that player.
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Game theory is the study of mathematical models of strategic interaction between rational decision-makers.[1] It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.
Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.
Game theory was developed extensively in the 1950s by many scholars. It was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. As of 2014, with the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole, eleven game theorists have won the economics Nobel Prize. John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.
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The following is an article on game theory in the water field
Best Regards H. Naderpour
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The strategy of product packaging used several times has extra fixed cost and it is more price sensitive. The consumers have extra expense but it's refundable as a deposit , so that the fraction of extra cost can be return back to the consumers. Returnable packaging can achieve the best financial and environmental performance only with consumers behavior or price sensitivity. Thus, the game depends mostly on the consumer's willingness to send back and pay more for expensive packaging with the refundable deposit.
The aim of this game theory is to offer a suitable framework for the low carbon strategy in the processes of packaging planning via a product returnable package.
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Paul: In the United States, some states have a "Beverage Container Deposit Law".
"...When a retailer (store) buys beverages from a distributor, a deposit is paid to the distributor for each container (bottle or can) purchased. The consumer pays the deposit (fee) to the retailer when buying the beverage, and receives a refund when the empty container is returned to a supermarket... The distributor then reimburses the retailer (store) the deposit amount for each container, plus an additional handling fee.."
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Hello Everyone,
I am student of PhD (MS &E) and i am working in Linear/non-Linear Programming of Operations Management. I have a Profit Maximization problem with In-equality constraint which need to use KKT condition for optimality. I already got first order condition for my decision variable by KKT ussage.
I want to know how to code this problem in MATLAB. any example from Solver-based and Problem-based solutions can be helpful. Thanks in Advance.
Kind Regards,
Abaidullah
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Mahamad Nabab Alam Thank you for your guidance. I will definitely try these examples for better understanding.
Thank you for your time!
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As we know, Theorems in differential topology and algebraic topology facilitated the development of many crucial concepts in economics, namely the Nash equilibrium—a solution concept in game theory established by John F. Nash, Jr.—which was ultimately proved by the Brouwer fixed-point theorem in topology (Dilkina et al. 42- 43). Many other economic theories, such as the microeconomic general equilibrium theory, largely depend on topological theorems. Moreover, analyzing different topological networks of economic systems can provide mathematical insight into how the society is financially functioning. For instance, by producing empirical models of labor markets which connect individuals’ employment situations, economists found that the differences in the topology of such networks greatly influence the inequalities in wages as well as the duration and correlation of their unemployment rates (Klinedinst et al. 11). but I ask if there any other applications in economic.
Given the importance of the economy in sustaining life. what you see?
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Dear K. Hussein A.,
We have also topology in “qualitative input-output analysis” (QIOA) when we examine which productive j sector is connected (following a given criteria) with other productive sectors i (i's adjacency), the i sectors being themselves connected with other productive sectors k (i's adjacency of the adjacency), etc., up to infinite. See for example:
- de Mesnard L. 2001. “On Boolean topological methods of structural analysis”, in Input-Output Analysis: Frontiers and Extensions, in honor to Ronald E. Miller, Michael Lahr and Erik Dietzenbacher Eds., Palgrave: 269-80.
- de Mesnard L. 1995. “A Note on Qualitative Input-Output Analysis”, Economic Systems Research, 7, 4: 439-45.
Yours sincerely
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How can i use game theory to FDI fall into particular country?
I believe one can use Game theory and come up with the model for the particular FDI investment fall into a given country.
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In addition to this, I want to know which one of these two is better in terms of computational complexity and with respect to the game.
Thank you.
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Uniqueness of Nash Equilibrium is a desired property of games, but in most cases not ensured. Even for games in extensive form there may be multiple Nash Equilibria. Some of them may be not very plausible, because they inherit incredible threats. Therefore, additional features of equilibria have been considered, such as subgame perfectness (proposed by R. Selten as far as I know). This concept is also useful under computational aspects. Decision trees (of games in extensive form) can be efficiently inspected by the "Backward Induction Algorithm". In case of strict preferences of players on the terminal nodes of the decision tree subgame perfect equilibrium is unique. Nevertheless, even in this case, there may exist other (not subgame perfect) equilibria, which might be interesting, because they require some coordination between players. It may be attractive for specific groups of players to deviate from the subgame perfect solution in order to achieve a preferred outcome. Normally, this works only, if the threat posed by the player group is strong enough.
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Game Theory
Game theory is a tool for the analysis of the interaction among usually rational agents, the formulation of hypotheses about their behaviour and the prediction of the results of each interaction. From this standpoint it is very suitable for the analysis of environmental problems and for the definition of self-enforcing environmental agreements that are founded on cooperation and stability.
Enter game theory
What we have here is a particular kind of group decision problem known as a game, where one party’s decision is influenced by the actions of another party and vice versa.
The mathematical theory of such games is rich, with many important applications. 
Game theory, as it is known, was originally developed during the Cold War to model the nuclear arms race and first strike strategies. 
Since then, the theory has become indispensable in economics and is enjoying applications in diverse areas such as ethics, biology, dating, and, more recently, in environmental management and policy.
One of the enduring lessons of game theory is that in certain common situations, cooperation can be hard to achieve and may be difficult to maintain.
What do you suggest for example for wastewater treatment? did you have experience of that? would you please help by sharing your documents, experience, knowledge and etc. ?
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Title of paper: Games Addiction or Not; Health Therapy or Business
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The Nash's equilibrium for prisoners' dilemma game theory is played so that each prisoner will inform on the other as they do not trust each other. However, we do not know if a human will follow through or have other social values.
Will AI problem solving be based on logic only or encompass the option to 'hold back'. What if two AI systems are opposing each other?
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Thank you for your answer and link to further information. I can see many applications for such modelling and strategy.
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Hello,
I am working on a three level supplier, manufacturer and retailer game. In a decentralized channel, I used backward induction method to get the optimal values. But is it possible that the supplier optimal profit values in Negative?
Please guide me or suggest me an article for my understanding.
Thank you in advance.
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Short answer: Yes, you can have negative profits.
Long answer: It really depends on what you are trying to prove. Negative profits may point out that a market structure with three players is unfeasible, and therefore, someone should quit the market. Basically, that results what is telling you is that at least one of those players (companies) prefers not to play the game (zero profits).
My suggestion: I will try to compare your results with the duopoly and monopoly cases, to observe to what extent the third company is driving profits down to the negative region.
I hope that helps you. Good luck!
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Hello,
I am trying to replicate the results from this paper by Nowak and May (1992) http://ped.fas.harvard.edu/files/ped/files/nature92_0.pdf
However, in my code I find I need to have a random element and thus my results are stochastic. This is because of my interpretation of the following part of Nowak and May's model:
"At the start of the next generation, each lattice-site is occupied by the player with the highest score among the previous owner and the immediate neighbours"
Thus my question is, if there are 2 or more neighbours with the same highest payoff, but with different strategies, which one do I pick to occupy the lattice-site? Currently I pick at random.
I am also keen to see a very clear step by step description of their algorithm, so would appreciate it if anyone knew of a paper where this is described.
Many thanks,
Liz
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آسف السؤال ليس من اختصاصي
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In other words, in what conditions the game theory is better than conventional optimization methods for solving optimization problems?
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I think it helps to distinguish between "decision situations" and "decision mechanisms". Your question is more about the situation than the mechanism. Imagine asking, "what is the nash equilibrium solution to strength maximizing shape of a beam?" It is the exact same solution as any conventional optimizing method would generate.
What is called conventional in the question probably means "Given an opportunity set, select the best". This is a mechanism.
A Nash equilibrium also does this, but it does something else before it "selects the best". First it figures out, given the specific situation, what is in fact the opportunity set. In game theory, this is the "core" and it represents the set of stable equilibria. If the core was mathematically ill-behaved, like most phisical problems are, then one might try eloborate "guess and check" routines like generic algorythms to figure out what is the best opportunity within the core. That is, with respect to the core, one solves a Nash Equilibrium just like the conventional problems.
The situations that call for game theory methods are ones where the opportunity set depends on my choice in a very specific way. The Hotelling "hotdog stand on the beach" problem illustrates this quite well. My initial assesment of opportunities along the beach are not those that I actually get, because the true opportunites depend on what I choose. In fact, it depends on my strategy and my opponent's strategy. The physical world typically does not present researchers with this kind of decision situation.
Here is one where it does: What is the cost minimizing combinations of intervention strategies when multiple infrastructure networks overlap? The opportunity set depends on the choices.
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Suppose I have an axiomatic bargaining problem (F,d) where F is the set of feasible utilities and d is the disagreement point. Let's say FU{d} is non-convex. Can I compute the Nash Bargaining solution under such a setting?
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If FU{d} is non-convex then some bargaining solutions might fall outside F. In that case constrained bargaining solution can be computed.
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In a leader-follower game (or Stackelberg ). Due to the leader's strategy if the follower's strategy (followers optimization problem ) becomes infeasible or vice versa, what to do?
1. Is there a chance to occur like this?
2. If so, what is the solution? Please refer to any literature?
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There is no equilibrium in a bilevel problem - the lower level is a slave. :-) The slave is just there to provide the solution to the lower-level problem, such that the real objective (at the upper level) can compute the objective function of the overall problem - i.e., the upper-level objective. The lower-level is a dummy, a slave.
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Emergent Properties of Complex Systems evolve through interactions between components of a complex system. How do we define them using applying game theory for both competitive and non-competitive games ?
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Incomplete Contract Theory (Nobel Prize 2016 in Economics) takes a view that as for unforeseen contingencies (which could be emergent), we cannot specify them ex ante, and so cannot design (and commit) elaborate arrangements (contracts, mechanisms) ex ante, including how to deal with them. Instead, ex post, that is, after emergency events actually occurred, those who have decision rights determine how to deal with them. So, it would be important who determines (who has the decision right) when emergency events occurred. For example, "Government" would determine various important things when (unforeseen) emergency disasters occurred. Incomplete Contract Theory can use both cooperative and non-cooperative games in its game theoretical modelling. This is just a quick response. Best wishes.
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Dear Colleagues.
I need your advice about the joining to a Scientific group worked on ( Game theory)... Since I am interesting to make use of Game theory in designing a proposed method for security evaluation of crypto -systems.
Please, any advice will be of great help to our research.
Best Regards
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Dear Dr. Sattar,
if you want to work a system of game theory , you need work on
1- Simulate the actual system in to the Virtual System(VS),
2- Convert the problems, into game Strategies  compatible with the VS.
3- Assumptions for a solutions (clear of selection)are available, depend on the choice of player.
4- must there more ranking (measurement) , and benefit to the player.
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.
.
thank you
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What is the relationship of Game Theory and Sexual Slelection with regards to mate competition?
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Thanks
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How do you know that from the almost infinite action (toolbox), which action you need to choose (which is A , B etc..) to get the next step within the progress toward the target. (Starting point (like sitting in the armchair) -> A -> B -> C -> Cooked a Pizza or Went out of the room through the door )
What algorith/method the most effective when the task is NEW, so you need planning, don't just solve this with previous experience.
And this method should be universally applicable because the animals can solve problems with a very high diversity interval.
I hope you get is what the question is.
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Hi Axel,
the answer might easily fill some books, but in short:
1. You have to know the contents of your toolbox. On the lowest level, it might contain less than 50 tools (like in robotics programming: speed, accel, move, moves, appro, appros, depart, departs, break, wait, delay etc.) On the physical level, you get to know your toolbox as a child; on the cognitive level, during your education (which is a livelong process if you don't lead a boring life).
2. If you have done a similar task in the past: If the result was satisfactory then do it in the same way. If not then introduce some promising change.
3. If the task is new to you then search your memory for analogous tasks you have done successfully. (Cooking a soup might not be very different from cooking a pizza.)
4. If the task is completely new: Use your planning ability, i. e. simulate (in your mind) yourself and your environment based on your general experience. If you hit a solution then try to implement the solution in reality.
5. If the task is complex then apply "divide and conquer": Generate a hierarchy with the task as root and subtasks on lower levels. Stop when all subtasks forming leaves look feasible to you. It's the same as writing a program. If you don't know how to solve certain subtasks then you have to gain knowledge in this domain first before continuing the planning (or programming).
6. If the task is not only new (to you or anyone else) and solving the problem involves obviously some creative processes then your picture with the virtually infinite toolbox is correct: The solving process might include a lot of dead ends, it might take weeks, years, or decades, and you might not succeed at all.
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IS GAME SOLVED BY ARTIFICIAL TECH
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It is unclear to me what you are thinking of. Could we have an example? And apell out what LLP stands for?
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The main goal is to collaborate in different countries, using an agreed methodology to identify the interaction among stakeholders and organizations by applying game theory and analysis of cooperative games. We can work it out via the internet, mail of social media, present the research in Congress or journals, citing all the researchers involved, and respecting everyone contribution. Using this strategy, we can multiply the research activities, internationally, in which we are directly or indirectly involved whit our work.
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I am intersted! I am researching cooperative game theory for my thesis.
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i want to work on game theory so i want to know the recent work on this topic
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Dear Saifullah Khan,
One of the most popular and entertaining topics in game theory is the
( Life and death game of John Conway) based on cellular automaton.
Best regards
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I need a basic program for understanding how to solve a Game theory using GAMS and find Nash equilibrium.
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Hi Monika,
maybe this link could be useful:
Hope this helps!
Best regards,
Marco
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Nash bargaining assumes that players are perfectly rational. However, the perfect rationality assumption does not hold for real-life bargaining scenarios with human as players. Therefore, is it possible to introduce bounded rationality theory into Nash bargaining problem? If it is possible, how to introduce?
Of course, the evolutionary model of bargaining in game theory drops the perfect rationality assumption, but it is based on large population of individuals as players and repeated interaction among players, not applicable to one shot bargaining scenarios with only two or three players. So I'm looking for methods of introducing bounded rationality into Nash bargaining problem.
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In this paper https://mpra.ub.uni-muenchen.de/57960/ we model dynamic bargaining of time inconsistent agents. We show that bargaining may break down if players are naive about the time inconsistency. The Nash bargaining solution can be derived from dynamic (Rubinstein) bargaining when players are rational. Maybe this is also possible for agents that are time inconsistent.
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If someone has any idea about backward induction method then please share.
Thank you
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There is a wonderful video on YouTube explaining backward induction, may be this helps you for a start: https://www.youtube.com/watch?v=pyLKkN5HpDY
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Hello everyone,
Can someone help me with references to solve a closed loop Stackelberg game for linear differential dynamic games for continuous system. The game is infinite horizon. Thank you.
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You should read the book of Basar and Olsder
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I want to compare two populations, but we can only measure 6 participants at a time at most (the total sample is larger of course). Therefore running the task classically is difficult.
A possible solution is having participants play against an algorithm (tit-for-tat, or adaptive pavlov). However, I can't find any literature of humans vs. algorithm in the prisoner's dilemma.
Am I missing something?
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Hi David,
Thanks for your input!
I looked at some of his research, yes.
I followed your suggestion and zeroed in on Axelrod's work. However, it's all simulations as well. Always algorithms vs. algorithms.
Oh well, thanks nevertheless!
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Suppose we have a set of players, i.e., {p1, p2, ..., pn} and each player has three different strategies, i.e., {s1, s2, s3}. They play m number of games. In each game, each player seeks to maximize its profit by selecting a strategy with highest playoff. The profit associated with each strategy is as follows.
1) Payoff for selecting strategy s1 is zero
2) Payoff for selecting strategy s2 is a real number, which is calculated using some formula f1
3) Payoff for selecting strategy s3 is also a real number, however, it is calculated using another formula f2
I want to prove the existence of Nash equilibrium when all the players select one of the available strategies.
I have searched on web and found several documents, however, I couldn't get a clear idea to prove it mathematically.
Any help is deeply appreciated. Please let me know if I have missed any information. Thank you in advance.
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@Felipe Please find attachment to see the formulas.
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I am looking for examples of the combination of ABM, MO optimization, and game theory, preferably the ones that have been used for practical purposes.
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Dear Ali,
The answer provided by Dr. Lafifi is recommendable. Please follow.
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Hi everyone, I am working on improving the accuracy and efficiency of some traditional machine learning models. As game theory illustrates the cooperation and conflict of different decision makers, it is maybe useful in some machine learning strategy. Could you recommend me some good cooperation in both field? Thank you.
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In a multi-option system, agents can use one of many options at a time; like a stock market that you want to buy just one stock at a time. Or, you want to be either a seller, or a buyer. One method to analyze this system is the mean field approximation. Now, what about the situation in which you want to acquire more than one resource simultaneously; like processes in a computer system.
Do we need quantum assumptions/computing? Is it possible to simplify the system? What do you think?
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Thank you for your answers.
Dear Dragos, considering time lags can give us an insight from a different angle. I will look into it.
Dear Joseph, I am wondering if the "multiple agent role" uses heterogeneous agents. Or, it can be an analogy to multi-resource but from a different perspective.
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Hi,
I would like to derive a mathematical model that can explain the change in frequencies of two genes that cause resistance to a particular antibiotic. Based on the literature, one of the genes is expressed only constitutive, while the other is a membrane protein. I would like to know the methods and protocols to follow for using evolutionary game theory. As I am learning it right now, any reference to similar articles or texts would be much appreciated.
Thanks.
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Mcelreath and Boyd's social evolution is a simple yet comprehensive start to help guide you in modeling these evolutionary processes using game theory (http://press.uchicago.edu/ucp/books/book/chicago/M/bo4343149.html).
Gintis's book "Game Theory Evolving" (https://press.princeton.edu/titles/8900.html) is a slightly more advanced but also easily accessible book. The topic is covered in two chapters on evolutionary dynamics.
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I would like to apply game theory, potentially the prisoner's dilemma, to aggression in fish. I have a lot of data in which to apply this theory, but have no experience myself on modeling decision probabilities. Please contact me if you would be interested in collaborating or further discussing this idea. Many thanks!
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Hi Amber,
I hope you've made progress, but if you're still looking for someone to bounce ideas off, I'd be happy to oblige. I'm an honours student at the Universtiy of Stellenbosch/AIMS in Cape Town, South Africa. My supervisor Cang Hui has a lot of experience in modelling agricultural and ecological phenomena, including using game theory. He may also be interested in being involved, and I'd certainly be happy to share ideas.
Jeremy
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I am trying to find a good SC simulation game for my students. Except for the beer gaming, all good games are not for free! Any recommendations? 
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I don't know any free game but Industry Giant 2 is best Supply Chain Game I have ever played. Its graphics are a bit old but I think it is very useful to simulate the production process. It is very cheap on Steam platform.
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Hello all, I am trying to human-machine interactions using game theory. My application is similar to a human wearing an exoskeleton where human is one agent who knows what the machine will do in achieving a control objective and the machine operates to help the human in the task. I believe this problem can be modeled using Stackelberg games where human is the leader and the machine is the follower. I am new to game theory, I would like to know whether the game theory will help me quantify the advantage I am getting in using both machine and human compared to just human.
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This may not be helpful - I am wondering if this application of game theory is a good fit. In my limited experience, game theory involves some kind of competition between players, say competing for a prize or a limited resource. 
Work on exoskeletons in the 1970s focussed on the concept of "man amplifiers", where applicable power (product of forces and velocities, torques and angular velocities) is amplified over multiple degrees of freedom, typically associated with the exoskeleton being larger and stronger than the human operator. The available degrees of freedom would be limited compared with the human operator on his/her own and the bandwidth of available power limited as well.
The human operator must plan the exoskeleton operation such that the degrees of freedom available match the task impedance or "degrees of constraint".  Also such that the available bandwidth is adequate.
An interesting issue with exoskeletons is the level of bilateral coupling through the mechanism, i.e. how well can the operator feel the interaction with the environment? 
To investigate the separation of the real-time control of the exoskeleton and the task planning I would immediately jump to a control hierarchy model where lower level "reflexive" control is governed by higher level task breakdowns.  NIST published a lot of work in this area, starting with the NASREM project.
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 I have a model with 2 players that each has 1 inequality constraint. They move simultaneously. 
I reformulated my model as kkt conditions; and after solving the cases, I had overlapping cases. 
For example (attached a depiction):
the input condition of case 1:  
a < x < b
the input condition of case 2:  
a < x   if  y > c
a > x   if  y < c
x, y, a, b and c  are all strictly positive input parameters.
 
My question is, is it possible to solve a simultaneous game with kkt? If so, is it possible to have overlapping cases? if so, what would than mean?
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I believe you mean a 'coupled constraint game' (CCE), also know as 'generalised Nash' (GN). There is software which solves games of this kind, see (GUI based) http://hdl.handle.net/10063/3414 and  (command driven) https://mpra.ub.uni-muenchen.de/1119/.  Many refereed papers have used this software see e.g. https://link.springer.com/article/10.1007/s10287-015-0247-9 and my (coauthored) publications there cited. Also have a look at Chapter 3 in https://ideas.repec.org/b/wsi/wsbook/8442.html . Let me know how you go. Good luck!
Jacek 
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is distributed gradient algorithm could be considered as a game theory method? 
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Well in my opinion the answer is no... and yes. It depends on the point of view. If you see the game theory as an optimization method where you have to optimize two or more coupled functions together (like many authors do) and you are solving a cooperative game by using multiobjective optimization, and you are using a multiobjective gradient algorithm for this, the answer could me considered as "yes". If you are using the classic gradient algorithm for the optimization of only one function then the answer is "no". You could also argue, your game has only one player, but this case makes no sense from the game theory point of view. Now, strictly speaking, the game theory is a "theory" and the gradient algorithm is a numerical procedure. You can use the second to solve a example of the first one, but at the end, they are two different things.  
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The modeling of these processes requires specifying, for each operation of production process, an interval of the authorized duration.
Considering the performance of the Petri Nets tool in terms of modeling synchronizations, parallels, conflicts and sharing of resources, this tool is seen as an important research way for modeling and evaluation of robustness. 
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I'd never heard of them, but a quick look at Wiki describes this as a way of distributing data and analysis across a network of processors, perhaps to optimize the overall load and production time.  Please correct me on anything here.  And, thanks for mentioning this particular field, I intend to have more of a look at the topic, since I am interested in distributed network operations/processing.
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In the field of game theory, can anyone refer me to papers dealing with multi-objective transportation games ?
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@Oren E. Nahum
U r welcome
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I have a solved a number of game problems using a co-evolutionary approach. A reviewer asked me to show some analyses of co-evolutionary progress measure/metrics.  
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 Basically I need the complete calculation of some numerical examples on multi-objective transportation problems. Solution of the problem is done either by Weight Goal programming or linear programming problems. Or it may be zero-one integer programming.
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I am embarking on research in the field of reinforcement learning and I would like to get a good grassroots grasp on the topic of Markov Decision Processes (MDP). I would be very glad if someone knowledgeable in this field would take some time out of his busy schedule and direct me towards some good study materials that would deal with the basics of MDP as well as go a bit deep into it.
Thanks
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Have you looked at Sutton and Barto (1998) "Reinforcement Learning: An Introduction"? The book is also available on-line in HTML form. If you want something more up-to-date, I can thoroughly recommend the Berkeley Deep RL course.
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For example, in game theory, externality framing is a good term for highlighting either the positive or negative consequence on others (the externality). However, I am failing to find a good overarching term when emphasizing either the individual or the group. Individual-group framing is the only thing I came up with, however, I find this term not satisfactory. neither would I call it individual framing, group framing, or label framing for that matter.
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Great question.  This idea has been discussed with different semantics, but I don't know if any of them are really accepted. 
You probably know this, but... Some of the early developers of game theory thought about a "Utility Vector" with the vector components being the considerations a player might care about.  The vector was multiplied times a "Utility Weighting Vector" 
The product reflected the utility for each player.
Some of this is out of style since Prospect Theory has come along, or so it seems to me. 
There is nothing to say you can't use this vector/weight approach (and we do, with prospect theory "distortion" ) but I don't know an accepted term for it.
I'd love to know if you get a good answer - I have this question too. 
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Dear colleagues,
What is special in 1109?
We can use straight lines as starting configurations in Game of Life. Then, if we check the equilibration time vs length, we will see that many lines with different lengths reach equilibrium exactly after 1109 steps. Why?
*More details in our project Mysteries of Game of Life
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Hello Rhoderick,
Thanks for your comment.
The question "What is special in 1109?" was just a way of saying. We decided to study lines as a first step to understand some facts of Life, and lines, despite being "simple starting configurations (the simplest possible?) " also present very interesting behaviour.
Now, the fact is that different lines (i.e, different values of L) reach equilibrium exactly at 1109 steps, and this special number is not the only one. the same thing happens for 1388 for example. So we can conjecture that there are infinite special numbers like these (when L goes to infinite).
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In a Nature article from 12 October 2015, named 'Price carbon — I will if you will', MacKay, Cramton, Ockenfels, and Soft argue that common commitments in a public goods game changes the Nash Equlibrium from free-riding, i.e. contributing nothing to the public good, to full contribution (cooperation).
They interpret this as a theoretical solution to climate change negotiations.
I wonder if there is an experimental investigation of this theoretical prediciton and would be happy if anyone could point me towards a paper that deals with this.
Thanks in advance.
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Hi Hendrik,
nicht genau das was in dem Paper beschrieben wird aber auf jeden Fall aehnlich:
Insgesamt muss man sich natuerlich fragen wie realistisch eine "Loesung" ist die external enforment braucht um druchgesezt zu werden.
Viele Gruesse
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Hi all, 
Can someone help with an algorithm to determine biasing for dynamic range expansion in picocell and subsequently to mitigate the resultant interference?
I am working on increasing capacity and coverage using cell range expansion, particularly picocells. Since this method introduces some interference to cell edge users, a game theory approach is intended to be used in mitigating the interference.
Any help on algorithms and codes for these? 
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 Hi Himadri,
Thank you. Your input was very helpful.
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For my master thesis on how perspective-taking can influence perceptions of procedural fairness, distributive justice and racial profiling in police-citizen encounters. I am using a Virtual Reality to let subjects experience the perspective. 
Since the topics in the VR experience (police violence/ethnic profiling) are quite sensitive, I have found no experiments where such negative experiences have been simulated or manipulated. I thus find it hard to base my power analysis on previous experiments on procedural fairness, distributive justice and racial profiling. I have found experiments of Mazerolle (2013) and Murphy (2014) on infuence of positive experiences with procedural fairness. 
My question is thus if anyone knows of previous experiments of these topics, and if not how I can still determine an effect size/ conduct a power analysis? 
Thanks in advance!
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Hi Jochem, there are not that many experiments in this field, with Mazerolle's QCET being one of the most well known experiments, but there was also a Scottish version of QCET conducted (MacQueen & Bradford, 2015) and another one I am aware of, comes from a doctoral thesis. Another paper that I would recommend is one from Matt Radburn (linked to this post also) - it didn't involve manipulating the encounter, but it did vary information given to the participant about the identity of the people who were in contact with the police.
In terms of effect sizes for the power calculation, you are likely to be much more limited in how many participants you can get for VR study versus how many participants studies of police-citizen encounters in the field are getting. From my understanding, the effect sizes are small even in those big samples, so if you based your calculations on those, then you would end up with a very big sample estimate. 
Have you tried looking at other VR studies to get some information on the typical sample sizes? That could give you a more informative and feasible answer, based on the methodology you are using.
All the best with your work - I would love to hear how you get on!
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Let's suppose we have x people voting, and there are n proposals. People vote by ranking the proposal. We know that if the proposal can be ordered, so that each person has a favorite proposal, and then as you move away from the favorite proposal they like the most, their appreciation for the proposals go down. So if the proposals are A, B, C, D E, and are ordered in lexicographic order. Then someone that likes B will always like C more than D, and D more than E. So it will either be
B>A>C>D>E or
B>C>A>D>E or 
B>C>D>A>E or
B>C>D>E>A 
And if everybody shares the same order, then there is a condorcet winner, which will be the choice of the median voter (see median voter theorem).
Now, what if the order is not on a line but on a cycle.
For example suppose we are deciding the time to have a meeting. Meeting that we are going to have each day, always at the same time. Each of us has their favorite time, and as you move away from that time each of us will like that time less.
Then:
1) Does it still exist always a Condorcet Winner?
2) Is it still true that the median voter is Condorcet Winner?
3) And how do you calculate the median voter in a cycle? For example if I have a set of times all around the clock, what is the "median time"?
4) And if there is no Condorcet Winner, can someone come up with a counter example?
Thanks to anyone who can chip in something. 
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Thank you! There is plenty of material to dig my teeth in.
Did you actually wrote all this to answer my question, or was it a question you have worked before in your career?
Best Regards,
Pietro
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