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The logic of animal conflict
... Traditional analytical models are insufficient for capturing the complex and adaptive behaviours among farmers, insurers, and policymakers, highlighting the need for a more nuanced understanding of the market dynamics that evolutionary game theory provides. This study improves this approach by employing three methodological improvements: First, it utilises the theory formulated by Smith and Price (1973) to integrate market evolutionary and long-term equilibria with an equilibrium level in the agricultural catastrophic insurance market. Second, a model based on Taylor and Jonker (1978) and Duncan and Myers (2000) dynamically analyses sequential decision-making for market groups, guaranteeing that the 'replicating dynamic equation system' accurately reflects the actual market conditions. ...
... Maynard Smith and Price's (1973) work on evolutionary game theory integrates Darwinian concepts into game strategy, with Friedman (1991) expanding this by linking Nash equilibrium with evolutionary stability. This theory extends classical game theory by incorporating bounded rationality and strategy evolution, offering a novel perspective on analysing game situations, especially in addressing the market's nonequilibrium issues (Liao et al. 2021;Fu et al. 2022). ...
... Farmers, influenced by their cultural background, traditional habits, and inherited experience in decision-making, tend to exhibit 'herd behaviour' during the initial decision-making stages. Such herd behaviours exemplify the low rationality game party described by evolutionary game theory, where decision-making is primarily based on imitating the crowd (Smith and Price 1973). ...
In China's agricultural catastrophe insurance market, issues of non-equilibrium are prominent. To understand the causes of non-equilibrium in agricultural catastrophe insurance and to develop prevention strategies, this study employs an Evolutionary Game Model, incorporating disaster and insurance data for three types of cereal crops in Henan Province to analyse the Evolutionarily Stable Strategies in the agricultural catastrophe insurance market. The research also considers government policies and disaster reinsurance as implicit participants in the model. The findings reveal significant differences in the impact of non-equilibrium in the agricultural catastrophe insurance market and the choice of game strategies, dependent on the scale of farm operations, the type of crops cultivated, and regional variations. Significantly, decision-making evolutionary paths vary between small and medium-scale farmers, with rice growers emphasising income insurance more. In regions prone to frequent catastrophes, the insurance rates for agricultural catastrophe insurance exhibit greater flexibility. By scientifically delineating agricultural catastrophe risk zones, appropriately expanding the scale of cultivation, reducing insurance rates, and adjusting agricultural catastrophe insurance products, a balanced development in the agricultural catastrophe insurance market can be promoted.
... [2][3][4][5][6][7] Rates of aggression are often highest among the densest populations 1 and it is a general assumption that aggressive traits evolve when the individual benefits of aggressive behavior (such as access to limited resources) outweigh the costs of aggressive behavior (such as risk of injury, loss of time, and energy). [8][9][10] However, it is not clear how the emergence and fixation of aggressive behavioral traits takes place in environments where the effects of habitat size and quality experience temporal variation. 5 On islands, species typically become more tame, as part of a complex of changes often described as island syndrome, [11][12][13][14][15] although the reverse has been observed with small or fluctuating population sizes. ...
... To explore the emergence and fixation of aggressive territory behavior in the dodo and solitaire we used a novel modeling approach in which we integrated a Hawk-Dove game model 8,9 for territory competition into a population model. Our aim is to develop a model that could help to understand the difference in aggressiveness between dodos and solitaires, while keeping the model as simple as possible. ...
... The probability of displaying aggressive behavior in the model with mixed strategies is the same as the fraction of aggressive individuals in the model with the pure strategies. 8,9 Overall, our model demonstrates mathematically that aggressive behavior might become fixed in an island population if the island size and therewith the resources fluctuate substantially. In our model, island size does not directly determine the behavior of individuals and the fixation of aggressive behavior is caused by the ecological dynamics of the population. ...
Why aggressive traits evolve in some species but not in others is poorly understood. We modeled the population dynamics of the extinct Mauritius dodo and Rodrigues solitaire to examine divergent pathways in the evolution of aggression. Whereas the dodo conformed to island syndrome predictions of tameness, its sister-taxon the solitaire evolved strong sexual dimorphism and aggressive traits. We computed rates of change in island size from sea level modeling and connected island size change to population dynamics by integrating a Hawk-Dove game theory model for territory competition with a population model. We find that the rapid rate of decrease in island size likely was an important trigger for the onset of aggressive behavior and that aggressive behavior becomes fixed if a tipping point is reached where island size falls below a critical threshold.
... Hawk -Dove strategies and payoff distribution [51]. ...
... Hawk Table 2 shows the payoff distribution scheme reported in literature where V is the resource contested and C is the cost for escalating the fight for that resource [51]. If both players choose Hawk, they share the resource, and each gets V− C 2 . ...
... Physical closeness, including touch and exchanging bodily fluids, correlates with communal sharing relationships and strength of relationships in many cultures and species, and it is also related to mothers caring for their young. Physical size tends to highly correlate with formidability, which is what determines dominance rank in many species (Huntingford, 2013;Smith & Price, 1973). Infants may need very little or even no input to form expectations about the relation between differences in size and asymmetrical relationships (refer to Authority Ranking section below). ...
... Many dominance hierarchies form because it is in the interest of weaker individuals to yield in conflicts that they would otherwise lose. Therefore, in dominance hierarchies, patterns of yielding in conflicts could be reliable cues about social rank (Smith & Price, 1973;van Vugt & Tybur, 2014). ...
In the human mind, what is a social relationship, and what are the developmental origins of this representation? I consider findings from infant psychology and propose that our representations of social relationships are intuitive theories built on core knowledge. I propose three central components of this intuitive theory. The purpose of the first component is to recognize whether a relationship exists, the purpose of the second is to characterize the relationship by categorizing it into a model and to compute its strength (i.e., intensity, pull, or thickness), and the purpose of the third is to understand how to change relationships through explicit or implicit communication. I propose that infants possess core knowledge on which this intuitive theory is built. This paper focuses on the second component and considers evidence that infants characterize relationships. Following Relational Models Theory (A. P. Fiske, 1992, 2004) I propose that from infancy humans recognize relationships that belong to three models: communal sharing (where people are ‘one’), authority ranking (where people are ranked), and equality matching (where people are separate, but evenly balanced). I further propose that humans, and potentially infants, recognize a relationship's strength which can be thought of as a continuous representation of obligations (the extent to which certain actions are expected), and commitment (the likelihood that people will continue the relationship). These representations and the assumption that others share them allow us to form, maintain, and change social relationships throughout our lives by informing how we interpret and evaluate the actions of others and plan our own.
... Evolutionary game theory provides a robust framework for modelling many biological and social interactions [1]. Traditional models largely exclude time delays, instead assuming that the actions of an individual are instantaneous and their impacts on fitness are immediate. ...
... where the i j entry is the payoff of the first (row) player when it plays the strategy i and the second (column) player plays the strategy j, with i, j ∈ {C, D}. We assume that both players are the same, and hence, payoffs of the column player are given by the matrix transposed to (1); such games are called symmetric. ...
Real-world processes often exhibit temporal separation between actions and reactions - a characteristic frequently ignored in many modelling frameworks. Adding temporal aspects, like time delays, introduces a higher complexity of problems and leads to models that are challenging to analyse and computationally expensive to solve. In this work, we propose an intermediate solution to resolve the issue in the framework of evolutionary game theory. Our compartment-based model includes time delays while remaining relatively simple and straightforward to analyse. We show that this model yields qualitatively comparable results with models incorporating explicit delays. Particularly, we focus on the case of delays between parents' interaction and an offspring joining the population, with the magnitude of the delay depending on the parents' strategy. We analyse Stag-Hunt, Snowdrift, and the Prisoner's Dilemma game and show that strategy-dependent delays are detrimental to affected strategies. Additionally, we present how including delays may change the effective games played in the population, subsequently emphasising the importance of considering the studied systems' temporal aspects to model them accurately.
... Spatial prisoner's dilemma (SPD) is a well-known spatial game theory that addresses the evolution of two types of strategies [1][2][3][4][5]. In SPD, defectors and cooperators interact with each other and update their strategies with the opponent. ...
... In SPD, defectors and cooperators interact with each other and update their strategies with the opponent. When two defectors meet, they get a punishment payoff P, but when two cooperators meet, they have a win-win relationship by PLOS earning a reward payoff R. If a defector and a co-operator meet, then a defector receives temptation payoff T, while a co-operator receives sucker payoff S. Defectors become dominant when they obtain a larger payoff T during interaction with cooperators [1][2][3][4][5][6][7][8]. However, evolutions of cooperative behavior have received attention from researchers because some animals show cooperative behaviors, which may flourish the species [9,10]. ...
Spatial prisoner’s dilemma (SPD) has attracted researchers’ attention as a model of conflict for players. In SPD, players have two different strategies, namely, defectors and cooperators. A defector earns a high payoff from an opponent co-operator while getting nothing from an opponent defector. On the contrary, cooperators promote a win–win relationship between the two cooperators. These mechanisms influence population dynamics in SPD, and many SPD models have been developed. However, little is known about the emergence of an unstable or unpredictable evolution in population dynamics using an SPD model, which may be observed in living systems. In addressing this issue, two SPD models were proposed. In both models, players change the neighborhood definition in accordance with their strategies and sometimes select the rule for this change using probability or local information. Result showed that our models generated characteristic population patterns that may be linked to a self-organized criticality (SOC), a term referring to many systems of interconnected, nonlinear elements that evolve over time into a critical state. In fact, the second model could be spontaneously close to the critical point using local information.
... Thus, the social part of the environment is underpinned by genes and can evolve in response to selection (Kirkpatrick and Lande 1989;Wolf et al. 1998;West-Eberhard 1979). Furthermore, the optimal phenotype for an individual depends in part on the genetic and phenotypic characteristics of the individuals with whom it interacts (Maynard-Smith and Price 1973;McNamara and Weissing 2010). This implies that social evolution creates a feedback between ecological and evolutionary processes, because the evolving phenotypes are also the ecological drivers of selection. ...
... The former is often formulated by the Snowdrift game for pairwise interactions (Doebeli & Hauert 2005) and by the public good game for group interactions (Fehr & Gächter 2002;Hauert et al. 2002;Semmann et al. 2003), whilst the latter by the Prisoner's Dilemma game (Axelrod 1984). These models show that if a cooperating individual receives some of the benefit of his or her own labors-as in Snowdrift games or some nonlinear public goods games-then evolutionary dynamics may lead to an equilibrium in which cooperators and cheaters coexist (Maynard Smith & Price 1973;Archetti & Scheuring 2012). On the other hand, if benefits accrue only to others-as in Prisoners' Dilemma games-then cooperation is expected to disappear unless some mechanism is present to support it (Nowak 2006a). ...
... Notably, it has achieved significant success in explaining some phenomena in the process of biological evolution. The most classic research results can be traced back to 1973 when Smith and Price first used evolutionary game theory to explain the struggle behavior between animals and first proposed the concept of evolutionarily stable strategies [18]. Building on Smith and Price's work, further developments in the field have expanded our understanding of evolutionary game theory. ...
... Evolutionary game theory provides a theoretical framework for examining the interaction between individual behavior and fitness. The theory views the evolutionary process as a dynamic process of strategy selection, where an individual's fitness depends not only on the strategy it adopts but also on its interactions with other individuals [18]. Within the application of game theory, the primary objective is to identify a suitable strategy to resolve existing conflicts or to uncover the optimal decision sequence yielding maximum returns. ...
This study investigates the potential impact of "LK-99," a novel material developed by a Korean research team, on the power equipment industry. Using evolutionary game theory, the interactions between governmental subsidies and technology adoption by power companies are modeled. A key innovation of this research is the introduction of sensitivity analyses concerning time delays and initial subsidy amounts, which significantly influence the strategic decisions of both government and corporate entities. The findings indicate that these factors are critical in determining the rate of technology adoption and the efficiency of the market as a whole. Due to existing data limitations, the study offers a broad overview of likely trends and recommends the inclusion of real-world data for more precise modeling once the material demonstrates room-temperature superconducting characteristics. The research contributes foundational insights valuable for future policy design and has significant implications for advancing the understanding of technology adoption and market dynamics.
... The Battle of the Sexes game has two pure strategy Nash equilibria, where both players coordinate on the same outcome: Both players choose Outcome A. The payoffs are (2, 1). Both players choose Outcome B. The payoffs are (1,2). ...
This paper presents a physics-informed deep learning approach for predicting the replicator equation, allowing accurate forecasting of population dynamics. This methodological innovation allows us to derive governing differential or difference equations for systems that lack explicit mathematical models. We used the SINDy model first introduced by Fasel, Kaiser, Kutz, Brunton, and Brunt 2016a to get the replicator equation, which will significantly advance our understanding of evolutionary biology, economic systems, and social dynamics. By refining predictive models across multiple disciplines, including ecology, social structures, and moral behaviours, our work offers new insights into the complex interplay of variables shaping evolutionary outcomes in dynamic systems
... One of the most effective methods of analyzing and controlling the spread of viral and bacterial infection is mathematical modeling, namely the development of an individual Blue boxes describe models based on ordinary differential equations [3,4,[10][11][12][13][14][15][16], orange boxesmodels based on partial differential equations [5,17], pink boxes-mean-field game models [18][19][20][21][22][23][24][25], and green boxes are associated with agent-based models [6,[26][27][28][29][30][31][32]. Grey box describes ordinary differential equations that came from chemical kinetics [33]. ...
This paper proposes and analyzes a mathematical model of tuberculosis and HIV co-infection that specifies for Russian Federation regions, based on mass balance law and described by eight ordinary differential equations. A sensitivity-based identifiability analysis of this mathematical model was performed, which revealed the sensitivity of the averaged parameters of the models to statistical real data of infectious individuals based on the Sobol method. The problem of identifying the sensitive epidemiological parameters (contagiousness, the rate of tuberculosis activation, additional mortality rate, etc.) for the model was reduced to the problem of minimization of the quadratic misfit function. The numerical results of the modeling of the number of people expected to be infected with tuberculosis and HIV were shown and discussed for the Sverdlovsk and Moscow regions of the Russian Federation. It has been shown that increasing the capacity of the medical system by 10% will make it possible to reduce the number of diagnosed cases of active tuberculosis by 2 times over the next 3 years in some regions of Russian Federation.
... Peace emerges as a dynamic balance between opposing forces, including cooperation and competition, aggression and deterrence. The interactions between societies involve strategic considerations where each group's actions influence the other's responses, leading to an ever-evolving state of relations (Axelrod & Hamilton, 1981;Smith & Price, 1973). ...
Recent geopolitical events have exposed critical gaps in the ability of peace and conflict psychology (PCP) to engage with conflicts beyond intractable or postwar contexts. This paper introduces the concept of "naïve pacifism" to describe underlying assumptions in PCP that hinder its ability to address complex modern conflicts effectively. Three pillars of naïve pacifism are identified: (1) the homeostatic view of peace as the natural state and violence as a dysfunction, (2) the belief in the reactive nature of violence, and (3) a perspectivist approach that overlooks objective features of conflicts. These assumptions lead PCP researchers to oversimplify, perpetuate pseudoscientific views of and promote ineffective interventions to solve violent conflicts. By challenging these pillars and proposing a more nuanced framework, this paper aims to advance PCP toward a true science of peace-making that is better equipped to address contemporary global conflicts.
... This scenario is the most common and challenging to study how cooperation can emerge between selfish actors. Another example is the Snowdrift game (SD), which depicts competition for shared resources and escalation of conflict [27][28][29]. In the SD game, players can maximize their gain by choosing the opposite strategy from the other player -even if it would be beneficial for the collective if both cooperated. ...
Social dilemmas where the good of a group is at odds with individual interests are usually considered as static -- the dilemma does not change over time. In the COVID-19 pandemic, social dilemmas occurred in the mitigation of epidemic spread: Should I reduce my contacts or wear a mask to protect others? In the context of respiratory diseases, which are predominantly spreading during the winter months, some of these situations re-occur seasonally. We couple a game theoretical model, where individuals can adjust their behavior, to an epidemiological model with seasonal forcing. We find that social dilemmas can occur annually and that behavioral reactions to them can either decrease or increase the peaks of infections in a population. Our work has not only implications for seasonal infectious diseases, but also more generally for oscillatory social dilemmas: A complex interdependence between behavior and external dynamics emerges. To be effective and to exploit behavioral dynamics, intervention measures to mitigate re-occuring social dilemmas have to be timed carefully.
... Evolutionary Game Theory (EGT) extends classical game theory to the study of evolving populations. It originated from John Maynard Smith and George Robert Price, who laid the mathematical foundations of the field [18,27]. Notably, Smith and Price introduced the concept of Evolutionarily Stable Strategies, formalizing how types are maintained in evolving populations. ...
The universe involves many independent co-learning agents as an ever-evolving part of our observed environment. Yet, in practice, Multi-Agent Reinforcement Learning (MARL) applications are usually constrained to small, homogeneous populations and remain computationally intensive. In this paper, we study how large heterogeneous populations of learning agents evolve in normal-form games. We show how, under assumptions commonly made in the multi-armed bandit literature, Multi-Agent Policy Gradient closely resembles the Replicator Dynamic, and we further derive a fast, parallelizable implementation of Opponent-Learning Awareness tailored for evolutionary simulations. This enables us to simulate the evolution of very large populations made of heterogeneous co-learning agents, under both naive and advanced learning strategies. We demonstrate our approach in simulations of 200,000 agents, evolving in the classic games of Hawk-Dove, Stag-Hunt, and Rock-Paper-Scissors. Each game highlights distinct ways in which Opponent-Learning Awareness affects evolution.
... In 1973 Smith and Price [34] introduced concepts of Game Theory into the Biology, coining the notion of Evolutionary Stable Strategies (ESS). Roughly speaking, given a game between two or more players (modeling for example a conflict between different species of animals), an ESS is a strategy such that if most of the players follows it, then there is no disruptive strategy that would give higher advantages for the other players. ...
This paper studies the number of centers and limit cycles of the family of planar quartic polynomial vector fields that has the invariant algebraic curve The main interest for this type of vector fields comes from their appearance in some mathematical models in Game Theory composed by two players. In particular, we find examples with five nested limit cycles surrounding the same singularity, as well as examples with four limit cycles formed by two disjoint nests, each one of them with two limit cycles. We also prove a Berlinskii's type result for this family of vector fields.
... The repeated attempts to initiate struggles, even after expulsion, were another characteristic of the agonistic behavior in P. angustipennis other than return. Generally, avoiding more fighting than necessary can reduce energy costs and maintain higher expectations of reproductive success (Arnott & Elwood, 2008;Smith & Price, 1973). ...
Competition is one of the most critical factors affecting animal behaviors. Aggressive interactions are central to acquiring resources or mating partners. Agonistic behavior is more common among males than females. Although laboratory observations of these behaviors give detailed descriptions under controlled conditions, field observations without human intervention are required because those supply information that provides insights into their function. In this paper, we report on the field observation and auxiliary laboratory experiments of male–male agonistic behavior of a wood‐feeding cockroach, Panesthia angustipennis, and discuss its strategy. In the field, a male pushed the opponent with the horn on the pronotum out of a gap between two logs, under which a female was. After pushing, the male repeatedly returned to a place close to the female, even if it did not subdue the opponent entirely. It suggests that the male–male agonistic behavior in P. angustipennis has both attack and avoidance. The bout was repeated as the ejected male reapproached the male. In contrast, the inferior male often escaped in the laboratory recording after field observation. Keeping the fighting experience for several days may contribute to the males avoiding a “losing battle.” This study significantly enhances our understanding of the mating strategy of P. angustipennis through male–male agonistic behavior and provides possibilities for its cognitive aspects from the fighting experience.
... ESS was first used and defined by J.M. Smith and G.R. Price in the year 1973 [60]. One of the main outcome of this early work is that natural selection prefers the "best strategy" among a group of individuals exhibiting a variety of strategies. ...
We propose and analyze a single-species population model subject to fear and its carry-over effect with the help of evolutionary game theory (EGT). We incorporate fear and carry-over cost in the growth of a single species resource population and the extensive analysis of our non-evolutionary model suggests that it can exhibit both weak and strong Allee effects. From the game theoretical viewpoint, we assume that the intrinsic growth rate r of the resource population and the attack rate a of the consumer population are functions of a mean phenotypic trait (u) of the resource, following a Normal distribution. Evolutionary stable strategies (ESS) are determined by using ESS maximum principle. Our study of ESS suggests that species extinction may be avoided as a result of evolution, though the extinct equilibrium can also be an ESS under certain conditions. The ratio of variation in the intrinsic growth rate and the attack rate plays a significant role in the ESS conditions of different equilibria as well as the global dynamics of our EGT model. Numerical simulations are performed to support our theoretical analysis.
... There are two possible explanations for this. First, in long-lived iteroparous species, inferior competitors should employ a risk-averse strategy by avoiding costly combats for mates against superior competitors (Clutton-Brock et al., 1979;Enquist & Leimar, 1987;Maynard Smith & Price, 1973). ...
Biting is a common male–male combat tactic across jawed vertebrates, in which teeth or bony beaks serve as weapons. Because biting can cause severe injuries in some species, bite scars provide critical information about the degrees and patterns of fights.
Amphibians have a remarkable diversity in tooth morphology and arrangement. However, the functional ecology of amphibian teeth is poorly studied. For example, unlike aquatic suction‐feeding frogs that lost teeth, aquatic salamanders that suction‐feed prey retain numerous sharp teeth, suggesting that teeth as weapons may partially explain their retention.
Here, we analysed long‐term injury records of one of the fully aquatic, suction‐feeding salamanders (Japanese Giant Salamander, Andrias japonicus ) to examine the previously unexplored potential of amphibian teeth as weapons for male–male combat. The majority of the injuries were missing toes and limbs, which most likely occurred during intra‐specific combat. We explored associations between injuries and independent variables such as sex, body size, body condition and stream sections. We also investigated possible injury‐pattern biases along the lateral (i.e. right vs. left) and longitudinal (i.e. anterior vs. posterior) axes, which could reveal how these animals fight.
We found that males had more injuries, larger individuals had more injuries, and males with poorer conditions had more injuries. There was no association between injuries and stream sections. In addition, we found that salamanders had more injuries on the right and posterior sides of the body. The lateral asymmetry in injuries is likely associated with turning asymmetry during combat.
Our results revealed the intense male–male combats of giant salamanders, providing evidence of the use of teeth as weapons. Combats via biting in amphibians may be much more common and severe than currently known. Our research suggests the function of amphibian teeth as weapons, which is likely to be a vital selective agent shaping its remarkable diversity.
... Evolutionary game theory, initially proposed by Smith and Price [65], is founded on the principle of bounded rationality and assumes that a single player in a game represents a population consisting of numerous individuals. The ultimate strategic choice of a given population is determined by the choices made by its individual members. ...
Car-sharing is a travel mode that can serve as an alternative to private cars, helping to reduce urban pollution. However, currently, there is a low willingness among travelers to use car-sharing, which is reflected in both low market penetration and user frequency. Therefore, it is essential for the government to encourage the use of car-sharing by providing subsidies. To better encourage the usage of car-sharing, this paper applies a two-fold evolutionary game model involving travelers and the government to explore the impact of subsidies on travelers’ choices, and the factors that could affect the subsidies’ efficiency. A simulation, using data from Beijing, was conducted to determine the implications of subsidy policies. The results show that a mileage-based subsidy and a fixed subsidy are applicable to travel of high and low mileages respectively, and under both subsidy modes, subsidies for trips with short duration or short pick-up and return time are more effective. Furthermore, we find that the efficiency of subsidies increases as the scale of car-sharing users, demand elasticity, or total number of travelers increases. Additionally, the subsidy levels should be lower than the environmental benefits of car-sharing but higher than the difference in travel costs between private cars and car-sharing. Future work will involve other game players such as car-sharing operators in order to draw deeper conclusions, and will involve the collection of data from more countries and cities to develop the robustness of the conclusions.
... 123 See McCullough et al. (2013). 124 See Lorenz (1992Lorenz ( [1963: 115, 201), or Smith and Price (1973). 125 See also Miller (2001). ...
The most important social skill is being able to effectively manage our relationships with others. Despite psychology's long history of studying human relationships, to this date, there has been no theory that satisfactorily explains this complex phenomenon. Moreover, most of the current relationship theories are impractical for everyday use. This book, Relationship Theory: A Scientific Method to Manage Your Relationships, aims to rectify this by proposing an intuitive approach to the study of human relationships called “Causal Mechanism Relationship Theory” (CMRT). By understanding the underlying logic of all human relationships, readers will learn to analyse their own relationships more effectively and manage them according to their preferences. The book uses accessible language and is primarily intended for the general public, although the scientific community will benefit from it as well. The book is available here: https://www.amazon.com/dp/B0D8WBW7RX
... The concept of Nash equilibrium was initially used in games with the motivation of economic programs. Then, thanks to its various applications in social sciences [2], biology [3,4], computer science [5,6], energy problems [7][8][9][10], environment modeling [11,12], etc., it has received more attention. Therefore, there was a need to develop NEPs. ...
The generalized Nash equilibrium problem (GNEP) is an extension of the Nash equilibrium problem (NEP), which allows the strategies and the objective function of each player to depend on the decision variables of all other players. In this paper, we consider a GNEP where the objective and constraint functions are not necessarily differentiable or convex. By proposing an alternative approach based on the equivalence with a single constrained optimization problem, we then present new sharp KKT-type necessary optimality conditions for a solution of this problem under a weak constraint qualification. We also offer an example to show that these conditions are more efficient for such problems than the previous ones. Further under weak convexity assumptions, we prove that these necessary conditions are also sufficient for optimality. Finally, we extend the definitions of some constraint qualifications from classical optimization to GNEP and study their interrelations.
... Evolutionary game theory was first proposed by biologists in 1973 [1], which has become one of the hot research topics in game theory nowadays. In the early research, it is always considered that the player plays with all the other players, but in the actual game, the player just plays with some specific players in general, so the concept of networked evolutionary games (NEGs) was proposed [2]. ...
In networked evolutionary games (NEGs), some elements in the payoff matrix of players may change due to environmental factors. In this article, the stability of NEGs with payoff perturbation is studied using the semi‐tensor product (STP) of matrices, and some new results are given. First, the perturbation of a column of the payoff matrix is considered, and a necessary and sufficient condition to ensure that the transition matrix of the profiles evolution dynamics to remain unchanged is provided. Second, the case that multiple columns of the game profile transition matrix are perturbed is investigated, and a necessary and sufficient condition for the stability of the NEGs is proposed. Finally, the validity of the results is illustrated by an example.
... Arratia et al., 1990) to bound the error in the distribution of the sum of dependent random variables. This method was also used by Rinott and Scarsini (2000) to derive results on the distribution of pure Nash There is a long tradition of studying dynamics to Nash equilibrium, cf., e.g., Smith and Price (1973); Weibull (1995); Fudenberg and Levine (1998);Young (1998). equilibria. ...
In a each agent plays one of their k best pure actions, but not necessarily their best action. We show that satisficing equilibria in which agents play only their best or second-best action exist in almost all games. In fact, in almost all games, there exist satisficing equilibria in which all but one agent best-respond and the remaining agent plays at least a second-best action. By contrast, more than one third of games possess no pure Nash equilibrium. In addition to providing static foundations for satisficing equilibria, we show that a parsimonious dynamic converges to satisficing equilibria in almost all games. We apply our results to market design and show that a mediator who can control a single agent can enforce stability in most games. Finally, we use our results to study the existence of -equilibria.
... players compete for a good (valued at V) and simultaneously decide to play the Hawk or Dove tactics, that consist of behaving aggressively or peacefully, respectively [5]. It predicts that Hawk is a pure Evolutionary Stable Strategy (ESS) when the value of the good exceeds the cost of losing a fight, while both tactics coexist otherwise. ...
Background
While most game theoretical models assume that individuals randomly interact with all other group members, strong evidence indicates that individuals tend to preferentially interact with some of them. The position of an individual in a network affects, among other factors related to survival, its predation risk and competitive success. Here I then modified the Hawk-Dove game to explore the effect of social network structure on competitive strategy of individuals that differ in their fighting ability and may adjust their use of the Hawk, Dove and Assessor tactics to maximize their foraging success when they meet opponents they are connected with.
Results
From randomly generated networks, I demonstrate that phenotypic assortment by fighting ability reduces individuals’ aggressiveness and, as such, favours cooperative interactions. Furthermore, the success of individuals with the weakest fighting ability is usually highest within networks where they most frequently meet opponents with the same fighting ability as their own, suggesting they might benefit from breaking connections with strong contestants. This might be the case when strong contestants systematically rely on the aggressive Hawk tactic or the risk of being predated is low and independent of the number of neighbours. Thus, I extended the model and built a dynamic model to allow individuals not only to adjust their behaviour to local conditions but also to modify the structure of the social network. The number of connections and degree of phenotypic assortment are then affected by ecological factors (e.g. resources value and predation risk), but above all by whether individuals can reliably assess the competitive ability of their opponents and adjust their behaviour accordingly.
Conclusions
These findings provide strong evidence that behaviour can play a key role in shaping network structure and highlight the importance of considering the coevolution of network and behaviour to apprehend its consequences on population dynamics.
... Evolutionary games theory was first proposed for describing the evolutionary of living things in nature [1]. Since then, evolutionary games theory has been widely developed, representative scholars are Maynard Smith and Price [2]. With the rapid development of evolutionary games theory, many related problems in large and small fields have been effectively solved, such as biology, economics, mathematics and so on [3], [4]. ...
... Evolutionary game theory is based on bounded rationality of the decision makers who can only adjust their strategies according to existing payoff information [53]. For this reason, the theory focuses on the mutual feedback effects of driving forces among different decision makers and specifies evolutionary stabilization strategies [54]. To further promote innovation development, industrial parks have increased their efforts to attract high-technology talents, flexibly introduced academicians and other experts in the leading industrial fields to work in the parks. ...
Industrial parks are the important carriers to promote regional innovation and economic development. The policy preferences of the government, the support orientation of the industrial park and the innovation willingness of the enterprises in the park play a significant role in promoting the high-quality development of the industrial parks. In order to clarify the decision-making process of each subject, this paper constructs a triple evolutionary game model between the government, industrial park and enterprises in the park, Matlab software is used to conduct simulation research, and the strategy selection of each subject in the process of promoting high-quality development of the park is analyzed, as well as the influence of variables on the evolutionary game. Through numerical simulation, this study finds that the strategy choice of the government and the industrial park is influenced by the cost of innovation management for enterprises. In addition, the innovation willingness of enterprises is affected by the policy preference of the government and the support orientation of the industrial park, the excessive tax preference of the government will lead to negative innovation behaviors of the enterprises, the “inward incentives” support orientation of the industrial park can stimulate the enterprises’ innovation willingness on “active innovation”, the enterprises behavior of “active innovation” will strengthen the “inward incentives” support orientation of the industrial park in turn. The difference of the benefits and the costs between the two support orientations by the industrial park will lead to the equilibrium points stabilized at different strategy combinations. Based on these findings, countermeasures and suggestions are proposed in this study.
... Researchers have long been fascinated by the evolution of cooperative behavior in populations for many years as it can have important implications for understanding the behavior of individuals in various settings, including social, economic, and biological systems. Foundational publications by Smith (1974); Axelrod and Hamilton (1981); Smith and Price (1973) in the 1970 s marked the inception of evolutionary game theory, laying the groundwork for subsequent investigations. Following the publishing of the first papers on evolutionary game theory, researchers in various fields became interested. ...
Examining the interaction between agents in a well-mixed population has been a prevalent area of research. Previous studies have emphasized the evolution of the impact of network architecture and payoff differences on agents’ behavior in various games. There has been a recent surge in interest in incorporating popularity among researchers in this field. In this study, we employ a game theoretic approach to gain insight into the strategic behavior and decision-making processes of individuals in a network and how these decisions impact the diffusion of information when an individual’s popularity is considered. The Fermi function is used to model the probability of information diffusion and the spread of influence within the network. We introduce a simulation module that models the dynamic process of evolutionary game theory in both synthetic and real-world networks, leveraging the Fermi update rule as a critical component. Furthermore, the implementation is modified to analyze the influence of each individual by incorporating metrics that account for individual popularity and its effect on the overall network dynamics. This modification allows for a more granular understanding of how individual agents contribute to the propagation of information and the development of cooperative behaviors. The simulation results provide valuable insight into the evolution of cooperative behavior in complex networks and hold potential for further exploration into various aspects of evolutionary game theory.
... EGT came was created in the 1990s as a refinement and development of CGT (Smith and Price 1973). In contrast to CGT, EGT states that human rationality is finite and that complete informational conditions are not needed. ...
This paper focuses on the social, economic, and environmental benefits of village development during the construction and operation of a pumped-storage power station (PSPS) in China. This paper provides an innovative perspective on new energy development in the context of rural revitalization. A four-party evolutionary game model was established that included the central government, local governments, PSPSs, and villagers. The evolution and stabilization strategies used in the development process of the rural revitalization were analyzed. The results show the following: (1) The greater the strength or amount of fines and penalties, the lower the cost of supervision, making it more conducive to the central government's evolution towards strict supervision. (2) The greater the tax revenues, the more likely local governments are to evolve towards active implementation. (3) The greater the social benefits, the more likely PSPSs are to evolve toward active participation. (4) The greater the resettlement compensation fees, wages, and donations, the more likely villagers are to evolve toward positive cooperation. We then provide appropriate suggestions on how PSPSs contribute to rural revitalization. This paper is important for improving the investment decision plan of PSPSs for rural revitalization and promoting China’s sustainable new energy.
... On the other hand, in economics, social agents are typically assumed to be rational. Game theory provides a mathematical framework to describe the interactions among rational individuals and has been widely applied to various areas, such as ecology and epidemic spread [17][18][19][20][21][22][23]. Early game-theoretic studies assume that individuals are homogeneously mixed and fully rational, making decisions to achieve the most advantageous outcomes for themselves [24]. ...
Threshold-driven models and game theory are two fundamental paradigms for describing human interactions in social systems. However, in mimicking social contagion processes, models that simultaneously incorporate these two mechanisms have been largely overlooked. Here, we study a general model that integrates hybrid interaction forms by assuming that a part of nodes in a network are driven by the threshold mechanism, while the remaining nodes exhibit imitation behavior governed by their rationality (under the game-theoretic framework). Our results reveal that the spreading dynamics are determined by the payoff of adoption. For positive payoffs, increasing the density of highly rational nodes can promote the adoption process, accompanied by a hybrid phase transition. The degree of rationality can regulate the spreading speed, with less rational imitators slowing down the spread. We further find that the results are opposite for negative payoffs of adoption. This model may provide valuable insights into understanding the complex dynamics of social contagion phenomena in real-world social networks.
... Beyond the assumptions of complete rationality and information of traditional game theory, evolutionary game theory is a useful approach to depict the equilibrium strategies of multiple stakeholders within the system by providing the dynamic evolutionary process 31 , which has been widely applied to the analysis of complex multi-actors system, including the waste management systems 19,32,33 . In the polycentric waste governance system, each governance agent will make a decision based on the premise of economic rationality due to the economic attributes of waste, which means that the strategy with higher economic benefits will be selected. ...
The mismanagement of waste is jeopardizing urban sustainability. Although polycentric waste governance (PWG) has been introduced, characterizing the PWG remains challenging. This paper employs game theory to illustrate polycentricity by investigating the equilibrium state from the stakeholders’ perspective. Shanghai, Tokyo, and Hong Kong are selected as target cities for comparative analysis. The findings reveal the heterogeneous characteristics in three megacities’ PWG—the
collaboration by principal stakeholders (formal recyclers, informal recyclers, households) in Shanghai, the exclusion of informal recyclers in Tokyo, and the limited contribution provided by the formal recyclers in Hong Kong. The divergent PWG characteristics can be attributed to variations in governance patterns,
socioeconomic factors, and policy formulation. Regarding urban sustainability, Tokyo and Shanghai’s PWG contribute to the circular economy’s expansion, while Hong Kong’ potential, in this regard, is undervalued. Despite Tokyo’s improved social recognition to practitioners, this PWG mode, primarily driven by formal recyclers and households, presents limited inclusion of low-income groups. Additionally, it is crucial for the authorities in Shanghai and Hong Kong to acknowledge the potential pollution of informal recyclers’ non-environmental behavior. This paper offers a valuable model for characterizing and analyzing PWG across different cities, facilitating knowledge aggregation and the implementation of PWG practice.
Trust and reciprocation of it form the foundation of economic, social and other interactions. While the Trust Game is widely used to study these concepts for interactions between two players, often alternating different roles (i.e., investor and trustee), its extensions to multi-player scenarios have been restricted to instances where players assume only one role. We propose a symmetric N-player Trust Game, in which players alternate between two roles, and the payoff of the player is defined as the average across their two roles and drives the evolutionary game dynamics. We find that prosocial strategies are harder to evolve with the present symmetric N-player Trust Game than with the Public Goods Game, which is well studied. In particular, trust fails to evolve regardless of payoff function nonlinearity in well-mixed populations in the case of the symmetric N-player trust game. In structured populations, nonlinear payoffs can have strong impacts on the evolution of trust. The same nonlinearity can yield substantially different outcomes, depending on the nature of the underlying network. Our results highlight the importance of considering both payoff structures and network topologies in understanding the emergence and maintenance of prosocial behaviours.
Understanding the evolution of cooperation in multi-player games is of vital significance for natural and social systems. An important challenge is that group interactions often lead to nonlinear synergistic effects. However, previous models mainly focus on deterministic nonlinearity, where synergy or discounting effects occur under specific conditions, not accounting for uncertainty and stochasticity in real-world systems. Here, we develop a probabilistic framework to study the cooperative behavior in stochastic nonlinear public goods games. Through both analytical treatment and Monte Carlo simulations, we provide a comprehensive understanding of social dilemmas with stochastic nonlinearity in both well-mixed and structured populations. We find that increasing the degree of nonlinearity makes synergy more advantageous when competing with discounting, thereby promoting cooperation. Furthermore, we show that network reciprocity loses effectiveness when the probability of synergy is small. Moreover, group size exhibits nonlinear effects on group cooperation regardless of the underlying structure. Our findings thus provide insights into how stochastic nonlinearity influences the emergence of prosocial behavior.
Background
We focus on Haldane’s familial selection in monogamous families in a diploid population, where the survival probability of each sibling is determined by altruistic food sharing with its siblings during starvation. An autosomal recessive-dominant or intermediate allele pair uniquely determines the altruistic or selfish behavior, which are coded by homozygotes. We focus on the case when additive cost and benefit functions determine the survival probability of each full sibling.
Results
We provide conditions for the existence of the altruistic and selfish homozygote. We show that the condition of evolutionary stability of altruism depends on the genotype-phenotype mapping. Furthermore, if the offspring size increases then the condition of evolutionary stability of altruism becomes stricter. Contrary to that, for the evolutionary stability of selfish behavior it is enough if the classical Hamilton’s rule does not hold. Moreover, when the classical Hamilton’s rule holds and the condition of evolutionary stability of altruism does not hold, then the selfish and altruistic phenotypes coexist.
Conclusions
In summary, the classical Hamilton’s rule is a sufficient condition for the existence of altruism, but it alone does not imply the evolutionary stability of the pure altruistic homozygote population when the altruistic siblings share the cost of altruism.
From the second half of 1970s to the end of 2000s, the romanzo accademico, the Italian version of the traditionally Anglophone campus novel, has usually portrayed mainly established professors, but recently a new generation of authors emerged, portraying the lives of doctoral students and precarious researchers. This change in perspective, accompanied by a sharpening of criticism directed at the institution, coincided with the hybridization of the romanzo accademico with various literary genres: from the industrial novel La cospirazione delle colombe (2011) by Vincenzo Latronico to coming-of-age novels such as La fine dell’altro mondo (2012) by Filippo D’Angelo or Elena Ferrante’s Storia del nuovo cognome (2012), and even the graphic novel Il segreto di Majorana (2015) by Francesca Riccioni and Silvia Rocchi. Moreover, recent attempts such as Il pieno di felicità (2019) by Cecilia Ghidotti, Raffaele Donnarumma’s La vita nascosta (2022), and Dario Ferrari’s La ricreazione è finita (2023) have been made to define the genre more precisely, contributing to its development as a subgenre of working class literature. The aim of this paper is to analyze some works from the last fifteen years in order to trace on one hand the portrayal of the dynamics that animate the academic field according to the studies of Bourdieu and Passeron – criteria for access, time management, mentor-student relationships, internal rivalries, etc. –, on the other hand the depiction of research activity as work.
Density dependence plays an important role in population regulation in the wild. It involves a decrease in population growth rate when the population size increases. Fifty years ago, Charlesworth introduced the concept of ‘critical age group’, denoting the age classes in which variation in the number of individuals most strongly contributes to density regulation. Since this pioneering work, this concept has rarely been used. In light of Charlesworth’s concept, we discuss the need to develop work between behavioural ecology, demography and evolutionary biology to better understand the mechanisms acting in density-regulated age-structured populations. We highlight demographic studies that explored age-specific contributions to density dependence and discuss the underlying evolutionary processes. Understanding competitive interactions among individuals is pivotal to identify the ages contributing most strongly to density regulation, highlighting the need to move towards behavioural ecology to decipher mechanisms acting in density-regulated age-structured populations. Because individual characteristics other than age can be linked to competitive abilities, expanding the concept of critical age to other structures (e.g. sex, dominance rank) offers interesting perspectives. Linking research fields based on the concept of the critical age group is key to move from a pattern-oriented view of density regulation to a process-oriented approach.
This article is part of the discussion meeting issue ‘Understanding age and society using natural populations’.
In this paper, I intend to offer an evolutionary interpretation of the concept of sympathy in Hume’s ethical theory based on the general tenets of contemporary evolutionary ethical theory. By presenting the conceptual frameworks that make up these theories, my argument involves specifying that, for both of them, the psychological mechanism of sympathy seems to figure as an essential evolutionary trait of moral and altruistic behavior in the human species. In the context of evolutionary biology, two evolutionary models have been developed to explain the logic of human altruistic behavior: i) kin selection and ii) multilevel selection. I argue, based on textual evidence in Hume’s work, that the psychological mechanism of sympathy seems to be best explained by the multilevel selection model. I conclude, then, by highlighting some important contributions that this evolutionary interpretation can make to the general plausibility of Hume’s ethical theory.
Keywords
Hume; altruism; sympathy; kin selection; multilevel selection; evolutionary ethics
This study incorporates environmental feedback into the optional prisoner’s dilemma and rock–paper–scissors games to examine the mutual influence of eco-evolutionary outcomes and strategy dynamics. A novel game-theoretic model is developed that integrates the optional prisoner’s dilemma and rock–paper–scissors games by incorporating an environmental state variable. By adjusting feedback parameters, chaos, oscillations and coexistence are observed that surpass the usual outcomes of social dilemmas when the environment transitions between depleted and replenished states. Defection is no longer advantageous in evolution; cooperation, abstention and cyclic dominance arise. The observed transitions align with natural economics, ecology and sociology phenomena. The inclusion of abstention options and environmental feedback has a significant impact on collective outcomes when compared with conventional games. This has important implications for studying adaptation and decision-making in situations with ecological constraints.
In many butterfly species, males emerge earlier than females as part of a strategy to maximize male reproductive success. Although behavioral ecological studies using mathematical models have been conducted to explain this phenomenon, certain emergence patterns remain unexplained. In the butterfly species Fabriciana nerippe , some males emerge at the same time as females, in addition to males that emerge earlier than the females. However, it is unclear what emergence patterns occur in populations with male dimorphism, as observed in this species. In this study, we showed the existence of male body size dimorphism in Fabriciana nerippe by conducting a comparative analysis of forewing lengths between males and females. In addition, we developed a comprehensive mathematical model to investigate emergence patterns in the presence of dimorphic males. By introducing a trade-off between large size and early emergence, the model considered a scenario where small early-emerging and large late-emerging males could coexist. Numerical analysis demonstrated the emergence patterns of these two male types with a switch in emergence time. Furthermore, the higher the death rate before emergence, the earlier the emergence switch. These findings suggested that the timing of the switch depends on the death rate and is influenced by environmental factors. This work contributes to ecological and theoretical studies on timing dimorphism in life-history strategies across a broader range of species.
Highlights
We confirmed the existence of male body-size dimorphism corresponding to emergence timing in Fabriciana nerippe .
We developed a comprehensive model of male emergence patterns incorporateing male dimorphism.
We assumed a trade-off between early emergence and large body size.
The timing of male emergence switching is influenced by death rate and reproductive advantage of large males.
Evolutionary graph theory has considerably advanced the process of modelling the evolution of structured populations, which models the interactions between individuals as pairwise contests. In recent years, these classical evolution models have been extended to incorporate more realistic features, e.g. multiplayer games. A recent series of papers have developed a new evolutionary framework including structure, multiplayer interactions, evolutionary dynamics, and movement. However, so far, the developed models have mainly considered independent movement without coordinated behaviour. Although the theory underlying the framework has been developed and explored in various directions, several movement mechanisms have been produced which characterise coordinated movement, for example, herding. By embedding these newly constructed movement distributions, within the evolutionary setting of the framework, we demonstrate that certain levels of aggregation and dispersal benefit specific types of individuals. Moreover, by extending existing parameters within the framework, we are not only able to develop a general process of embedding any of the considered movement distributions into the evolutionary setting on complete graphs but also analytically produce the probability of fixation of a mutant on a complete N-sized network, for the multiplayer Public Goods and Hawk–Dove games. Also, by applying weak selection methods, we extended existing previous analyses on the pairwise Hawk–Dove Game to encompass the multiplayer version considered in this paper. By producing neutrality and equilibrium conditions, we show that hawks generally do worse in our models due to the multiplayer nature of the interactions.
The game as an important part of everyday life, thousands of years in the life of Berder Eddava Da Dese Esda, Emda
Comsadder of Hassaddad Seddal Asdada Kodde N Dedhebarrasddi and DDDDD Moiddo Ddor Baddas N Ddari and
Verbandihaifeni is placed in the same class. This article, in Falsai's view, is for playing and playing
- Ver Kehbandir deals with open actions in strategic situations.
They did not come and did not support the claims of some of the abusers. Madda Badda Arseddi are the grades
And the presenters, we will present Varez Abi and his coordinators' opinions about the game. Then it's bad
Do not forget to play the roles of Heda Masdal.
We strongly ask men to consider these two hairstyles for Eid.
It looks expensive again. After expressing the response of Ayamli's strategy to this problem, Badr Asdir's criticisms
d. Email will also be checked
Key words: game knowledge, game-making tools, dams, dams, dams, fences
Iamli
THREE KINDS OF VIOLENCE AND THE DYNAMICS OF THE ENVY TRIANGLE
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In this talk we will look at physical, emotional, and cognitive forms of violence, including attacks on reputation and the capture of institutions. We will set these in a context of Girardian contest, with political, commercial and academic examples. Then we will draw out the dynamics of Girard’s envy triangle graphically, with the usual two end-states: covert rivalry (or ressentiment) and overt contest. These dynamics can be extended to show a third end-state: a stable state of bullying, where status or power itself has been contested and the moral structure inverted.
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Copyright Paul Duggan, 2024
The moral right of the author has been asserted
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presentation text tbc
Greater knowledge is always an advantage for a rational individual. However, this article shows that for a group of rational individuals greater knowledge can backfire, leading to a worse outcome for all. Surprisingly, this can happen even when new knowledge does not mean the discovery of a new action but simply provides a deeper understanding of the interaction at stake. More specifically, enhanced knowledge about the current state of nature may hinder cooperation among purely self-interested individuals. The paper describes this paradoxical possibility—a ‘knowledge curse’—and analyses the evolutionary process that occurs if, initially, only a few people have access to the greater knowledge. It concludes with a tentative comment on ways to avert this potential knowledge backlash.
Lunar rhythms shape spawning phenology and subsequent risks and rewards for early life-history stages in the sea. Here, we consider a perplexing spawning phenology of the sixbar wrasse (Thalassoma hardwicke), in which parents spawn disproportionately around the new moon, despite the low survival of these larvae. Because primary sex determination in this system is highly plastic and sensitive to social environments experienced early in development, we ask whether this puzzling pattern of spawning is explained by fitness trade-offs associated with primary sexual maturation. We used otoliths from 871 fish to explore how spawning on different phases of the moon shapes the environments and phenotypes of settling larvae. Offspring that were born at the new moon were more likely to settle (i) before other larvae, (ii) at a larger body size, (iii) at an older age, (iv) to the best quality sites, and (v) as part of a social group—all increasing the likelihood of primary maturation to male. Selection of birthdates across life stage transitions suggests that the perplexing spawning phenology of adults may reflect an evolutionarily stable strategy that includes new moon spawning for compensatory benefits later in life, including preferential production of primary males at certain times.
Rabies, a fatal zoonotic disease caused by the Lyssavirus, remains a major global health concern. The review critically examines the virus's origin, transmission, and the immune response triggered in the host following infection. It also evaluates the current state of rabies prevention and control strategies, with a focus on vaccination approaches, diagnostic techniques, and preventive measures. By highlighting key developments and challenges in rabies research, this review aims to contribute valuable insights into combatting the disease and safeguarding human and animal populations.
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