Game Theory and the Humanities - Bridging Two Worlds.
Abstract
Game theory models are ubiquitous in economics, common in political science, and increasingly used in psychology and sociology; in evolutionary biology, they offer compelling explanations for competition in nature. But game theory has been only sporadically applied to the humanities; indeed, we almost never associate mathematical calculations of strategic choice with the worlds of literature, history, and philosophy. And yet, as Steven Brams shows, game theory can illuminate the rational choices made by characters in texts ranging from the Bible to Joseph Heller's Catch-22 and can explicate strategic questions in law, history, and philosophy. Brams's strategic exegesis of texts helps the reader relate characters' goals to their choices and the consequences of those choices. Much of his analysis is based on the theory of moves (TOM), which is grounded in game theory, and which he develops gradually and applies systematically throughout. TOM illuminates the dynamics of player choices, including their misperceptions, deceptions, and uses of different kinds of power. Brams examines such topics as Abraham’s decision to offer his son for sacrifice when God commanded him to do so; the outcome and payoff matrix of Pascal’s wager on the existence of God; and the strategic games played by presidents and Supreme Court justices; frustration games, as illustrated by the strategic use of sexual abstinence in Aristophanes’s Lysistrata; and how information was slowly uncovered in the game played by Hamlet and Claudius. Going beyond the explication of these specific situations, Brams also derives propositions about "generic games," applicable to a broad class of situations. The reader gains not just new insights into the actions of certain literary and historical characters but also a larger strategic perspective on the choices that make us human.
... Of the 57 distinct 2 9 2 conflict games that contain no mutually best (4,4) outcome, 45 (79%) have either one or two cooperative outcomes; the maximin outcomes in the other 12 conflict games are (2,4), (4,2), (2,3), or (3,2). 7 The cooperative outcomes in the 45 games in which each player receives at least its next-best payoff of 3 are, with one exception (game 22 in the appendices of Brams, 1994Brams, , 2011, NMEs. This exception is shown in Fig. 2. ...
... This section followsBrams (1994), who gives a full account of the theory of moves (TOM), whose main equilibrium concept is an NME. This account also includes an analysis of three different kinds of power (moving, order, and threat) and several applications; for other applications, seeBrams (2011Brams ( , 2018. Our purpose in this section, after defining NMEs for 2 9 2 games-the focus of previous studies-is to give general results for larger 2-person and n-person games. ...
... However, if one player has ''order power,'' it can determine the order of moves and, therefore, that its preferred outcome will be the NME from that state(Brams, 1994). 5 Prisoners' Dilemma is game 32 in the classification scheme ofBrams (1994Brams ( , 2011Brams ( , 2018 for the 57 2 9 2 conflict games; the other 2 9 2 game we discuss in this section is game 22, which does not have a name. 6 Effectively, this is a game tree, or game in extensive form, showing a sequence of alternating choices of the players, except that instead of branching from top to bottom, as in the usual representation, the choices of the players go sideways, from left to right. ...
It is well known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: every finite normal-form game of complete information and common knowledge has at least one Pareto-optimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a Nash equilibrium. We use some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis.
... For the human, I use the preferences that are standard in decision-theoretic analyses of Pascal's Wager (e.g. Hájek 2003: 28), and for the deity, I use the reasonable preference ordering stipulated in Brams (1982Brams ( , 2007Brams ( , 2011. 5 It turns out that there is an equilibrium in which the human chooses to wager that the deity exists and Pascal's Wager thus operates. However, unlike in the decision-theoretic setting, there is also an equilibrium in which the human chooses to not wager. ...
... On the other hand, if H 5 is finite, then even the human strictly prefers the Wager Equilibrium, which thus Pareto-dominates the Don't-Wager Equilibrium. 12 Brams (1982Brams ( , 2007Brams ( , 2011 presents the only other game-theoretic analyses in which a deity and a human are decision-makers. His 'Revelation Game' (Brams 2011: 82), which is the one most similar to this model, is a 2 × 2 simultaneous-move game of complete information. ...
... Using the standard infinite-utility-for-heaven Pascal's Wager preferences for the human, and Brams' (1982and Brams' ( , 2007and Brams' ( , 2011 plausible contingentrevealer preference ordering for the deity, it turns out that a Wager Equilibrium exists in which the human chooses to wager and Pascal's Wager thus operates, but a Don't-Wager Equilibrium also exists (even if the human has the first wager preferences in which there is nothing to lose by wagering). Thus, in a game-theoretic setting Pascal's Wager is indeterminate: wagering and not wagering are both consistent with equilibrium behaviour. ...
Formal analyses of Pascal’s Wager have almost all been decision-theoretic, with a human as the sole decision-maker. This paper analyses Pascal’s Wager in a game-theoretic setting in which the deity whose existence the human is considering wagering on is also a decision-maker. There is an equilibrium in which the human chooses to wager that the deity exists and Pascal’s Wager thus operates, but also one in which the human does not wager. Thus, in a game-theoretic setting, Pascal’s Wager is indeterminate: wagering and not wagering are both consistent with equilibrium behaviour.
... Literature is not new to humanistic applications of game theory, and such application ranges from short stories to operas (Brams, 2011). The field of literature, then, has for a few years been actively encouraged as fertile ground for strategic analysis. ...
... The field of literature, then, has for a few years been actively encouraged as fertile ground for strategic analysis. Using game theory to study literature can not only explain the strategic choices characters make in a work of fiction, but it can help explain decisions uncharacteristic to certain characters, like those in tragedies (Brams, 2011). ...
... However, they use the name Alibi for two different ordinal games (Stag Hunt × Dilemma and Assurance × Dilemma). For the third game with a Pareto-inferior equilibrium (Coordination × Dilemma) they use Steven Brams' name, Revelation (which comes from his analysis of Biblical stories) [7,26]. The nomenclature, based on twelve strict symmetric games and seven types of tie transformations, provides an efficient way to locate similar and different games within the multitude of possibilities. ...
... Brams is one of the few researchers who has paid systematic attention to asymmetric games, one reason that Robinson and Goforth's periodic table [18] includes many of his names. However, in some cases, Brams gives the same name to several different ordinal games, and so designates a set games, which he calls a generic game [26], (and which may form a connected region in the topology). By providing unique names, the nomenclature could facilitate systematic attention to these and other asymmetric games. ...
Prisoner’s Dilemma, Chicken, Stag Hunts, and other two-person two-move (2 × 2) models of strategic situations have played a central role in the development of game theory. The Robinson–Goforth topology of payoff swaps reveals a natural order in the payoff space of 2 × 2 games, visualized in their four-layer “periodic table” format that elegantly organizes the diversity of 2 × 2 games, showing relationships and potential transformations between neighboring games. This article presents additional visualizations of the topology, and a naming system for locating all 2 × 2 games as combinations of game payoff patterns from the symmetric ordinal 2 × 2 games. The symmetric ordinal games act as coordinates locating games in maps of the payoff space of 2 × 2 games, including not only asymmetric ordinal games and the complete set of games with ties, but also ordinal and normalized equivalents of all games with ratio or real-value payoffs. An efficient nomenclature can contribute to a systematic understanding of the diversity of elementary social situations; clarify relationships between social dilemmas and other joint preference structures; identify interesting games; show potential solutions available through transforming incentives; catalog the variety of models of 2 × 2 strategic situations available for experimentation, simulation, and analysis; and facilitate cumulative and comparative research in game theory.
... The motive care refers to altruism and prosociality including models of other-regarding preferences, positive reciprocity, guilt aversion and signaling of preferences (see Rotemberg (2014) for a comprehensive summary). The motive anger has been studied theoretically (Battigalli et al., 2019;Akerlof, 2016;Aina et al., 2020;Winter et al., 2016;Brams, 2011;Passarelli & Tabellini, 2017), in the context of pricing (Anderson & Simester, 2010;Rotemberg, 2005) and experimentally (Gneezy & Imas, 2014;Van Leeuwen et al., 2017;Persson, 2018;Castagnetti & Proto, 2020). ...
This paper provides evidence for the following novel insights: (1) People’s economic decisions depend on their psychological motives, which are shaped predictably by the social context. (2) In particular, the social context influences people’s other-regarding preferences, their beliefs and their perceptions. (3) The influence of the social context on psychological motives can be measured experimentally by priming two antagonistic motives—care and anger—in one player towards another by means of an observance or a violation of a fairness norm. Using a mediation approach, we find that the care motive leads to higher levels of cooperation which are driven by more optimistic beliefs, a different perception of the game as well as by a shift towards more pro-social preferences.
... Litres of ink have already been spilled in the debate between proponents of blockchain technology and its critics. The first camp believes that as a result of consensus [Schwartz et al., 2014] in a game [Brams, 2011] with N individual players, blockchain is the ultimate guarantee of "trust" in the volatile cyberworld where falsity tends to spread faster than truth [Vosoughi et al., 2018]. The other camp points out that in 10 years since its conception, billions of dollars invested, gigawatts of energy burned in the name of human vanity, the blockchain technology -materialized in postmodern divinities [Namztohoto, 2013] like Bitcoin or Ethereum -in fact, did not bring about anything useful for a common man [Stinchcombe, 2018]. ...
This document describes fundamental concepts and principles governing the transformation of an opaque content-publishing community economy into a fully transparent publicly available ledger. Inspired by existing public ledger technologies and cryptocurrencies like Ripple, our Kyberia’s Open Ledger (KOL) proposal aims to use minimalist variant of a blockchain technology as a guarantee of trust and value-holder serving a well-defined, local (i.e. non-global) human community. Special care is taken so
that the transformation of existing emotion-carrying K tokens into fully exchangeable blockchain-tokens would minimize the social inequality between users while still being fair to those, who already contributed the most to Kyberia’s flourishment. Other properties of the digital currency hereby introduced include: its minimal ecological footprint, absence of transaction fees and demurrage-based redistribution of wealth.
... This series of possible moves and countermoves end when the player considering the next move decides to stop the game at the given stage, or when the sequential moves complete a cycle and the players return to the original outcome. Motivated by farsighted calculations of where play will terminate, after a finite series of sequential moves and countermoves within the original game, if the game started in any of the four outcomes of the original game, a rational player will choose to move only if it leads safely to a better outcome than the status quo (Brams 1994(Brams , 2011. Thus, by postulating different rules, the theory of moves tolerates nonmyopic playersmunicipalities in our example-that consider a broader horizon. ...
Is it beneficial for municipalities to cooperate or compete with one another to attract visitors? The myopic rationality of game theory favors competition for short-term gains, whereas the nonmyopic theory of moves suggests that cooperation in this regard might be more farsighted, consensual, inclusive, and sustainable. To understand why popular cities switched to cooperation when faced with the crisis of overtourism, even though the players’ preferences about the outcomes did not change, we analyzed the case study of Amsterdam. The results indicate that the theories are appropriate in different situations. Thus, the theory of moves’ rules—alternating choices, thinking ahead in making choices—are more appropriate to finding a solution that would be stable in the future, not just one that is myopically stable in the present. We conclude that cooperation remains a more beneficial approach to managing tourism even in periods of undertourism. Policy directions are provided.
... Following Brams (2011) methodology, it will be assumed here that at certain time, one player decides to depart from the status quo, and adopts a long-term strategic objective(s) to improve his standing. Thereafter, the second player has to react, carefully taking into consideration his best option for addressing the new situation. ...
... The theory is the heterodox game "theory of moves" (Brams, 1993(Brams, , 2011. This theory asks the analyst to generate a plausible rank ordering of the four outcomes pertaining to each interactant. ...
The experimental research paradigm lies at the core of empirical psychology. New data analytical and computational tools continually enrich its methodological arsenal, while the paradigm’s mission remains the testing of theoretical predictions and causal explanations. Predictions regarding experimental results necessarily point to the future. Once the data are collected, the causal inferences refer to a hypothesis now lying in the past. The experimental paradigm is not designed to permit strong inferences about particular incidents that occurred before predictions were made. In contrast, historical research and scholarship in other humanities focus on this backward direction of inference. The disconnect between forward-looking experimental psychology and backward-looking historical (i.e., narrative) psychology is a challenge in the postmodern era, which can be addressed. To illustrate this possibility, I discuss three historical case studies in light of theory and research in contemporary psychology.
... En "los juegos" que permiten ganancia mutua (o pérdida mutua), ¿es "racional" cooperar para realizar la ganancia mutua (o para evitar la pérdida mutua) o es "racional" actuar agresivamente en busca de la ganancia individual sin importar la ganancia o pérdida mutua? Éstas pueden ser algunas de las preguntas a las que se enfrentan los teóricos de los juegos (Brams, 2011). Algunos de los juegos más citados y más replicados dentro de la teoría son: juegos bancarios, la batalla de los medios, el dilema del prisionero, escape y evasión, entre otros. ...
Dentro del amplio espectro de la utilización de la Teoría de Juegos en la actividad económica, de entre sus muchas aplicaciones teóricas y empíricas concernientes a la toma de decisiones empresariales en forma de juegos, resaltamos aquella que tiene por objeto de estudio entender las relaciones entre las empresas en un contexto microeconómico. Específicamente, en el contexto del comercio electrónico, que actualmente ha alcanzado un nivel de inserción muy importante y diverso en todos los sectores. El presente artículo es el resultado de una investigación exploratoria en tres fases donde, por medio de la metodología de investigación de acción participativa, se logra una contrastación del modelo de Ciudad Circular, propuesto por Salop en 1979, en el contexto de los negocios electrónicos, específicamente en eBay.
... Its strategies cannot be analysed quantitatively, because they are essentially subjective, and constitute in their best expression an art form rather than a formal discipline (Sindermann, 2001, p. vii) The remaining parts of the book confirm this statement in making no further reference to game theory, but it should perhaps be stressed that Sindermann's comment about art and science is perhaps more a reflection of his own personal philosophy than a reflection of how game theory works. As illustrated by Brams (2011), there is nothing preventing dilemmas of conflict and corporation in art, religion, literature and the rest of the humanities from being analysed by means of game theory. Nevertheless, what makes Sindermann's writing theoretically important is not the detailed descriptions of games and strategies in academic career development, but it is the way he is opening up the domain for scientific analysis through the use of the game perspective. ...
One of the brutal realities of modern society is that life as a governmental scientist has become more difficult. In some cases, research careers spanning decades are suddenly terminated, and the only way to follow one's vocation is to look for work elsewhere, preferably in academia. However, academic life has also become more competitive, with a stronger focus on issues like citation indexes and impact factors. Intentionally or not, the emphasis on scoring mechanisms turns the environment more game-like. This paper hypothesises a game strategy for governmental researchers to enter academic life by focusing their scores on places like Google Scholar and ResearchGate and making sure the scores look acceptable. As means for testing the hypothesis, the author has done action research on his own situation by keeping track of online academic scores and applying for jobs, assuming that good scores would play a fundamental part in how the evaluation committees would be ranking of candidates. Contrary to what was expected, the applicants ranked highest in the various application processes were the applicants with the lowest scores. The lesson learned is that the rules of the game are not rigged in favour of governmental scientists.
... Perhaps sensing this, Steven J. Brams developed a more general dynamic modeling framework called the "Theory of Moves" (or TOM) and used it to offer several (plausible) explanations of the crisis (Brams, [35], pp. 48-62; [46], pp. 226-240). ...
This chapter surveys and evaluates previous attempts to use game theory to explain the strategic dynamic of the Cuban missile crisis of 1962, including, but not limited to, explanations developed in the style of Thomas Schelling, Nigel Howard, and Steven Brams. All of these explanations are judged to be either incomplete or deficient in some way. Schelling’s explanation is both empirically and theoretically inconsistent with the consensus interpretation of the crisis; Howard’s metagame theory is at odds with the contemporary understanding of rational strategic behavior; and Brams’s theory of moves explanation is inconsistent with the full sweep of the events that define the crisis. As game theory has evolved, so have the explanations fashioned by its practitioners. An additional purpose of this chapter is to trace these explanatory refinements, using the Cuban crisis as a mooring.
... Most recent studies are empirical or experimental, indicative of hostile action occurring in economic situations, based on either observational data or experimental data. 9 A few studies do present theory, including Rotemberg (2005Rotemberg ( , 2008Rotemberg ( , 2011); Brams (2011); Winter (2014Winter ( , 2016); Akerlof (2016); and Passarelli & Tabellini (2017) (cf. the reference to riots in Case 3). We compare and contrast our approach with these theories and with models of distributional preferences and reciprocity in Section 7. Our approach differs from the previous literature in that we do not start with data, but with notions from psychology which we incorporate into general games, and we are led to use assumptions which differ substantially from previous theoretical work. ...
Frustration, anger, and blame have important consequences for economic and social behavior, concerning for example monopoly pricing, contracting, bargaining, violence, and politics. Drawing on insights from psychology, we develop a formal approach to exploring how frustration and anger, via blame and aggression, shape interaction and outcomes in strategic settings.
... Główną zaletą teorii przejść jest umożliwienie graczom dokonywania zmian strategii, co często ma miejsce w toku realnych negocjacji. Właśnie dzięki tym właściwościom teoria przejść znajduje obecnie szerokie zastosowanie w naukach społecznych, a w szczególności w analizie decyzji politycznych i związanych z nimi procesów negocjacyjnych (Brams, 2011;Kiryluk-Dryjska, 2012, 2016Simon, 1996;Zeager i Bascom, 1996). ...
The recent increase of national interests in Europe makes the results of the future negotiations on the UE Multiannual Financial Framework (MFF) uncertain. The objective of the paper is to present the budget negotiations of two recent MFF (2007-2013 and 2014-2020) and to forecast its potential shape beyond 2020. Standard game theory and the theory of moves are used to model the negotiations on the budget between the European Commission and net payers of the UE budget. The results demonstrate that net payers can initially accept an increase of the budgets of both the Common Agricultural Policy (CAP) and Cohesion Policy. However, attempts to over increase the financing of the CAP in reference to Cohesion Policy can motivate them to freeze the budget at the current level.
... Could game theory elaborate the motivations and actions of myth characters, estimate equilibriums and simultaneously players achieve their goals? According to Brams (2011), emotions, like frustration and anger, are "compatible with acting rationally". Depending on the actions of others, a person will react by expressing an emotion. ...
Water was viewed as sacred by the very early civilisations. Ancient Greeks had rendered religious reverence and homage to many water deities. The Alpheus River and the Achelous River, worshiped as gods in ancient times, had a central part in Greek mythology and cultural heritage. The present article narrates some of the myths about these two rivers and interprets these stories on a game theory perspective. Through this narration, an alternative way of viewing game theory is presented, by highlighting two river myths and applying illustrations to the study of conflict resolution and the fundamental notion of game theory; strategy.
... data patterns (Rotemberg 2005Rotemberg , 2008Rotemberg , 2011 Akerlof 2013; Passarelli & Tabellini 2013). Our approach di¤ers in that we do not start with data, but with notions from psychology which we incorporate into general games, and we are led to use assumptions which di¤er substantially (Section 7 elaborates, in regards to Rotemberg's work). Brams (2011), in his book Game Theory and the Humanities, building on his earlier (1994) " theory of moves, " includes negative emotions like anger in the analysis of sequential 2 Psychologists often refer to this as " goal-blockage; " cf. p.3 of the (op.cit.) Handbook. 3 See Anderson & Simester (2010) and Rotemberg (2005) on pricing, Card & Dahl on ...
... data patterns (Rotemberg 2005Rotemberg , 2008Rotemberg , 2011 Akerlof 2013; Passarelli & Tabellini 2013). Our approach di¤ers in that we do not start with data, but with notions from psychology which we incorporate into general games, and we are led to use assumptions which di¤er substantially (Section 7 elaborates, in regards to Rotemberg's work). Brams (2011), in his book Game Theory and the Humanities, building on his earlier (1994) " theory of moves, " includes negative emotions like anger in the analysis of sequential 2 Psychologists often refer to this as " goal-blockage; " cf. p.3 of the (op.cit.) Handbook. 3 See Anderson & Simester (2010) and Rotemberg (2005) on pricing, Card & Dahl on ...
Frustration, anger, and aggression have important consequences for economic and social behavior, concerning for example monopoly pricing, contracting, bargaining, traffic safety, violence, and politics. Drawing on insights from psychology, we develop a formal approach to exploring how frustration and anger, via blame and aggression, shape interaction and outcomes in economic settings.
KEYWORDS: frustration, anger, blame, belief-dependent preferences, psychological games
JEL codes: C72, D03
... Perhaps sensing this, Steven J. Brams developed a more general dynamic modeling framework called the "Theory of Moves" (or TOM) and used it to offer several (plausible) explanations of the crisis (Brams, [35], pp. 48-62; [46], pp. 226-240). ...
This study surveys and evaluates previous attempts to use game theory to explain the strategic dynamic of the Cuban missile crisis, including, but not limited to, explanations developed in the style of Thomas Schelling, Nigel Howard and Steven Brams. All of the explanations were judged to be either incomplete or deficient in some way. Schelling’s explanation is both empirically and theoretically inconsistent with the consensus interpretation of the crisis; Howard’s with the contemporary understanding of rational strategic behavior; and Brams’ with the full sweep of the events that define the crisis. The broad outlines of a more general explanation that addresses all of the foundational questions associated with the crisis within the confines of a single, integrated, game-theoretic model with incomplete information are laid out.
... But economic exegesis of pre-modern texts can also lead to a meaningful engagement between economics and history. Brams (2011), for instance, has been using game theory for " strategic exegesis " of Biblical texts since early 1980s. But he has not systematically developed strategic exegesis as a tool to, say, distinguish among different strata of thought in texts or to detect interpolations contrary to the overall strategic structure of the text. ...
This paper examines the legal-economic dimension of collusive manipulation of prices from the perspective of the Kautiliya Arthasastra, an ancient Indian treatise on law and statecraft, which is among the oldest sources of information about cartels. It identifies cartels in the treatise, shows that cartels were treated more severely than individuals who manipulated prices, assesses the efficacy of penalties from the perspective of deterrence, and discusses the evolution of relevant laws. The economic analysis presented in the paper throws new light on the controversy surrounding the internal consistency of the Arthasastra. The paper also highlights the need to take note of the moral-legal environment within which pre-modern markets operated before studying them with the help of models developed for modern markets.
Game theory is the examination of strategic interactions between two or more individuals known as players who act based on their individual self-interest within a framework known as the game. Every player possesses a set of possible actions referred to as strategies, from which they make selections. In a two-person zero sum game, each of the two players has at least two strategies. In such a game problem where both players have no inferior strategies, we can determine the optimal mixed strategies of the game problem by converting it to a linear programming problem and solving it using the simplex method or variations of it. In this paper, consideration of some existing models along with our proposed model on the conversion of game problem to LPP was made. We compared the results across the various models considered. The results obtained revealed that our proposed model on the conversion of game problem to LPP produced a higher value of the game compared to the others considered; and thus, produced better performance.
The revolt of member states of the Delian League during the Peloponnesian War can be described as the result of an economic phenomenon called the Tragedy of the Commons. The tragedy itself was the complete dissolution of the league caused by an increase in the inequality between the coalition’s revenue maximisers and wage earners. This article is an investigation into Thomas Piketty’s theory of the capital–labour split and whether this theoretical framework is applicable to ancient studies, employing the Peloponnesian War as a case study. First, I identify the limits of the evidence and quantification, then delve into an analysis of the labour and capital market shocks during the war. Finally, I present the economic data in terms of the likely strategic behaviour of historical figures.KeywordsInequalityGame theoryPeloponnesian warCapitalLabour
Lacan’s contribution in applying and promoting game theory in the early 1950s is mostly ignored in the history of game theory. Yet his early analyses of logical reasoning made him one of the first social scientists to consider the importance of the hypothesis of common knowledge. By retracing Lacan's path in his discovery of game theory, we show how much he has been a precursor in applying it. While accommodating a narrative approach, he demonstrated rigour and originality. Soliciting mathematicians open to interdisciplinarity, he introduced as early as 1945 modes of reasoning which corresponds to reasoning based on common knowledge.
This paper investigates strategic thinking in the fictional world of Edgar Allan Poe’s ‘The Purloined Letter’. This short story has been rightly celebrated for its explicit analysis of strategic reasoning in which players attempt to outwit one another, which involves accounting for how they are all attempting to outwit one another. I differ from previous analyses by examining how the actors can often be wrong in their explicit analysis and consider the strategic actions they take rather than those they claim to take. Using elementary game theory, I describe the five games (and suggest a sixth) that make up the strategic heart of the story. These include games of signalling, screening, negotiation, revenge and a unique game called the ‘pincer’. I consider how literary sources like ‘The Purloined Letter’ can provide insights into the applicability of strategic analysis in the ‘real world’.
2 Dublin ehir Üniversitesi, Bilgisayar Bilimleri ve Mühendisli §i Bölümü, Dublin, rlanda murat.yilmaz@dcu.ie Özet. nsanlk tarihi kadar eski olan dijital olmayan oyunlar bireylerin hayatnda özellikle sosyal etkile³imi güçlendirmek adna önemli bir yer tutmaktadr. Ki³iler bu oyunlar yardmyla daha etkin bir biçimde et-kile³im kurmakta ve kendilerine verilen görevleri daha hzl bir biçimde kavrayabilmektedirler. Çevik yazlm geli³tirme süreçleri di §er mühendis-lik disiplinlerinde tanmlanan üretim süreçlerine göre daha fazla sosyal etkile³im içermektedir. Çevik dönü³üm konusunda bir yldan fazla sü-redir çal³malarn sürdüren Huawei Türkiye AR-GE Merkezi bu dönü-³ümü sa §lamak adna yürüttü §ü e §itim ve çal³taylarda dijital olmayan oyunlar aktif olarak kullanmaktadr. Bu oyunlar sayesinde yazlm ta-kmlarndaki çevik dönü³üm faaliyetlerinin önemli bir ivme kazand § gözlemlenmektedir. Huawei Türkiye AR-GE Merkezi bünyesindeki farkl departmanlarda çal³makta olan ki³ilerin i³ birli §i yeteneklerinin artrl-mas, bilgi payla³m kabiliyetlerinin iyile³tirilmesi ve dolaysyla yazlm takmlarnn sosyal etkile³im becerilerinin artrlmas hedeenmektedir. Bu deneyim bildirisinde belirlenen hedeer do §rultusunda Huawei Tür-kiye AR-GE Merkezi Kalite ve Operasyon Departman tarafndan yazlm uzmanlarna özel olarak tasarlanm³ (dijital olmayan) bir oyun tantla-cak ve endüstriyel ortamda edinilen deneyimler payla³lacaktr.
The chapter discusses the extensive form of a game when sequences of moves may matter. In general, the game tree is an adequate representation of the sequential structure of a game. Using the game tree representation, the implications of missing recall, solutions to sharing a cake, and a sequential form of the Battle of Sexes are analysed. Moves can also be ingredients of thought experiments and backward induction can stabilize strategy choices which do not constitute a Nash equilibrium. This is the message of the Theory of Moves discussed in the concluding section of the chapter.
On the Ides of March, 44 BC, in the Senate House of Pompey in Rome, Julius Caesar was assassinated by conspirators, the most famous of those being Brutus. Are there objectively valid reasons to confirm the possibility of a suicidal wish on the part of Caesar raised by Suetonius? By building and solving a two-player non-cooperative game that models the historical strategic aspects of the relationship between Caesar and Brutus, our article shows that there is no need to subscribe to the suicide thesis to explain Caesar’s death. We formulate our conclusion via the solution concept of mixed-strategy Nash equilibrium.
Epistemic Logic has recently acquired importance as a growing field with influence in Distributed Computing, Philosophy, Economics, and of late even in Social Science and Animal behavior. Here, on a relatively light note, we give examples of epistemic reasoning occurring in literature and used very effectively by writers like Shakespeare, Shaw, Arthur Conan Doyle, and O’Henry. For variety we also give an example of epistemic reasoning used by fireflies, although it is far fetched to suppose that fireflies use epistemic reasoning in any kind of a conscious way. Surely they are getting a lot of help from Darwin. It is this writer’s hope that epistemic reasoning as a formal discipline will some day acquire importance comparable to that of Statistics. Hopefully these examples make part of the case.
Benefit-cost analysis (BCA), a discipline best known for guiding policy choices, can also guide personal decisions. In either application, traditional BCA tallies benefits and costs using market values or willingness to pay. When future outcomes are uncertain, as they are across a wide array of situations, BCA must call as well on the methods of decision analysis. Thus, von Neumann–Morgenstern utilities, subjective probabilities, and sequential decision strategies are brought into play.
Traditional decision analysis distinguishes between risk and uncertainty. With risk, the probabilities of possible outcomes are known; with uncertainty, those outcomes are known, but not their probabilities. We introduce the concept of ignorance: a third, less tractable category. With ignorance, even the possible outcomes of decisions cannot be identified. Ignorance takes particular importance when high payoffs are associated with these unidentified outcomes, as is often the case. We identify such outcomes as
consequential amazing developments
(
CADs
). In the policy realm, the 2008 financial meltdown or the Arab Spring would represent a CAD. For an individual, a CAD might be that one’s secure tenured position had been inexplicably terminated, or that one’s trusted business partner had long been shuttling corporate secrets to a competitor. We distinguish between
unrecognized
and
recognized
ignorance. In the latter category, we identify specific cognitive biases that impair decision making.
Consequential ignorance cannot be studied in a controlled laboratory setting, since its payoffs are high, its time delays often long, and merely introducing the subject would tend to give away the game. Thus we develop a descriptive understanding of ignorance drawing on great works of literature, from antiquity to the present day, positing that skilled writers understand how humans make decisions and respond to unanticipated outcomes. Shakespearean examples would be Hamlet’s ignorance of his father’s killer, and Macbeth’s lack of awareness of the tragic ramifications following his actions to seize the Scottish crown.
Following this descriptive analysis, we turn to prescription. We draw on decision analysis to develop a formula for calculating consequential ignorance; it incorporates the expected magnitudes and assessed base rates for CADs. Finally, we propose a decision-analytic framework for measured decision making, given ignorance. Our recommended approach explicitly recognizes decision-making costs, and thus proposes when to use quick and intuitive as opposed to more deliberative approaches to decision, or the labels Kahneman has popularized as System 1 and System 2.
Studying ignorance through literature has important implications for BCA. Given the potential for ignorance, there are two key goals for prudent decision making. First, steps should be taken to recognize when ignorance might be present. Second, efforts should be made not to respond in a suboptimal fashion when ignorance is anticipated or when a CAD springs upon us. Great literature can provide the equivalent of widespread life experience, and can help a decision maker reach both goals. At its heart, this essay represents a benefit-cost approach to dealing with ignorance. Numerous connections to BCA are made throughout.
This paper intends to interpret Martin Crimp's theatrical territory whose characters consist of lonely and mysterious occupants trapped together in the British suburbs. Crimp has written innovative plays in which he explores a symbolic and absurdist landscape of cruel personal relationships and psychological disorders. He employs various theatrical possibilities where incidents are reflected and refracted through multiple perspectives. The diversity of form and styles he employs in his plays makes Crimp one of the most innovative and original playwrights of new writing in Britain. He has structured The Country (2000) in the form of the children's game of rock-paper-scissors in order to highlight the power games among adults; hence empowering his innovative style once more. The play's five scenes unfold the plot through a series of evasive stories that consist of shapeless dialogues, hesitations, interruptions and repetitions. The Country exemplifies domestic space in which modern marriages have become prisons. The contrasts in suburban life and the unknowability of the other are depicted through a game of question and negation, and tricks of language which will be evaluated by the vocabulary of Game Theory.
This article models the birth of a new religion from the ashes of apocalyptic prophecy. Christianity started around the imminent expectation of God’s Kingdom. Followers forsook worldly opportunities to prepare for the event. As the Kingdom’s arrival tarried, they found themselves “trapped” because those sacrifices—like transaction-specific investments—were wasted if they dropped out. This provided incentives to stay and transform the faith. Such effort, enhanced by reaction to the cognitive dissonance caused by prophecy failure, turned an apocalyptic movement into an established church. A survey of other apocalyptic groups confirms that dropout costs are critical to explaining outcomes.
Cahier de Recherche du Groupe HEC 915
The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy.
This paper provides a formal assessment of the effectiveness of the use of fear and anger on the decision to initiate a crisis. The formalization employs the finding that fearful decision-makers are risk-averting across frames and make pessimistic risk assessments, and that angry decision-makers are risk-seeking across frames and make optimistic risk assessments. The work presented here employs a sequential decision analysis based on the two-sided incomplete information version of the Traditional Deterrence Game. The analysis shows when the use of the emotions of fear and anger is effective, ineffective, and counterproductive in altering the decision to initiate or not initiate a crisis.
Fairness of resource allocation remains one of the basic criteria of public choice. Taking fairness into account in public resource allocation is critically important when decision-making creates conflicts of interest among potential stakeholders. The European Union’s structural policy budget allocation is especially prone to such conflicts, mainly due to its complexity and lack of commonly accepted indexes to measure its effects. The objective of this paper is to evaluate if a fair-division algorithm can be effectively implemented in practice to diminish conflicts and provide a fair allocation of resources. The practical application involves a problem of the EU’s rural-development policy budget in Poland. The algorithm provides a simple formal framework for budget allocation and utilizes structural program evaluation questionnaires of the key stakeholder groups. The provided example demonstrates that the implementation of a fair division algorithm is feasible in practice. The algorithm is flexible, robust to variation in pre-set budget constraints, and results in a sensible solution that achieves consensus among the stakeholder groups.
The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modeling of Napoleon's last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoleon made on 17 June 1815 to detach part of his army against the Prussians he had defeated, though not destroyed, on 16 June at Ligny. Military historians agree that this decision was crucial but disagree about whether it was rational. Hypothesizing a zero-sum game between Napoleon and Blücher, and computing its solution, we show that it could have been a cautious strategy on the former's part to divide his army, a conclusion which runs counter to the charges of misjudgement commonly heard since Clausewitz. On the other hand, the paper addresses methodological issues. We defend its case study against the objections of irrelevance that have been raised elsewhere against "analytic narratives", and conclude that military campaigns provide an opportunity for successful application of the formal theories of rational choice. Generalizing the argument, we finally investigate the conflict between narrative accounts – the historians' standard mode of expression – and mathematical modeling.
The author argues that the theory of moves, which has gained popularity in recent years as an alternative to game-theoretic analysis of strategic interaction, is fundamentally flawed. The theory's adherents argue that it makes theoretical progress by endogenizing the structure of games and introducing new ways of analyzing repeated interactions. The author analyzes the theory of moves from a game-theoretic perspective and challenges its theoretical claims. The author then reanalyzes several recent articles that have used the theory of moves, showing that its application to empirical cases is strained and that game theory can provide models that do a better job of fitting the stories the authors tell about them.
The standard model of an extensive form game rules out an important phenomenon in situations of strategic interaction: deception. Using examples from the world of ancient Greece and from modern-day Wall Street, we show how the model can be generalized to incorporate this phenomenon. Deception takes place when the action observed by a player is different from the action actually taken. The standard model does allow imperfect information (modeled by non-singleton information sets), but not deception: the actual action taken is never ruled out. Our extension of extensive form games relaxes the assumption that the information sets partition the set of nodes, so that the set of nodes considered possible after a certain action is taken might not include the actual node. We discuss the implications of this relaxation, and show that in certain games deception is inconsistent with common knowledge of rationality even along the backward induction path. `You are to hear now how the Greeks tricked us. From this one proof of their perfidy you may understand them all` (Aeneas).
I model an attempt by radical parties to topple a modus vivendi between a ruling government and a moderate opposition group. Cooperation between the regime and the moderate opposition is possible if each player prefers mutual cooperation to mutual confrontation. If each player also prefers mutual confrontation to cooperating while the other defects then radical parties have a chance at breaking up this accord. Radical parties can succeed in bringing the government and opposition to mutual confrontation if they can agree on power-sharing arrangements after regime change. This paper also resolves central questions surrounding the trial and crucifixion of Jesus Christ. I use an institutional approach to infer player preferences from historical and biblical sources and then use game theory to model the interactions between participants in these events. In so doing, I clarify aspects of the Gospel narrative that have puzzled readers for the past 2000 years.
Two or more players rank a set of indivisible items from best to worst. An efficient allocation of items is characterized, which may satisfy such properties as maximin, Borda maximin, and envy-avoidance. Whereas the two maximin properties are in conflict with envy-avoidance, there is always an efficient allocation that does not ensure envy, but it may not be maximin or Borda maximin. Computer calculations show that maximin allocations lead to envy quite often, but Borda maximin allocations do so only rarely. Implications of the theoretical findings for real-world fair-division problems are discussed.
The 1994 Cuban refugee crisis is modeled as a prisoners' dilemma game for Cuba and the United States. A threat power version of the theory of moves yields a cooperative outcome in the game, sustained by mutual threats that deter defections by each player, which is consistent with moves made by the players. After the countries implemented deterrent threats, they agreed that Cuba would patrol its borders and the United States would admit 20,000 Cubans each year. We show that the analysis, suitably adapted, also illuminates strategic choices in the 1965 and 1980 Cuban refugee crises.
This paper focuses on the fair division of a set of indivisible items between two people when both have the same linear preference
order on the items but may have different preferences over subsets of items. Surprisingly, divisions that are envy-free, Pareto-optimal,
and ensure that the less well-off person does as well as possible (i.e., are equitable) can often be achieved. Preferences
between subsets are assumed to satisfy axioms of qualitative probability without implying the existence of additive utilities,
which is treated as a special case. Algorithms that render fair division practicable are proposed, and their vulnerability
to strategic manipulation is investigated.
Two collective action problems plague successful revolution. On the one hand, would-be revolutionaries confront a “participation problem,” whereby no rationally self-interested individual has an incentive to participate in rebellion. On the other hand, individuals face a “first-mover problem” whereby no rationally self-interested individual has an incentive to lead rebellion. This paper argues that 18th-century merchant sailors who confronted these problems devised a novel institution to facilitate maritime revolution and assist them in overthrowing abusive captains. This institution was called a “Round Robin.” Round Robins helped overcome both the participation and first-mover problems by aligning the interests of individual sailors desiring mutiny and restructuring the payoffs of leading versus following maritime rebellion.
Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or ‘bads’ like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, ‘I cut, you choose’, the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide ‘envy-free’ allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.
Two or more players are required to divide up a set of indivisible items that they can rank from best to worst. They may, as well, be able to indicate preferences over subsets, or packages, of items. The main criteria used to assess the fairness of a division are efficiency (Pareto-optimality) and envy-freeness. Other criteria are also suggested, including a Rawlsian criterion that the worst-off player be made as well off as possible and a scoring procedure, based on the Borda count, that helps to render allocations as equal as possible. Eight paradoxes, all of which involve unexpected conflicts among the criteria, are described and classified into three categories, reflecting (1) incompatibilities between efficiency and envy-freeness, (2) the failure of a unique efficient and envy-free division to satisfy other criteria, and (3) the desirability, on occasion, of dividing up items unequally. While troublesome, the paradoxes also indicate opportunities for achieving fair division, which will depend on the fairness criteria one deems important and the trade-offs one considers acceptable.