Game Theory, Misc

Certain apparently simple problems of coming to an agreement are surprisingly difficult to analyze in terms of individually rational behavior with a given set of preferences and beliefs. Though initially the solution appears obvious, the reasoning that would be needed to reach the solution on the part of a pair of rational individuals seems baroque and doubtful. This is used to suggest that a more fruitful tack is to analyze the situation in terms of a kind of joint or shared (...) intentionality. If that can be invoked, what appears simple in practice will turn out to be simple in theory as well. (shrink)

Background: A fundamental tension exists between Rational Choice Theory (which predicts rapid optimization) and Sociological Theory (which predicts inertia and lag). Standard Evolutionary Game Theory models adoption as a linear function of utility, failing to account for ”Threshold Behavior” observed in social change. Method: We perform a formal synthesis of the standard Replicator Dynamic Equation and the Time-Dependent Agency model proposed by Da˘g (2026). By scaling the micro-level ontogenetic parameters to the macro-level, we derive a ”Sigmoidal Inertia Equation.” Results: We (...) demonstrate that cultural plasticity is not linear but logistic. The adoption of a new norm requires the utility gap (∆π) to exceed a specific ”Social Activation Energy.” Conclusion: This framework mathematically resolves four historical anomalies: Ogburn’s Cultural Lag, Granovetter’s Tipping Points, Pluralistic Ignorance, and Institutional Path Dependence. (shrink)

In this article I interpret resilience and evolution in view of the philosophy of Leibniz. First, I discuss resilience as a substance’s or a monad’s “quantity of essence” — its “degree of perfection” — which I express as the quality of the Whole with respect to the sum of the qualities of the Parts. Then I discuss evolution, which I interpret here as the autopoietic Principle that sets Itself in motion and creates all reality, including Itself. This Principle may be (...) considered as a sort of ante-litteram metaphysical Darwinian Selection. My interpretations provide a different formulation for questions such as “why natural evolution evolves?” and “why is this the best of all possible worlds?” In this article I also provide a geometrical interpretation of a key aspect behind the “divine mathematics” of the autopoietic Principle. (shrink)

In his 1938 book The Mysterious Mr Bull, the disgraceful Wyndham Lewis writes, "Nothing can be got in England by direct action. Some day things may change, but at present there is no exception to that rule. In politics, art, business, law, or whatever it may be, if you do not recognize that you are engaging in a game - and a game with very elaborate rules, to break one of which is tantamount to moral misdemeanour, involving social disgrace - (...) you can make no headway. Such an eminent politician as Mr. Churchill has discovered that to his cost. And he has committed the further sin - a mortal one in England - of making a disgusting exhibition of "brains." " (1938: 92) Wyndham Lewis sounds like just a straight-talking guy giving a frank description of English culture or a part of it (at least as it struck him). But if what he says is true and he managed to publish this book from which the quotation comes (or get published), should we not regard him as a player in an elaborate game, at least metaphorically? The moment you take him as speaking truly you should lose confidence in him as a speaker of truth! (I have put this in "Liar Paradox" as the closest category.). (shrink)

I consider cases in which risk or ignorance create barriers to our discovery of what we ought to do. I argue that neither expected utility theory, nor the maximin principle, nor a timid gambling temperament, is relevant to discovering what we ought to do in one-off or infrequently recurring types of decisions involving risk, or to decisions involving ignorance. I argue, contra Kolodny and MacFarlane, that the miners case does not require us to give up any classical logical principle in (...) order to avoid contradiction. I reject Graham’s claim that the appearance of contradiction depends upon a confusion between acting rightly and not being blameworthy. In the cases of risk and ignorance discussed, we cannot know what we ought to do; and any way of deciding what we shall do is objectively arbitrary even if it reflects our gambling temperament. Subjective probability and the subjective ought should be repudiated. (shrink)

This paper provides a survey of epistemic approaches to game theory, focusing on the roles of cognitive models and common knowledge in the analysis of game solutions. It reviews how players’ beliefs, higher-order beliefs, and assumptions about rationality are formally represented, and how these epistemic structures underpin standard solution concepts such as Nash equilibrium and its refinements. Particular attention is paid to Aumann’s notion of common knowledge and its significance for coordination, agreement, and equilibrium reasoning. By clarifying the relationships between (...) belief models, informational assumptions, and solution concepts, the paper aims to offer a systematic overview of the epistemic foundations of game-theoretic analysis. (shrink)

The paper is an addition to the intensionalist approach to decision theory, with emphasis on game theoretic modelling. Extensionality in games is an a priori requirement that players exhibit the same behavior in all algebraically equivalent games on pain of irrationality. Intensionalism denies that it is always irrational to play differently in differently represented but algebraically equivalent versions of a game. I offer a framework to integrate game non-extensionality with the more familiar idea of linguistic non-extensionality from philosophy of language, (...) followed by applications of it based on toy examples of well-known game models. I argue that the notion of what I call “Intensional Nash Equilibrium” is, in effect, very useful in understanding human decision-making. (shrink)

The at-issue/not-at-issue distinction is based on a diverse collection of contrasts, both pragmatic and semantic. Providing a unified explanation of these contrasts remains an important open problem. In this paper, I show how the pragmatic differences between at-issue and not-at-issue content can be explained as the product of interlocutors’ strategic reasoning in response to their semantic differences. This explanation is first offered informally and then developed more formally within a game-theoretic setting using a modified version of the rejection game discussed (...) in Sbardolini (2022) and Incurvati & Sbardolini (2024). (shrink)

This study investigates the factors contributing to perceived difficulty in video games, integrating user scores, cognitive requirements, novelty, and structural complexity. Using a dataset of 100 video games across multiple genres, we performed logistic regression analyses to identify the relative contributions of various gameplay and cognitive factors to player-perceived difficulty. Our findings indicate that task complexity and cognitive load are primary predictors of perceived difficulty, whereas narrative novelty and kinetic demands exert secondary but meaningful influences. This framework provides a quantitative (...) approach for evaluating and predicting game difficulty in both design and research contexts. (shrink)

Two Two-D Systems Equals One Zero-D System: Understanding Motionless Computing and The Motionless Computer called Mind (What it Has to Do with Sustainable Society Building).

This article introduces a strategic decision-game theoretic approach, the Pardoner’s Dilemma, and juxtaposes it with the Prisoner’s Dilemma. Game theory has emerged as a significant approach in the twentieth century for explaining strategic decision-making in numerous arenas, including economics, business, politics, ethics, international relations, biology, law, and war studies. ‘Game theory’ explains how and why players/actors/agents cooperate or conflict to procure their self-interests in a social world. Life is a game, and human, corporate, and artificial intelligent agents are players who (...) play different games to maximise utility or minimise disutility. The Prisoner’s Dilemma is a promising game-theoretic approach that explains strategic decision-making in zero-sum and non-zero-sum games. ‘Strategic decision-making’ means that the outcome does not depend upon the actions of a player but upon all players. There are numerous essential game strategies, including tossing, negotiation, bargaining, balloting, competition, chance, power, and arbitration. Although the Prisoner’s Dilemma is a good game-theoretic approach, it does not allow players to use the key game strategies. In contrast, Pardoner’s Dilemma is a game theoretic approach that not only explains zero-sum and non-zero-sum games but also allows the players to use different game strategies, such as negotiation, bargaining, tossing, chance, balloting, competition, arbitration, and power. The article develops and defends the Pardoner’s Dilemma in the game-theoretic approach as an alternative to the Prisoner’s Dilemma. The article claims that the Pardoner’s Dilemma is a more promising approach than the Prisoner’s Dilemma in the decision-game theoretic framework. By introducing the Pardoner’s Dilemma, the article enhances the scope of decision/game theory in social sciences. (shrink)

A critique of John Rawls' gamification of justice.

There is an important analogy between languages and games. Just as a scoresheet records features of the evolution of a game to determine the effect of a move in that game, a conversational score records features of the evolution of a conversation to determine the effect of the linguistic moves that speakers make. Chess is particularly interesting for the study of conversational dynamics because it has language-like notations, and so serves as a simplified study in how the effect of an (...) assertion depends on, as well as evolves, the scoreboard. In this paper, we offer a compositional semantics for chess notation and a simple formal picture for determining the full information conveyed by an entry. We will also discuss an alternative model resembling accounts of centered assertion. (shrink)

For every countable wellordering $\alpha $ greater than $\omega $, it is shown that clopen determinacy for games of length $\alpha $ with moves in $\mathbb {N}$ is equivalent to determinacy for a class of shorter games, but with more complicated payoff. In particular, it is shown that clopen determinacy for games of length $\omega ^2$ is equivalent to $\sigma $ -projective determinacy for games of length $\omega $ and that clopen determinacy for games of length $\omega ^3$ is equivalent (...) to determinacy for games of length $\omega ^2$ in the smallest $\sigma $ -algebra on $\mathbb {R}$ containing all open sets and closed under the real game quantifier. (shrink)

According to some accounts, an individual participates in joint intentional cooperative action by virtue of conceiving of him- or herself and other participants as if they were parts of a single agent or body that performs the action. I argue that this notional singularization move fails if they act as if they were parts of a single agent. It can succeed, however, if the participants act as if to bring about the goal of a properly functioning single body in action (...) of which they would be parts. This latter version of the move manages to capture the cooperative character of joint intentional cooperative action. It does this without requiring of participants that they act on higher-order interlocking intentions. (shrink)

In a number of works, James M. Buchanan set out a proposal for a ‘demogrant’— a form of universal basic income that applied the principles of generality and non discrimination to the tax and the transfer sides of the scheme and was to be implemented as a constitutional rule outside the realm of day-to-day politics. The demogrant has received surprisingly little scholarly attention, but this article locates it in Buchanan’s broader constitutional political economy project and shows it was a logical (...) application of his theoretical framework to the problem of inefficient and unfair welfare systems when reform to the basic institutions of majoritarian democracy was not forthcoming. The demogrant aims to end the problems of majority cycling and rent seeking that plague contemporary welfare states and therefore offers a model of welfare without rent seeking—a constitutional welfare state. We compare Buchanan’s demogrant model to other universal basic income and negative income tax models and consider the most important criticisms. We conclude that rescuing the demogrant model from relative obscurity would be a fruitful future task of applied constitutional political economy and public choice. (shrink)

This paper develops an argument against causal decision theory. I formulate a principle of preference, which I call the Guaranteed Principle. I argue that the preferences of rational agents satisfy the Guaranteed Principle, that the preferences of agents who embody causal decision theory do not, and hence that causal decision theory is false.

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for L, (...) that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (shrink)

History based models suggest a process-based approach to epistemic and temporal reasoning. In this work, we introduce preferences to history based models. Motivated by game theoretical observations, we discuss how preferences can dynamically be updated in history based models. Following, we consider arrow update logic and event calculus, and give history based models for these logics. This allows us to relate dynamic logics of history based models to a broader framework.

Much of the theoretical work on strategic voting makes strong assumptions about what voters know about the voting situation. A strategizing voter is typically assumed to know how other voters will vote and to know the rules of the voting method. A growing body of literature explores strategic voting when there is uncertainty about how others will vote. In this paper, we study strategic voting when there is uncertainty about the voting method. We introduce three notions of manipulability for a (...) set of voting methods: sure, safe, and expected manipulability. With the help of a computer program, we identify voting scenarios in which uncertainty about the voting method may reduce or even eliminate a voter's incentive to misrepresent her preferences. Thus, it may be in the interest of an election designer who wishes to reduce strategic voting to leave voters uncertain about which of several reasonable voting methods will be used to determine the winners of an election. (shrink)

We modify the payment rule of the standard divide the dollar (DD) game by introducing a second stage and thereby resolve the multiplicity problem and implement equal division of the dollar in equilibrium. In the standard DD game, if the sum of players’ demands is less than or equal to a dollar, each player receives what he demanded; if the sum of demands is greater than a dollar, all players receive zero. We modify this second part, which involves a harsh (...) punishment. In the modified game $(D\!D^{\prime })$, if the demands are incompatible, then players have one more chance. In particular, they play an ultimatum game to avoid the excess. In the two-player version of this game, there is a unique subgame perfect Nash equilibrium in which players demand (and receive) an equal share of the dollar. We also provide an $n$ -player extension of our mechanism. Finally, the mechanism we propose eliminates not only all pure strategy equilibria involving unequal divisions of the dollar, but also all equilibria where players mix over different demands in the first stage. (shrink)

This book contains an advanced debate on the nature of scalar implicatures, one of the most popular topics in philosophical linguistics over the past 20 years. Leading authorities in the study of the semantics–pragmatics interface have contributed chapters from a range of perspectives; they address the crucial components of scalar implicatures, including the exhaustivity operator, alternatives and contextual optionality. The book offers an up-to-date presentation of the phenomenon of scalar implicatures in a way that will help readers to orient themselves (...) within the vast literature on the topic. It will be of great interest to students and researchers of semantics, cognitive science, psychology and philosophy of language. (shrink)

Phenomena like meat sharing in hunter-gatherers, altruistic self-sacrifice in intergroup conflicts, and contribution to the production of public goods in laboratory experiments have led to the development of numerous theories trying to explain human prosocial preferences and behavior. Many of these focus on direct and indirect reciprocity, assortment, or (cultural) group selection. Here, I investigate analytically how genetic relatedness changes the incentive structure of that paradigmatic game which is conventionally used to model and experimentally investigate collective action problems: the public (...) goods game. Using data on contemporary hunter-gatherer societies I then estimate a threshold value determining when biological altruism turns into maximizing inclusive fitness in this game. I find that, on average, contributing no less than about 40% of individual fitness to public goods production still is an optimal strategy from an inclusive fitness perspective under plausible socio-ecological conditions. (shrink)

Recent work on the resource curse argues that the effect of resource wealth on development outcomes is a conditional one: resource dependent countries with low quality institutions are vulnerable to a resource curse, while resource dependent countries with high quality institutions are not. But extant models neglect the ways in which the inflow of resource revenue impacts the institutional environment itself. In this paper, I present a formal model to show that where domestic institutions do not limit state leaders' discretion (...) over policy prior to becoming fiscally reliant on resources, those leaders have little incentive in the wake of resource windfalls to establish institutional mechanisms that limit their discretion. Importantly, this shows that simple calls for domestic institutional reform are unlikely to be effective. Among other things, future prescriptions to mitigate the resource curse must focus on decreasing rulers' fiscal reliance on resources. (shrink)

This eighth book of the author on gambling math presents in accessible terms the cold mathematics behind the sparkling slot machines, either physical or virtual. It contains all the mathematical facts grounding the configuration, functionality, outcome, and profits of the slot games. Therefore, it is not a so-called how-to-win book, but a complete, rigorous mathematical guide for the slot player and also for game producers, being unique in this respect. As it is primarily addressed to the slot player, its goal (...) is to present practical applications of the mathematical models of slot games, in order to provide numerical results that a player can use as criteria for gaming decisions or just as information for any slot game and any predicted winning event. These results are focused on probability and expected value, these being the most important parameters for decisional criteria in slots. The book is packed with plenty of figures, tables, and formulas. The content is organized so that readers can skip the theoretical parts and go picking the practical results (numerical, in tables of values where possible, or ready-to-compute formulas) for the desired situation. The practical results are gathered in the last chapter, titled "Practical Applications and Numerical Results," the largest part of the book, for the most popular categories of slot machines, namely with 3, 5, 9, and 16 reels. Any other category of slot games is covered in the theoretical part of the book, where the general formulas apply not only to existing slot games, but also to possible future slot games of any design and configuration. The author does not just throw the slot mathematics to the audience and run away, but offers an ultimate practical contribution with the chapter "How to estimate the number of stops and the symbol distribution on a reel", a surprise for both players and producers, where one can see that mathematics provides players with some statistical methods as well as methods based on physical measurements for retrieving these missing data. Having these data along with the mathematical results of this book, anyone can generate the PAR sheet of any slot machine. In the last decade, mathematics has been taken more and more seriously into account in gaming, as being the essence that governs the games of chance and the only rigorous tool providing information on optimal play, where possible. For the popular game of slots, mathematics already fulfilled its duty by providing all the data that it can provide and that cannot be found on the display of the slot machines - it is all here in this book. (shrink)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the principles (...) that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

We evaluate the asymptotic performance of boundedly-rational strategies in multi-armed bandit problems, where performance is measured in terms of the tendency (in the limit) to play optimal actions in either (i) isolation or (ii) networks of other learners. We show that, for many strategies commonly employed in economics, psychology, and machine learning, performance in isolation and performance in networks are essentially unrelated. Our results suggest that the appropriateness of various, common boundedly-rational strategies depends crucially upon the social context (if any) (...) in which such strategies are to be employed. (shrink)

Recent years have witnessed an increased number of game-theoretic approaches to social norms, which apparently share some common vocabulary and methods. We describe three major approaches of this kind (due to Binmore, Bicchieri and Gintis), before comparing them systematically on five crucial themes: generality of the solution, preference transformation, punishment, epistemic conditions and type of explanation. This allows us to show that these theories are, by and large, less compatible than they seem. We then argue that those three theories struggle (...) to account for three phenomena pertaining to social norms (namely context-dependence, conflicting norms and self-evidence), with which any complete game-theoretic account should in principle be able to deal. (shrink)

The Prisoner’s Dilemma (PD) is widely used to model social interaction between unrelated individuals in the study of the evolution of cooperative behaviour in humans and other species. Many effective mechanisms and promotive scenarios have been studied which allow for small founding groups of cooperative individuals to prevail even when all social interaction is characterised as a PD. Here, a brief critical discussion of the role of the PD as the most prominent tool in cooperation research is presented, followed by (...) two new objections to such an exclusive focus on PD-based models of social interaction. It is highlighted that only 2 of the 726 combinatorially possible strategically unique ordinal 2x2 games have the detrimental characteristics of a PD and that the frequency of PD-type games in a space of games with random payoffs does not exceed about 3.5%. Although these purely mathematical considerations do not compellingly imply that the relevance of PDs is overestimated, it is proposed that, in the absence of convergent empirical information about the ancestral human social niche, this finding can be interpreted in favour of a so far rather neglected answer to the question of how the founding groups of human cooperation themselves came to cooperate: Behavioural and/or psychological mechanisms which evolved for other, possibly more frequent, social interaction situations might have been applied to PD-type dilemmas only later. Human cooperative behaviour might thus partly have begun as a cooptation. (shrink)

A survey of some game-theoretic accounts of the emergence and evolution of spontaneuous cooperation in social and public-good dilemmas.

Pascal’s Wager holds that one has pragmatic reason to believe in God, since that course of action has infinite expected utility. The mixed strategy objection holds that one could just as well follow a course of action that has infinite expected utility but is unlikely to end with one believing in God. Monton (2011. Mixed strategies can’t evade Pascal’s Wager. Analysis 71: 642–45.) has argued that mixed strategies can’t evade Pascal’s Wager, while Robertson (2012. Some mixed strategies can evade Pascal’s (...) Wager: a reply to Monton. Analysis 72: 295–98.) has argued that Monton is mistaken. We show that Monton is correct, highlight the crucial assumptions that he relies on, and shed some light on the role of mixed strategies in decision theory. (shrink)

We examine a special case of inquiry games and give an account of the informational import of asking questions. We focus on yes-or-no questions, which always carry information about the questioner's strategy, but never about the state of Nature, and show how strategic information reduces uncertainty through inferences about other players' goals and strategies. This uncertainty cannot always be captured by information structures of classical game theory. We conclude by discussing the connection with Gricean pragmatics and contextual constraints on interpretation.

We study ultimatum and dictator variants of the generosity game. In this game, the first mover chooses the amount of money to be distributed between the players within a given interval, knowing that her own share is fixed. Thus, the first mover is not confronted with the typical trade-off between her own and the other’s payoff. For each variant of the game, we study three treatments that vary the range of potential pie sizes so as to assess the influence of (...) these changes on the first movers’ generosity. We find that removing the trade-off inspires significant generosity, which is not always affected by the second mover’s veto power. Moreover, the manipulation of the choice set indicates that choices are influenced by the available alternatives. (shrink)

Groups of people perform acts. For example, a committee passes a resolution, a team wins a game, and an orchestra performs a symphony. These collective acts may be evaluated for rationality. Take a committee’s passing a resolution. This act may be evaluated not only for fairness but also for rationality. Did it take account of all available information? Is the resolution consistent with the committee’s past resolutions? Standards of collective rationality apply to collective acts, that is, acts that groups of (...) people perform. What makes a collective act evaluable for rationality? What methods of evaluation apply to collective acts? This paper addresses these two questions. Collective rationality is rationality’s extension from individuals to groups. The paper’s first few sections review key points about rationality. They identify the features of an individual’s act that make it evaluable for rationality and distinguish rationality’s methods of evaluating acts directly and indirectly controlled. This preliminary work yields general principles of rationality for all agents, both individuals and groups. Applying the general principles to groups answers the paper’s two main questions about collective rationality. (shrink)

The paper focuses on Anthony de Jasay's "anarcho-liberalism" as based oon his game-theoretic approach to the problem of public goods provision.

Contents. Introduction. 1. Preliminaries. 2. Normal Form Games. 3. Extensive Games. 4. Applications of Game Theory. 5. The Methodology of Game Theory. Conclusion. Appendix. Bibliography. Index. Does game theory—the mathematical theory of strategic interaction—provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory—the first monograph on the philosophy of game theory—is an attempt to combine insights from epistemic logic and the philosophy of science to (...) investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. I prove new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and explore in detail the logical form of game theory as it is used in explanatory and normative contexts. I argue that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, I argue, has been rather successful in achieving this aim. "The 'epistemic' approach to game theory has emerged over the past twenty-five years. What is this approach? How does it differ from the conventional equilibrium-based approach to game theory? What have been its strengths and weaknesses to date? To find out, read this comprehensive and excellently written account". Adam Brandenburger, J. P. Valles Professor of Business Economics and Strategy, Stern School of Business, New York University "Reading Boudewijn de Bruin's book should be rewarding both for game theorists interested in the conceptual foundations of their discipline and for philosophers who want to learn more about formal analysis of strategic interaction. It provides an in-depth logical study of the currently dominant epistemic approaches to non-cooperative games, with an eye both to the attractions and to the serious challenges facing the Epistemic Programme". Wlodek Rabinowicz, Professor of Practical Philosophy, Department of Philosophy, Lund University. (shrink)

Jeffrey (1983) proposed a generalization of conditioning as a means of updating probability distributions when new evidence drives no event to certainty. His rule requires the stability of certain conditional probabilities through time. We tested this assumption (“invariance”) from the psychological point of view. In Experiment 1 participants offered probability estimates for events in Jeffrey’s candlelight example. Two further scenarios were investigated in Experiment 2, one in which invariance seems justified, the other in which it does not. Results were in (...) rough conformity to Jeffrey (1983)’s principle. (shrink)

Decision theory is concerned with how agents should act when the consequences of their actions are uncertain. The central principle of contemporary decision theory is that the rational choice is the choice that maximizes subjective expected utility. This entry explains what this means, and discusses the philosophical motivations and consequences of the theory. The entry will consider some of the main problems and paradoxes that decision theory faces, and some of responses that can be given. Finally the entry will briefly (...) consider how decision theory applies to choices involving more than one agent. (shrink)

I. Levi has advocated a decision-theoretic account of belief revision. We argue that the game-theoretic framework of Interrogative Inquiry Games, proposed by J. Hintikka, can extend and clarify this account. We show that some strategic use of the game rules generate Expansions, Contractions and Revisions, and we give representation results. We then extend the framework to represent explicitly sources of answers, and apply it to discuss the Recovery Postulate. We conclude with some remarks about the potential extensions of interrogative games, (...) with respect to some issues in the theory of belief change. (shrink)

Hintikka and Sandu's Independence-friendly logic (Hintikka, 1996; Hintikka and Sandu, 1997) has traditionally been associated with extensive games of imperfect information. In this paper we set up a strategic framework for the evaluation of IF logic à la Hintikka and Sandu. We show that the traditional semantic interpretation of IF logic can be characterized in terms of Nash equilibria. We note that moving to the strategic framework we get rid of IF semantic games that violate the principle of perfect recall. (...) We explore the strategic framework by replacing the notion of Nash equilibrium by other solution concepts, that are inspired by weakly dominant strategies and iterated removal thereof, charting the expressive power of IF logic under the resulting semantics. (shrink)

This volume is a collects papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT), held at the University of Liverpool in July 2006. LOFT is a key venue for presenting research at the intersection of logic, economics, and computer science, and this collection gives a lively and wide-ranging view of an exciting and rapidly growing area.

This is the introductory essay to the Italian translation of Anthony de Jasay's "Choice, contract, and consent. A restatement of liberalism".

The Ultimatum Game is one of the most successful experimental designs in the history of the social sciences. In this article I try to explain this success—what makes it a “paradigmatic experiment”—stressing in particular its versatility. Despite the intentions of its inventors, the Ultimatum Game was never a good design to test economic theory, and it is now mostly used as a heuristic tool for the observation of nonstandard preferences or as a “social thermometer” for the observation of culture‐specific norms. (...) †To contact the author, please write to: Department of Sociology and Philosophy, University of Exeter, Amory Building, Exeter EX4 4DT, UK; e‐mail: [email protected]. (shrink)

The ultimatum game is a simple bargaining situation where the behavior of people frequently contradicts the optimal strategy according to classical game theory. Thus, according to many scholars, the commonly observed behavior should be considered irrational. We argue that this putative irrationality stems from a wrong conception of metanormativity (the study of norms about the establishment of norms). After discussing different metanormative conceptions, we defend a Quinean, naturalistic approach to the evaluation of norms. After reviewing empirical literature on the ultimatum (...) game, we argue that the common behavior in the ultimatum game is rational and justified. We therefore suggest that the norms of economic rationality should be amended. (shrink)

In this article we explore an argumentative pattern that provides a normative justification for expected utility functions grounded on empirical evidence, showing how it worked in three different episodes of their development. The argument claims that we should prudentially maximize our expected utility since this is the criterion effectively applied by those who are considered wisest in making risky choices (be it gamblers or businessmen). Yet, to justify the adoption of this rule, it should be proven that this is empirically (...) true: i.e. that a given function allows us to predict the choices of that particular class of agents. We show how expected utility functions were introduced and contested in accordance with this pattern in the 18th century and how it recurred in the 1950s when Allais made his case against the neo-Bernoullians. (shrink)

Kinship and reciprocity are two main predictors of altruism. The ultimatum game has been used to study altruism in many small-scale societies. We used the ultimatum game to examine effects of individuals’ family and kin relations on altruistic behavior in a kin-based horticultural community in rural Dominica. Results show sex-specific effects of kin on ultimatum game play. Average coefficient of relatedness to the village was negatively associated with women’s ultimatum game proposals and had little effect on men’s proposals. Number of (...) brothers in the village was positively associated with men’s ultimatum game proposals and negatively associated with women’s proposals. Similarly, presence of father in the village was associated with higher proposals by men and lower proposals by women. We interpret the effect of brothers on men’s proposals as a consequence of local competition among brothers. We speculate that daughter-biased parental care in this community creates a sense of entitlement among women with brothers, which may explain the inverse relation between number of brothers and women’s ultimatum game proposals. The pattern of results may be consistent with how matrifocality affects cultural models of fairness differently along gender and family lines. (shrink)

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in terms of those games. The (...) measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation . New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling . Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19 , 95–125). (shrink)