We now move to the demonstration of the left-to-right direction of the equivalence result. Let us assume that there is a winning $$\mathbf {P}$$ P -strategy in the dialogical game for $$\varphi $$ φ.

Game theoretic explanations of the evolution of human behavior have become increasingly widespread. At their best, they allow us to abstract from misleading particulars in order to better recognize and appreciate broad patterns in the phenomena of human social life. We discuss this explanatory strategy, contrasting it with the particularist methodology of contemporary evolutionary psychology. We introduce some guidelines for the assessment of evolutionary game theoretic explanations of human behavior: such explanations should be representative, robust, and flexible. Distinguishing (...) these features sharply can help to clarify the import and accuracy of game theorists' claims about the robustness and stability of their explanatory schemes. Our central example is the work of Brian Skyrms, who offers a game theoretic account of the evolution of our sense of justice. Modeling the same Nash game as Skyrms, we show that, while Skyrms' account is robust with respect to certain kinds of variation, it fares less well in other respects. (shrink)

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. (shrink)

In this paper we propose and analyze a game-theoretic model of the epistemology of peer disagreement. In this model, the peers' rationality is evaluated in terms of their probability of ending the disagreement with a true belief. We find that different strategies---in particular, one based on the Steadfast View and one based on the Conciliatory View---are rational depending on the truth-sensitivity of the individuals involved in the disagreement. Interestingly, the Steadfast and the Conciliatory Views can even be rational (...) simultaneously in some circumstances. We tentatively provide some reasons to favor the Conciliatory View in such cases. We argue that the game-theoretic perspective is a fruitful one in this debate, and this fruitfulness has not been exhausted by the present paper. (shrink)

Evolutionary game theory and public goods games offer an important framework to understand cooperation during pandemics. From this perspective, the COVID-19 situation can be conceptualized as a dilemma where people who neglect safety precautions act as free riders, because they get to enjoy the benefits of decreased health risk from others’ compliance with policies despite not contributing to or even undermining public safety themselves. At the same time, humans appear to carry a suite of evolved psychological mechanisms aimed at (...) curbing free riding in order to ensure the continued provision of public goods, which can be leveraged to develop more effective measures to promote compliance with regulations. We also highlight factors beyond free riding that reduce compliance rates, such as the emergence of conspiratorial thinking, which seriously undermine the effectiveness of measures to suppress free riding. Together, the current paper outlines the social dynamics that occur in public goods dilemmas involving the spread of infectious disease, highlights the utility and limits of evolutionary game-theoretic approaches for COVID-19 management, and suggests novel directions based on emerging challenges to cooperation. (shrink)

Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different (...) verification games and prove the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values. (shrink)

In this paper I present a game-theoretical approach to the problem of induction. I investigate the comparative success of prediction methods by mathematical analysis and computer programming. Hume's problem lies in the fact that although the success of object-inductive prediction strategies is quite robust, they cannot be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. I show that there exist meta-inductive prediction strategies whose success is universally optimal, modulo short-run losses (...) which are upper-bounded. I then turn to the implications of my approach for the evolution of cognition. In the final section I suggest a revision of the paradigm of bounded rationality by introducing the distinction between local, general and universal prediction strategies. (shrink)

The structure of strategies for semantical games is studied by means of a new formalism developed for the purpose. Rigorous definitions of strategy, winning strategy, truth, and falsity are presented. Non-contradiction and bivalence are demonstrated for the truth-definition. The problem of the justification of deduction is examined from this perspective. The rules of a natural deduction system are justified: they are seen to guarantee existence of a winning strategy for the defender in the semantical game for the conclusion, (...) given winning strategies for that player in the games for the premises. Finally, it is shown how semantical games and the truth-definition can be given for languages lacking individual constants. *** DIRECT SUPPORT *** AZ902009 00003. (shrink)

The conceptual foundations, features, and scope of the notion of rationality are increasingly being affected by developments in embodied cognitive science. This article starts from the idea of embodied rationality, and aims to develop a frame in which a debate with the classical, possibly bounded, notion of rationality-as-consistency can take place. To this end, I develop a game theoretic description of a real time interaction setup in which participants' behaviors can be used to compare the enactive approach, which underlies (...) embodied rationality, with game theoretic approaches to human interaction. The Perceptual Crossing Paradigm is a minimal interaction interface where two participants each control an avatar on a shared virtual line, and are tasked with cooperatively finding each other among distractor objects. It is well known that the best performance on this task is obtained when both participants let their movements coordinate with the objects they encounter, which they do without any prior knowledge of efficient interaction strategies in the system. A game theoretic model of this paradigm shows that this task can be described as an Assurance game, which allows for comparing game theoretical approaches and the enactive approach on two main fronts. First, accounting for the ability of participants to interactively solve the Assurance game; second, accounting for the evolution of choice landscapes resulting from evolving normative realms in the task. Similarly to the series of paradoxes which have fueled debates in economics in the past century, this analysis aims to serve as an interpretation testbed which can fuel the current debate on rationality. (shrink)

This study presents an evolutionary game to model interactions among stakeholders with potential conflicts, including the operational enterprise of incineration plant, the local government, and the residents nearby. System dynamics is used to simulate the change of strategic actions corresponding to the three players, in order to seek for the evolutionary stability strategies. A numerical case is proposed to demonstrate the game theory application, in which the impacts of governmental incentive and punishment on the player’s actions are (...) investigated. The results indicated that administrative penalty is effective not only in motivating the enterprises to upgrade treatment facilities for ensuring environmental quality but also in helping the local government and residents to approach dominant strategies. Policy implications are given based on the results to lay out a foundation for the alleviation of the conflicts. (shrink)

I n order to appreciate properly what we are doing in this book it is necessary to realize that our approach to linguistic theorizing differs from the prevailing views. Our approach can be described by indicating what distinguishes it from the methodological ideas current in theoretical linguistics, which I consider seriously misguided. Linguists typically construe their task in these days as that of making exceptionless generalizations from particular examples. This explanatory strategy is wrong in several different ways. It presupposes (...) that we can have "intuitions" about particular examples, usually examples invented by the linguist himself or herself, reliable and sharp enough to serve as a basis of sharp generalizations. It also presupposes that we cannot have equally reliable direct access to general linguistic regularities. Both assumptions appear to me extremely dubious, and the first of them has in effect been challenged by linguists like Dwight Bol inger. There is also some evidence that the degree of unanimity among linguists is fairly low when it comes to less clear cases, even in connection with such relatively simple questions as grammaticality (acceptability). For this reason we have tried to rely more on quotations from contemporary fiction, newspapers and magazines than on linguists' and philosophers' ad hoc examples. I also find it strange that some of the same linguists as believe that we all possess innate ideas about general characteristics of humanly possible grammars assume that we can have access to them only via their particular consequences. (shrink)

This is an entry into the contemporary debate over contractarian theories of political obligation, with a particular focus on the "liberal" feminist critiques. It analyzes three prominent feminist critics of contractarianism, Susan Moller Okin, Carole Pateman and Nancy Hirschmann, selected because they each try to remain within the main premises and methodology of contractarian liberalism. The conclusion is that Okin's critique is too generous, Pateman's is radically incomplete, and Hirschmann's is too radical. ;It reviews the few remarks in the works (...) of Thomas Hobbes directed to issues of gender and families, and speculates that his originality might have been stimulated by a contemporary debate about gender in Seventeenth Century England. An appendix reviews the debate for its political contents. ;The analysis then turns to contractarianism in the contemporary mode of game theory. The contractarian exercise establishes the state of nature scenario, introduces male and female players, and characterizes the females as smaller, weaker, and vulnerable in childbirth and nursing. It then varies the players' moral psychologies along the egoism/altruism continuum. The exercise then applies the assumptions of contractarian game theory to analyze how a two-gender population would deal with the problems of violence and heterosexual sexual intercourse. The analysis concludes that the best strategy for females in contractarian terms is collective action and that institutions of the social contract state can be evaluated according to whether the institutions inhibit or advance that possibility. It then applies such an analysis to the theories of Robert Nozick and John Rawls and finally to three institutions of the liberal contractarian state: territorial representation, sexual individualism and individualism in employment. ;The work concludes that both theories and institutions are inadequate to provide for gender equality, because each is hostile to female collective action, the theories because of their insistence on the primacy of freedom over equality and the institutions because of their particular effects on the elements of cooperation. (shrink)

The Belief Game is a two-person, nonzero-sum game in which both players can do well [e.g., at (3, 4)] or badly [e.g., at (1,1)] simultaneously. The problem that occurs in the play of this game is that its rational outcome of (2, 3) is not only unappealing to both players, especially God, but also, paradoxically, there is an outcome, (3, 4), preferred by both players that is unattainable. Moreover, because God has a dominant strategy, His omniscience does (...) not remedy the situation, though - less plausibly - if man possessed this quality, and God were aware of it, (3, 4) would be attainable.How reasonable is it to use the device of a simple game to argue that nonrevelation by God, and nonbelief by man, are rational strategies? Like any model of a complex reality, the Belief Game abstracts a great deal from the problem that confronts the thoughtful agnostic asking the most profound of existential questions. Yet, to the degree that belief in God is seen as a personal question, conceptualized in terms of a possible relationship one might have with one's Creator, it seems appropriate to try to model this relationship as a game. The most difficult question to answer, I suppose, is, if God exists, what are His preferences in such a game?I have argued that He would first like to be believed, but at the same time not reveal Himself. These goals, in my opinion, are consistent with the role He assumes in many biblical stories, although this is not to say that the Bible offers the final word on philosophical and theological matters in the modern world. Nevertheless, it seems to me to be a logical place from which to start, and the clues it offers on God's preferences seem not contradicted by contemporary events.Of course, the Belief Game supposes that God not only has preferences but makes choices as well. To many people today - myself included - these choices are not apparent. But if He does make them, and in particular chooses not to reveal Himself, I think the Belief Game helps us to understand why nonrevelation is rational. Furthermore, it gives us insight into why, given this choice by God, our own reasons for believing in Him - in a game-theoretic context - may be rendered tenuous. (shrink)

As regimes move from illiberal to liberal, post-transition justice methodology has been employed to engender truth and reconciliation. These normative concepts have evolved into a policy of creating truth and reconciliation commissions that trade civil and criminal amnesty with applicants in ex change for information. This bargained-for exchange can be analyzed as an imperfect information game, where the commission attempts to maximize information while the applicant seeks amnesty for the lowest possible price. Using game-theoretic analysis, the authors model (...) the truth-amnesty game and predict the optimal commission strategy. The analysis leads to the recommendation that future transitional justice commissions employ various specific lexicographic ordering strategies to minimize dead weight loss in the transaction. (shrink)

As regimes move from illiberal to liberal, post-transition justice methodology has been employed to engender truth and reconciliation. These normative concepts have evolved into a policy of creating truth and reconciliation commissions that trade civil and criminal amnesty with applicants in exchange for information. This bargained-for exchange can be analyzed as an imperfect information game, where the commission attempts to maximize information while the applicant seeks amnesty for the lowest possible price. Using game-theoretic analysis, the authors model the (...) truth-amnesty game and predict the optimal commission strategy. The analysis leads to the recommendation that future transitional justice commissions employ various specific lexicographic ordering strategies to minimize dead weight loss in the transaction. (shrink)

Universal social institutions, such as marriage, commons management and property, have emerged independently in radically different cultures. This requires explanation. As Boyer and Petersen point out ‘in a purely localist framework would have to constitute massively improbable coincidences’ . According to Boyer and Petersen, those institutions emerged naturally out of genetically wired behavioural dispositions, such as marriage out of mating strategies and borders out of territorial behaviour. While I agree with Boyer and Petersen that ‘unnatural’ institutions cannot thrive, this (...) one-sided explanation of universal social institutions in terms of genetic human nature is unsatisfactory. Drawing on the literature on multi-level selection and gene-culture coevolution, I argue that universal social institutions are first and foremost the products of cultural selection. They occupy fitness peaks in the landscape of cultural possibilities, much in the same way that biological adaptations occupy fitness peaks in the landscape of biological possibilities. To show this, I use game-theory. By modelling the domains of social interaction in which marriage, commons management, and property emerged as Prisoner’s dilemma situations, it becomes clear how an institutional framework allows the group to move to an interactive equilibrium with a larger payoff. Institutions do so by incentivising all parties to adopt a cooperative strategy. They are culturally selected ways of optimising genetically constrained domains of human social interaction. (shrink)

To solve the current privacy leakage problems of cloud storage services, research on users’ payment intention for cloud storage services with privacy protection is extremely important for improving the sustainable development of cloud storage services. An evolutionary game model between cloud storage users and providers that considers privacy is constructed. Then, the model’s evolutionary stability strategies via solving the replication dynamic equations are analyzed. Finally, simulation experiments are carried out for verifying and demonstrating the influence of model parameters. (...) The results show that the evolutionary stable strategies are mainly affected by the privacy protection profit growth coefficient of both parties, input costs, free-riding gains, and other factors. If the profit growth coefficient is very small, users will not choose to pay and providers will not choose to actively protect user information. As the profit growth coefficient increases, both parties will promote the development of privacy protection with a higher probability. The results are beneficial for cloud storage providers to increase the number of paid users and thus to achieve the sustainable development of cloud storage service. (shrink)

The cultural red king effect occurs when discriminatory bargaining practices emerge because of a disparity in learning speed between members of a minority and a majority. This effect has been shown to occur in some Nash Demand Game models and has been proposed as a tool for shedding light on the origins of sexist and racist discrimination in academic collaborations. This paper argues that none of the three main strategies used in the literature to support the epistemic value (...) of these models—structural similarity, empirical confirmation, and how-possibly explanations—provides strong support for this modeling practice in its present form. (shrink)

Developing a good theoretical understanding of the role of trust in IR (such as in the events leading to the end of the Cold War) is still an open problem. Most game-theoretic studies of trust do not go beyond the limitations of an (ontologically) individualistic paradigm, thus assuming a pre-defined set of individual strategies. Yet, it is a fact that the predicament of collective trust is empirically resolved in many situations. This paper suggests a new game-theoretic (...) approach—Quantum Game Theory (QGT)—to understand and explain how the predicament of trust is resolved. In a quantum game of trust the actors play the game by simultaneously collectively reconstructing the strategic environment in such a way as to become mutually strategically entangled. Quantum strategic entanglement allows trust to emerge between the two actors without assuming a need for signaling, prior “contract” type of arrangement, or any form of third-party communication. The paper develops and solves such a model of quantum game of trust. (shrink)

In this paper I will discuss why (un) marked expressionstypically get an (un)marked interpretation: Horn''sdivision of pragmatic labor. It is argued that it is aconventional fact that we use language this way.This convention will be explained in terms ofthe equilibria of signalling games introduced byLewis (1969), but now in an evolutionary setting. Iwill also relate this signalling game analysis withParikh''s (1991, 2000, 2001) game-theoretical analysis ofsuccessful communication, which in turn is compared withBlutner''s: 2000) bi-directional optimality theory.

John Maynard Smith is the person most responsible for the use of game theory in evolutionary biology, having introduced and developed its major concepts, and later surveyed its uses. In this paper I look at some rhetorical work done by Maynard Smith and his co-author G.R. Price to make game theory a standard and common modelling tool for the evolutionary study of behavior. The original presentation of the ideas — in a 1973 Nature article — is frequently cited (...) but almost certainly rarely read. It took reformulation of the approach to create a usable model and an object of study. Perhaps paradoxically, the new model dealt with more abstract objects than did its predecessor, but because of that a better case could be made for its realism. The particular strategy of abstraction allowed game-theoretic modelling to gain a certain measure of autonomy from empirical problems, and thus to flourish. (shrink)

Here we argue that the concept of strategies, as it was introduced into biology by John Maynard Smith, is a prime illustration of the four dimensions of theoretical biology in the post-genomic era. These four dimensions are: data analysis and management, mathematical and computational model building and simulation, concept formation and analysis, and theory integration. We argue that all four dimensions of theoretical biology are crucial to future interactions between theoretical and empirical biologists as well as (...) with philosophers of biology. (shrink)

David Buss’s Sexual Strategies Theory is one of the major evolutionary psychological research programmes, but, as I try to show in this paper, its theoretical and empirical foundations cannot yet be seen to be fully compelling. This lack of cogency comes about due to Buss’s failure to attend to the interactive nature of his subject matter, which leads him to overlook two classic and well known issues of game theoretic and evolutionary biological analysis. Firstly, Buss pays insufficient (...) attention to the fact that, since mate choice is a cooperative decision, what is adaptive for the two sexes individually is irrelevant to the evolutionary explanation of our sexual strategies; instead, all that matters is what is adaptive given the choices made by the other sex. Secondly, Buss does not pay enough attention to the difference between polymorphic and monomorphic evolutionarily stable states in his attempt to empirically confirm his theory. Because of this, the data he presents and analyses are unable to show that natural selection is the most important element in the explanation of the origins of our sexual strategies. In this way, I try to make clear that, at least as things stand now, Buss has failed to provide compelling grounds for thinking that Sexual Strategies Theory can make a major contribution to human psychology. (shrink)

How do people survive under extreme conditions? Will selfish, non-cooperating free-rider types – the solo players – have the best chances of surviving? Or would cooperating, hard-working types – the team players – have higher chances? All morale put aside, it is interesting to know whether non-cooperation or cooperation pays off in a game characterized by scarcity and hard competition for survival. A study of people in such a Hobbesian state of nature can also teach us important lessons about (...) social dynamics in contemporary, prosperous societies. An interesting case of ‘The survival game’ can be found in Solzhenitsyn’s (1963 [1962]) self-biographical book, One Day in the Life of Ivan Denisovich, depicting life in a Soviet Gulag prison camp in Siberia January 1951. We use Solzhenitsyn’s work as evidence of the interplay between five player types among prisoners: Cooperative blind-riders (BRs), hard-riders (HRs) and tough-riders (TRs), i.e. the so-called ‘toilers’; non-cooperative easy-riders (ERs), looked upon by the toilers as ‘bastards’, ‘screws’ and ‘errand boys’; and finally Low-riders (LRs), comprising ‘goners’ and ‘jackals’. The main research question addresses the successfulness of the survival strategies of the five player types. Apart from a Multiple Player Approach (MPA) that may be seen as a further development of second-generation theory of collective action (Ostrom & Ahn, 2009), we apply Goffman’s (1959) dramaturgical theory on our case. Hence, we argue that impression management at two different ‘stages’ – the Brigade stage and the Camp stage – is crucial for survival for hard-riding as well as for easy-riding players, in particular strategic masking. Seeking to unite Goffman and game-theoretic MPA, our overall purpose is to make a theoretical contribution to “game-related sociology” (Swedberg, 2001). (shrink)

Causal reasoning and game-theoretic reasoning are fundamental topics in artificial intelligence, among many other disciplines: this paper is concerned with their intersection. Despite their importance, a formal framework that supports both these forms of reasoning has, until now, been lacking. We offer a solution in the form of (structural) causal games, which can be seen as extending Pearl's causal hierarchy to the game-theoretic domain, or as extending Koller and Milch's multi-agent influence diagrams to the causal domain. We then (...) consider three key questions: i) How can the (causal) dependencies in games - either between variables, or between strategies - be modelled in a uniform, principled manner? ii) How may causal queries be computed in causal games, and what assumptions does this require? iii) How do causal games compare to existing formalisms? To address question i), we introduce mechanised games, which encode dependencies between agents' decision rules and the distributions governing the game. In response to question ii), we present definitions of predictions, interventions, and counterfactuals, and discuss the assumptions required for each. Regarding question iii), we describe correspondences between causal games and other formalisms, and explain how causal games can be used to answer queries that other causal or game-theoretic models do not support. Finally, we highlight possible applications of causal games, aided by an extensive open-source Python library. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between [math] principles over [math]-models of [math]. They also introduced a version of this game that similarly captures provability over [math]. We generalize and extend this game-theoretic framework to other formal systems, and establish a certain compactness result that shows that if an (...) implication [math] between two principles holds, then there exists a winning strategy that achieves victory in a number of moves bounded by a number independent of the specific run of the game. This compactness result generalizes an old proof-theoretic fact noted by H. Wang (1981), and has applications to the reverse mathematics of combinatorial principles. We also demonstrate how this framework leads to a new kind of analysis of the logical strength of mathematical problems that refines both that of reverse mathematics and that of computability-theoretic notions such as Weihrauch reducibility, allowing for a kind of fine-structural comparison between [math] principles that has both computability-theoretic and proof-theoretic aspects, and can help us distinguish between these, for example by showing that a certain use of a principle in a proof is “purely proof-theoretic”, as opposed to relying on its computability-theoretic strength. We give examples of this analysis to a number of principles at the level of [math], uncovering new differences between their logical strengths. (shrink)

This paper provides a game-theoretic analysis of contrastive focus, extending insights from recent work on the role of noisy communication in prosodic accent placement to account for focus within sentences, sub-sentential phrases and words. The shared insight behind these models is that languages with prosodic focus marking assign prosodic prominence only within elements which constitute material critical for successful interpretation. We first take care to distinguish the information-structural notion of focus from an ontologically distinct notion of givenness marking, and (...) then outline the core properties of focus. We then introduce a signaling game between a speaker and hearer in which the goal is to transmit semantic content with the smallest signal possible. We apply the Iterated Best Response method of Franke to find equilibrium strategies in this game, where a unique equilibrium strategy in this case picks out the “critical information” of an utterance, which by hypothesis constitutes its focus. We show that iterating this game at different syntactic levels of a sentence makes correct predictions about the role of contrast in determining stress within words and phrases, and can be extended to account for association and second occurrence focus effects. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, (...) which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

The paper begins by providing a game-theoretic reconstruction of Gilbert’s (1989) philosophical critique of Lewis (1969) on the role of salience in selecting conventions. Gilbert’s insight is reformulated thus: Nash equilibrium is insufficiently powerful as a solution concept to rationalize conventions for unboundedly rational agents if conventions are solutions to the kinds of games Lewis supposes. Both refinements to NE and appeals to bounded rationality can plug this gap, but lack generality. As Binmore (this issue) argues, evolutive game (...) theory readily explains the origin of conventional behavior, but that is not Lewis’s project. Gilbert’s critique is generalized by reference to Bacharach’s (2006) work on team reasoning in games. The paper then argues that although Lewis’s account of the rationalization of conventions is shown by the reconstruction of Gilbert’s critique to be incomplete, Gilbert is wrong to conclude that classical (‘eductive’) game theory lacks the resources to explain conformity to conventions among people. A game-theoretic account of the dynamics of socialization, based on Ross’s (2005, 2006) idea of ‘game determination’, rationalizes choices of conventional strategies in overlapping generations contexts, provided agents are products of evolutionary selection and know that other players are also such products. (shrink)

In the presence of chance moves in a semantical game, the existence of pure optimal strategies does not guarantee the existence of winning ones. This fact provides a basis for constructing supervaluational semantical games with a chance move. Additional possibilities of using chance moves in game-theoretical semantics are also discussed.

We consider Effort Games, a game-theoretic model of cooperation in open environments, which is a variant of the principal-agent problem from economic theory. In our multiagent domain, a common project depends on various tasks; carrying out certain subsets of the tasks completes the project successfully, while carrying out other subsets does not. The probability of carrying out a task is higher when the agent in charge of it exerts effort, at a certain cost for that agent. A central authority, (...) called the principal, attempts to incentivize agents to exert effort, but can only reward agents based on the success of the entire project.We model this domain as a normal form game, where the payoffs for each strategy profile are defined based on the different probabilities of carrying out each task and on the boolean function that defines which task subsets complete the project, and which do not. We view this boolean function as a simple coalitional game, and call this game the underlying coalitional game. We suggest the Price of Myopia as a measure of the influence the model of rationality has on the minimal payments the principal has to make in order to motivate the agents in such a domain to exert effort.We consider the computational complexity of testing whether exerting effort is a dominant strategy for an agent, and of finding a reward strategy for this domain, using either a dominant strategy equilibrium or using iterated elimination of dominated strategies. We show these problems are generally #P-hard, and that they are at least as computationally hard as calculating the Banzhaf power index in the underlying coalitional game. We also show that in a certain restricted domain, where the underlying coalitional game is a weighted voting game with certain properties, it is possible to solve all of the above problems in polynomial time. We give bounds on PoM in weighted voting effort games, and provide simulation results regarding PoM in another restricted class of effort games, namely effort games played over Series-Parallel Graphs. (shrink)

Why games? How could anyone consider action games an experimental paradigm for Cognitive Science? In 1973, as one of three strategies he proposed for advancing Cognitive Science, Allen Newell exhorted us to “accept a single complex task and do all of it.” More specifically, he told us that rather than taking an “experimental psychology as usual approach,” we should “focus on a series of experimental and theoretical studies around a single complex task” so as to demonstrate that our (...) theories of human cognition were powerful enough to explain “a genuine slab of human behavior” with the studies fitting into a detailed theoretical picture. Action games represent the type of experimental paradigm that Newell was advocating and the current state of programming expertise and laboratory equipment, along with the emergence of Big Data and naturally occurring datasets, provide the technologies and data needed to realize his vision. Action games enable us to escape from our field's regrettable focus on novice performance to develop theories that account for the full range of expertise through a twin focus on expertise sampling and longitudinal studies of simple and complex tasks. (shrink)

SummaryTruth‐definitions play a crucial role in the foundations of logic and semantics. Tarsik‐type truth‐definitions are not possible to formulate in a usual first‐order language for itself, and they have been criticized because they do not account for what makes them definitions of truth. It has been suggested that truth should instead be characterized by reference to the «language‐games» of verification and falsification. The author's game‐theoretical semantics here explained for formal first‐order languages, can be thought of as a realization (...) of this idea. More technically speaking, GTS can also be thought of as a systematization of the well‐known aepsilon‐delta, definitions in the foundations of analysis. In GTS, truth is not defined by reference to winning a play of a game, but as the existence of a winning strategy in the game for the verifier. In a first‐order language, the game‐theoretical truth‐condition of a sentence S can accordingly be expressed by an explicit second‐order sentence asserting the existence of the Skolem function of S.The semantical games of GTS must be distinguished not only from the «games» of formal proof but also from the «games» in volved in our ordinary activities of verification and falsification. The latter have been modelled as games of inquiry by the author, and they are essentially epistemic games where the meaning of truth is taken for granted and where the aim of the game is to come to know certain truths. To assimilate them to the semantical games constitutive of truth is a form of Meno's paradox. (shrink)

This paper rebuts criticisms by Hintikka of the author's account of game-theoretic semantics for classical logic. At issue are (i) the role of the axiom of choice in proving the equivalence of the game-theoretic account with the standard truth-theoretic account; (ii) the alleged need for quantification over strategies when providing a game-theoretic semantics; and (iii) the role of Tarski's Convention T. As a result of the ideas marshalled in response to Hintikka, the author puts forward a (...) new conjecture concerning the relationship among truth, meaning and translation. (shrink)

This paper rebuts criticisms by Hintikka of the author's account of game-theoretic semantics for classical logic. At issue are (i) the role of the axiom of choice in proving the equivalence of the game-theoretic account with the standard truth-theoretic account; (ii) the alleged need for quantification over strategies when providing a game-theoretic semantics; and (iii) the role of Tarski's Convention T. As a result of the ideas marshalled in response to Hintikka, the author puts forward a (...) new conjecture concerning the relationship among truth, meaning and translation. (shrink)

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as (...) processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation. (shrink)

We describe a class of semantic extensive entailment game with algorithmic players, related to game-theoretic semantics, and generalized to classical first-order semantic entailment. Players have preferences for parsimonious spending of computational resources, and compute partial strategies, under qualitative uncertainty about future histories. We prove the existence of local preferences for moves, and strategic fixpoints, that allow to map eeg game-tree to the building rules and closure rules of Smullyan's semantic tableaux. We also exhibit a strategy profile (...) that solves the fixpoint selection problem, and can be mapped to systematic constructions of semantic trees, yielding a completeness result by translation. We conclude on possible generalizations of our games. (shrink)

Game experiments designed to test the effectiveness of reward and/or punishment incentives in promoting cooperative behavior among their participants are quite common. Results from two such recent experiments conducted in Beijing, based on the Prisoner’s Dilemma (PD) game and Public Goods Game respectively, are summarized here. The unexpected empirical outcomes for the repeated PD game, that cooperation actually decreased when the participants had the option of using a costly punishment strategy and that participants who used costly (...) punishment in some round of the repeated game often did so in the first round, are discussed in terms of differences in attitudes toward reputation in Chinese culture compared to other locations (mostly in Western society) where similar experiments have been conducted. The second experiment models an institution providing incentives to increase contribution levels (i.e., cooperation) to the public good. The results show that combined institutional reward and punishment is the most effective means to increase cooperation, followed by a scheme using only punishment. It is shown how these empirical results are related to the theoretical predictions that assume players play rationally by optimizing their personal payoff given their opponents’ actions in these multi-player games. (shrink)

How do people reason about their opponent in turn-taking games? Often, people do not make the decisions that game theory would prescribe. We present a logic that can play a key role in understanding how people make their decisions, by delineating all plausible reasoning strategies in a systematic manner. This in turn makes it possible to construct a corresponding set of computational models in a cognitive architecture. These models can be run and fitted to the participants’ data in (...) terms of decisions, response times, and answers to questions. We validate these claims on the basis of an earlier game-theoretic experiment about the turn-taking game “Marble Drop with Surprising Opponent”, in which the opponent often starts with a seemingly irrational move. We explore two ways of segregating the participants into reasonable “player types”. The first way is based on latent class analysis, which divides the players into three classes according to their first decisions in the game: Random players, Learners, and Expected players, who make decisions consistent with forward induction. The second way is based on participants’ answers to a question about their opponent, classified according to levels of theory of mind: zero-order, first-order and second-order. It turns out that increasing levels of decisions and theory of mind both correspond to increasing success as measured by monetary awards and increasing decision times. Next, we use the logical language to express different kinds of strategies that people apply when reasoning about their opponent and making decisions in turn-taking games, as well as the ‘reasoning types’ reflected in their behavior. Then, we translate the logical formulas into computational cognitive models in the PRIMs architecture. Finally, we run two of the resulting models, corresponding to the strategy of only being interested in one’s own payoff and to the myopic strategy, in which one can only look ahead to a limited number of nodes. It turns out that the participant data fit to the own-payoff strategy, not the myopic one. The article closes the circle from experiments via logic and cognitive modelling back to predictions about new experiments. (shrink)

When parties and interest groups interact, they can do so in several ways which could be on an informal level, lobbying for a party candidate, or group representatives approach party leaders in the parliament to lobby them on an issue. There is a plethora of studies on the extent to which major political parties and major interests have related in the past and continue to relate or interact at the organizational level. Researchers have investigated to what extent parties and groups (...) had formal organizational ties, cooperated in elections, or worked in concert on developing and implementing policies. Factors that for decades have determined the relationship between political parties and interest groups in liberal democracies are political system and subsystem development, political culture and political ideology, centralization of government and policymaking, nature of the party system, political party dependence on interest groups, encompassing characteristics of the interest group system, interest group development, ideology, and leadership. However, the pandemic has influenced to a great extend the relationship between interest groups and politics. While Covid-19 crisis has consolidated power within governments, leaving opposition parties in a bind, on the other hand it has galvanized interest groups and businesses to mobilize. The pandemic has opened up the lobbying playing field to many new players. The paper aims to investigate to what extend the pandemic has influenced the relationship between political parties, government and interest groups and what strategies have these last ones used to get heard in a time when social distancing has reduced the opportunities for face-to-face lobbying. (shrink)

Game theory has a prominent role in evolutionary biology, in particular in the ecological study of various phenomena ranging from conflict behaviour to altruism to signalling and beyond. The two central methodological tools in biological game theory are the concepts of Nash equilibrium and evolutionarily stable strategy. While both were inspired by a dynamic conception of evolution, these concepts are essentially static—they only show that a population is uninvadable, but not that a population is likely to evolve. In (...) this article, we argue that a static methodology can lead to misleading views about dynamic evolutionary processes. We advocate, instead, a more pluralistic methodology, which includes both static and dynamic game theoretic tools. Such an approach provides a more complete picture of the evolution of strategic behaviour. 1 Introduction2 The Equilibrium Methodology3 Common Interest Signalling3.1 Lewis’s signalling game3.2 Static analysis3.3 Dynamic analysis4 The Sir Philip Sidney Game4.1 Static analysis4.2 Other equilibria4.3 Dynamic analysis5 Related Literature6 Static and Dynamic Approaches. (shrink)

I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes (...) a contradictory set of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)

When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call (...) such games message exchange games, and we compare them to existing game theoretic frameworks used in linguistics—for example, signaling games—and show that message exchange games are needed to handle non-cooperative conversation. In this paper, we concentrate on conversational games where players’ interests are opposed. We provide a taxonomy of conversations based on their winning conditions, and we investigate some essential features of winning conditions like consistency and what we call rhetorical cooperativity. We show that these features make our games decomposition sensitive, a property we define formally in the paper. We show that this property has far-reaching implications for the existence of winning strategies and their complexity. There is a class of winning conditions for which message exchange games are equivalent to Banach- Mazur games, which have been extensively studied and enjoy nice topological results. But decomposition sensitive goals are much more the norm and much more interesting linguistically and philosophically. (shrink)

Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming.

Applications of game theory to moral philosophy are impededby foundational issues and troublesome examples. In the first part of this paper,questions are raised about the appropriate game-theoretical frameworks for applications to moralphilosophy and about the proper interpretations of the theoretical devices employed inthese frameworks. In the second part, five examples that should be of particular interest to thoseinterested in the connections between ethics and game theory are delineated and discussed. Thefirst example comprises games in which (...) there is an outcome unanimously preferred to the``solution'' of the game, appropriately defined. The second comprises games whose solution callsfor different players to employ different strategies. The third comprises games whosesolution calls for players to adopt mixed strategies. The fourth comprises games whose solutionrequires players to cycle among a variety of strategies. The fifth comprises games whose solutionrequires players to discriminate in morally inappropriate ways. (shrink)

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and (...) going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics. (shrink)

The game Gls(κ) is played on a complete Boolean algebra B, by two players. White and Black, in κ-many moves (where κ is an infinite cardinal). At the beginning White chooses a non-zero element p ∈ B. In the α-th move White chooses pα ∈ (0.p)p and Black responds choosing iα ∈ {0.1}. White wins the play iff $\bigwedge _{\beta \in \kappa}\bigvee _{\alpha \geq \beta }p_{\alpha}^{i\alpha}=0$ , where $p_{\alpha}^{0}=p_{\alpha}$ and $p_{\alpha}^{1}=p\ p_{\alpha}$ . The corresponding game theoretic properties of (...) c.B.a.'s are investigated. So. Black has a winning strategy (w.s) if κ ≥ π(B) or if B contains a κ -closed dense subset. On the other hand, if White has a w.s., then κ ∈ [h₂(B). π(B)). The existence of w.s. is characterized in a combinatorial way and in terms of forcing. In particular, if 2κ = κ ∈ Reg and forcing by B preserves the regularity of κ, then White has a w.s. iff the power 2κ is collapsed to κ in some extension. It is shown that, under the GCH, for each set S ⊆ Reg there is a c.B.a. B such that White (respectively. Black) has a w.s. for each infinite cardinal κ ∈ S (resp. κ ∉ S). Also it is shown consistent that for each κ ∈ Reg there is a c.B.a. on which the game Gls(κ) is undetermined. (shrink)

This textbook for advanced undergraduate and postgraduate students of Evolutionary Game Theory covers recent developments in the field, with an emphasis on economic contexts and applications. It begins with the basic ideas as they originated within the field of theoretical biology and then proceeds to the formulation of a theoretical framework that is suitable for the study of social and economic phenomena from an evolutionary perspective. Core topics include the Evolutionary Stable Strategy and Replicator Dynamics, deterministic dynamic (...) models, and stochastic perturbations. A set of short appendices presents some of the technical material referred to in the main text. Evolutionary theory is widely viewed as one of the most promising appraoches to understanding bounded rationality, learning, and change in complex social environments. New avenues of research are suggested by Vega-Redondo, and plentiful exmples illustrate the theory's potential applications. The recent boom experienced by this dscipline makes the book's systematic presentation of its essential contributions vital reading for newcomer to the field. (shrink)