I consider games with ambiguous payoffs played by non-Expected Utility decision makers. Three equilibrium solutions are studied. Nash equilibrium in which equilibrium mixed strategies must be best responses, Crawford equilibrium in beliefs and pure equilibrium in beliefs in which equilibrium strategies are mixtures of best responses, with the latter restricting best responses to pure actions. I study the interactions between ambiguity preferences on one side and equilibrium properties on the other. I show how the equilibrium concepts differ, computing necessary (...) and sufficient conditions for existence and equivalence. I also show how these solution concepts fare against two fundamental principles of Nash equilibrium in standard games: the principle of indifference and the reduction principle. Given both are central to the computation of Nash equilibrium in games with Expected Utility players, their failure indicates how relaxing the Expected Utility hypothesis may disrupt standard game theoretic results such as the characterization of equilibria in two-player games. (shrink)

In Book 1 of Plato’s Republic, Thrasymachus contends two major claims: (1) justice is the advantage of the stronger, and (2) justice is the good of the other, while injustice is to one’s own profit and advantage. In the beginning of Book II, Glaucon self-proclaims that he will be representing Thrasymachus’ claims in a better way, and provides a story of how justice has originated from a state of nature situation. However, Glaucon’s story of the origin of justice has an (...) implication that justice is the advantage of the weak rather than the stronger. This is inconsistent with Thrasymachus’ first claim which states that justice is the advantage of the stronger. This is a problem for Glaucon since Glaucon is supposed to be representing Thrasymachus’ original claims in a better way. In this paper, I provide two solutions to this puzzle with the help of elementary game theory. (shrink)

This paper includes a survey of decision theories directed toward exploring the adequacy of alternative approaches for application to game theoretic reasoning, a review of the classic results of von Neumann and Morgenstern and Nash about equilibrium solutions, an account of a recent challenge to the idea that solutions should be equilibria, and, finally, an explicit reconstruction and defense (using the resources of causal decision theory) of the classic indirect argument for equilibrium solutions.

I sketch the basic problem of vagueness - the sorites paradox and propose a new solution. I try to show that the paradoxical result of the sorites arguments arises from combining different language games or representation systems without sufficient care. I propose two solutions, two types of regimentating the sorites. They do not allow an inheritance of the vague property F in the whole sequence of objects. The first introduces some quantitatively determined predicates (quantitative regimentation) and the second (...) (relational regimentation) replaces the equivalence relation between successive objects with a suitable weaker asymmetrical relation ‘is at least as much F as’ (or ‘is at most as much F as’). (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on (...) variable and fixed player set. Specifications of several properties characterize specific solutions in this class. (shrink)

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference logic (cf. Hansson [10]) studies (...) formal systems that can express and analyze notions of preference between various sorts of entities: worlds, actions, or propositions. The art is of course to design a language that combines perspicuity and low complexity with reasonable expressive power. In this paper, we take a particularly simple approach. As preferences are binary relations between worlds, they naturally support standard unary modalities. In particular, our key modality ♦ϕ will just say that is ϕ true in some world which is at least as good as the current one. Of course, this notion can also be indexed to separate agents. The essence of this language is already in [4], but our semantics is more general, and so are our applications and later language extensions. Our modal language can express a variety of preference notions between propositions. Moreover, as already suggested in [9], it can “deconstruct” standard conditionals, providing an embedding of conditional logic into more standard modal logics. Next, we take the language to the analysis of games, where some sort of preference logic is evidently needed ([23] has a binary modal analysis different from ours). We show how a qualitative unary preference modality suffices for defining Nash Equilibrium in strategic games, and also the Backward Induction solution for finite extensive games. Finally, from a technical perspective, our treatment adds a new twist. Each application considered in this paper suggests the need for some additional access to worlds before the preference modality can unfold its true power.. (shrink)

ABSTRACTBernard Suits and other formalists endorse both the logical incompatibility thesis and the view that rule-breakings resulting in penalties can be a legitimate part of a game. This is what Fred D’Agostino calls ‘the problem of penalties’. In this paper, I reject both Suits’ and D’Agostino’s responses to the problem and argue instead that the solution is to abandon Suits’ view that the constitutive rules of all games are alike. Whereas the logical incompatibility thesis applies to games (...) in which players’ actions are perfectly controlled, it does not apply to sports. This insight not only justifies the rejection of formalism as a theory about the nature of sport but it also helps explain the greater normative complexity of sports, which in turn leads to the idea that in sports ‘cheating’ should be interpreted as a genus. (shrink)

This paper analyses the principles of stable cooperation for stochastic games. Starting from the non-cooperative version of a discounted, non zero-sum stochastic game, we build its cooperative form and find the cooperative solution. We then analyse the conditions under which this solution is stable. Principles of stability include subgame consistency, strategic stability and irrational behaviour proof of the cooperative solution. We finally discuss the existence of a stable cooperative solution, and consider a type of stochastic (...) games for which the cooperative solution is found and the principles of stable cooperation are checked. (shrink)

Although certain recent developments in mendacious political manipulation of public discourse are horrifying to the academic mind, I argue that we should not panic. Charles Peirce’s pragmatist epistemology with its teleological arc, long horizon, and rare balance between robust realism and contrite fallibilism offers guidance to weather the storm, and perhaps even see it as inevitable in our intellectual development. This paper explores Peirce’s classic “four methods of fixing belief”, which takes us on an entertaining and still very pertinent tour (...) through tenacity, authority and a priori speculation to the method of science – the only method which is both public and self-correcting. Although in the West we (mostly) proudly self-conceive as living in a ‘scientific age’, I argue that this is premature. Precisely insofar as we treat the misbehavior of governments as a harbinger of doom, we remain trapped in authoritarian modes of thinking which Peirce identified with medievalism, although modernity is increasingly quickening around us in worldwide information-sharing practices that are shaped entirely by mutual help. With this framework in mind, many tactics of recent media are most helpfully seen as belonging not to a post-truth, but a pre-truth stage of human intellectual development. Advice on this is sought from Plato, who of course also faced a world that was ‘pre-academic’. (shrink)

In this paper, we describe technological advances for supporting persons with aphasia in philosophical dialogues about personally relevant and contestable questions. A computer game-based application for iPads is developed and researched through Living Lab inspired workshops in order to promote the target group’s communicative participation during group argumentation. We outline some central parts of the background theory of the application and some of its main features, which are related to needs of the target group. Methodological issues connected to the design (...) and use of Living Labs with persons with aphasia are discussed. We describe a few problems with researching development of communicative participation during group argumentation using an app assisted intervention for the target group and suggest some possible solutions. (shrink)

In this paper, we study solution concepts for cooperative games with stochastic payoffs. we define four kinds of solution concepts, namely the most coalitional (marginal) stable solution and the fairest coalitional (marginal) solution, by minimizing the total variance of excesses of coalitions (individual players). All these four concepts are optimal solutions of corresponding optimal problem under the least square criterion. It turns out that the fairest coalitional (marginal) solution belongs to the set of the (...) most coalitional (marginal) stable solutions. Inspired by the definition of nucleolus, we propose various extended nucleolus based on lexicographic criterion. Furthermore, axiomatizations of the proposed solutions are exhibited through the linkage between the stochastic and deterministic models. (shrink)

Bernard Suits and other formalists endorse both the logical incompatibility thesis and the view that rule-breakings resulting in penalties can be a legitimate part of a game. This is what Fred D’Ag...

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on (...) variable and fixed player set. Specifications of several properties characterize specific solutions in this class. (shrink)

We propose a new notion of coalitional equilibria, the strong $$\beta$$ -hybrid solution, which is a refinement of the hybrid solution introduced by Zhao. Zhao’s solution is well suited to study situations where people cooperate within coalitions but where coalitions compete with one another. This paper’s solution, as opposed to the hybrid solution, assigns to each coalition a strategy profile that is strongly Pareto optimal. Moreover, like the $$\beta$$ -core, deviations by subcoalitions of any existing (...) coalition are deterred by the threat of a unique counter-strategy available to the non-deviating players. Zhao proved the existence of existence of strong $$\beta$$ -hybrid solution for transferable utility games with compact and convex strategy spaces and concave continuous payoff functions. Here, we extend his result to non-transferable utility games. (shrink)

A body of work proposes that social-norm change can be explained in terms of game theory. These game theoretic models, however, don't fully account for how and why utterances are used to change social norms. This paper describes the problem and some of the solution elements. There are three existing, relevant, game-based models. The first is a game theoretic model of social norm change (Bicchieri, 2005, 2016). This accounts for how individuals make decisions to adhere to or violate norms, (...) based on empirical expectations of how others will behave. The second is the idea of a conversational game (Lewis, 1979) and its extensions. This posits that speech acts are accommodated in a conversation to make what is said correct play. This feature can explain how some speech acts, such as slurring utterances, change the dynamics of a conversation. The third is a theory of pragmatic inference, known as Rational Speech Act theory (Goodman and Frank, 2016). This is a computational theory of pragmatics, of how listeners interpret utterances and how speakers construct utterances that can be understood. This paper proposes, without setting out the full formal model, that elements of these three theories need to be incorporated together into a game theoretic model of how utterances change long-term social norms. (shrink)

This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings (...) of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players. (shrink)

Games, which philosophers commonly invoke as models for diverse phenomena, are plausibly understood in terms of rules and goals, but this gives rise to two puzzles. The first concerns the identity of a single game over time. Intuitively one and the same game can undergo a change in rules, as when the rules of chess were modified so that a pawn could be moved two squares forward on its first move. Yet if games are individuated in terms of (...) their constitutive rules and goals, this is incoherent—new rules mean a new game. The second concerns the individuation of games at a point in time. Intuitively, there can be different versions of a single game, where the versions differ in the details of their rules. I offer a solution to this problem that draws on an analogy with individuating languages. The resulting theory should illuminate the metaphysics of games more generally. (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 its classical conception, game theory aspires to be a determinate decision theory for games, understood as elements of a structurally specified domain. Its aim is to determine for each game in the domain a complete solution to each player's decision problem, a solution valid for all real-world instantiations, regardless of context. "Permissiveness" would constrain the theory to designate as admissible for a player any conjecture consistent with the function's designation of admissible strategies for the other players. (...) Given permissiveness and other appropriate constraints, solution sets must contain only Nash equilibria and at least one pure-strategy equilibrium, and there is no solution to games in which no symmetry invariant set of pure-strategy equilibria forms a Cartesian product. These results imply that the classical program is unrealizable. Moreover, the program is implicitly committed to permissiveness, through its common-knowledge assumptions and its commitment to equilibrium. The resulting incoherence deeply undermines the classical conception in a way that consolidates a long series of contextualist criticisms. (shrink)

Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the game tree representation (...) and solution technique with other techniques for decision analysis such as decision trees, influence diagrams, and valuation networks. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general (...) the game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

Game theoretic pragmatics is a small but growing part of formal pragmatics, the linguistic subfield studying language use. The general logic of a game theoretic explanation of a pragmatic phenomenon is this: the conversational context is modelled as a game between speaker and hearer; an adequate solution concept then selects the to‐be‐explained behavior in the game model. For such an explanation to be convincing, both components, game model and solution concept, should be formulated and scrutinized as explicitly as (...) possible. The article demonstrates this by a concise overview of both evolutionary and non‐evolutionary approaches to game theoretic pragmatics, arguing for the use of agent‐based micro‐dynamics within evolutionary, and for the use of epistemic game theory within non‐evolutionary approaches. (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)

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)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

We propose a solution concept for games that are played among players with present-biased preferences that are possibly naive about their own, or about their opponent’s future time inconsistency. Our perception-perfect outcome essentially requires each player to take an action consistent with the subgame perfect equilibrium, given her perceptions concerning future types, and under the assumption that other present and future players have the same perceptions. Applications include a common pool problem and Rubinstein bargaining. When players are naive (...) about their own time inconsistency and sophisticated about their opponent’s, the common pool problem is exacerbated, and Rubinstein bargaining breaks down completely. (shrink)

We present and defend a view labeled “practiceism” which provides a solution to the incompatibility problems. The classic incompatibility problem is inconsistency of:1. Someone who intentionally violates the rules of a game is not playing the game.2. In many cases, players intentionally violate the rules as part of playing the game.The problem has a normative counterpart:1’. In normal cases, it is wrong for a player to intentionally violate the rules of the game.2’. In many normal cases, it is not (...) wrong for a player to intentionally violate the rules of the game.According to both formalism and informalism, the rules of the game include the formal rules of the game. Both traditional positions avoid the incompatibility problems by rejecting 1 and 1'. Practiceism rejects 2 and 2’: it maintains that the rules are the rules manifested in playing the game, not the formal rules.Practiceism presents two theses: (... (shrink)

A philosophical theory of explanation should provide solutions to a series of problems, both descriptive and normative. The aim of this essay is to establish the claim that this can be best done if one theorizes in terms of explanatory games rather than focusing on the explication of the concept of explanation. The position that is adopted is that of an explanatory pluralism and it is elaborated in terms of the rules that incorporate the normative standards that guide the (...) processes of discovery and justification of explanations as well as the modes of their communication, dissemination, and adoption. They constitute the rules of the explanatory game that the participants are playing. The philosophical project consists in describing and normatively appraising the rules that constitute these games. (shrink)

A generalization of the standard n-person game is presented, with flexible information requirements suitable for players constrained by bounded rationality. Strategies (complete contingency plans) are replaced by "policies," i. e., end-mean pairs of candidate goals and "controls" (partial contingency plans). The existence of individual objective functions over the joint policy choice set is axiomatized in terms of primitive preference and probability orders. Conditions are given for the existence of pure policy Nash equilibrium points in n-person games, and pure policy (...) Nash bargaining and equilibrium threat solutions in 2-person policy games. Connectedness of the policy and payoff sets is not required. (shrink)

Mediation is a process in which two parties agree to resolve their dispute by negotiating over alternative solutions presented by a mediator. In order to construct such solutions, the mediator brings more information and knowledge, and, if possible, resources to the negotiation table. In order to do so, the mediator faces the challenge of determining which information is relevant to the current problem, given a vast database of knowledge. The contribution of this paper is the automated mediation machinery to resolve (...) this issue. We define the concept of a Mediation Problem and show how it can be described in Game Description Language. Furthermore, we present an algorithm that allows the mediator to efficiently determine which information is relevant to the problem and collect this information from the negotiating agents. We show with several experiments that this algorithm is much more efficient than the naive solution that simply takes all available knowledge into account. (shrink)

Externality games are studied in Grafe et al. (1998, Math. Methods Op. Res. 48, 71). We define a generalization of this class of games and show, using the methodology in Izquierdo and Rafels (1996, 2001, Working paper, Univ Barcelona; Games Econ. Behav. 36, 174), some properties of the new class of generalized externality games. They include, among others, the algebraic structure of the game, convexity, and their implications for the study of cooperative solutions. Also the proportional (...) rule is characterized for this class of games. (shrink)

In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison (...) between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic–doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic–doxastic logic for belief and knowledge and the logic STIT by Belnap and colleagues. (shrink)

When social scientists began employing evolutionary game theory (EGT) in their disciplines, the question arose what the appropriate interpretation of the formal EGT framework would be. Social scientists have given different answer, of which I distinguish three basic kinds. I then proceed to uncover the conceptual tension between the formal framework of EGT, its application in the social sciences, and these three interpretations. First, I argue that EGT under the biological interpretation has a limited application in the social sciences, chiefly (...) because strategy replication often cannot be sensibly interpreted as strategy bearer reproduction in this domain. Second, I show that alternative replication mechanisms imply interpersonal comparability of strategy payoffs. Giving a meaningful interpretation to such comparisons is not an easy task for many social situations, and thus limits the applicability of EGT in this domain. Third, I argue that giving a new interpretation both to strategy replication and selection solves the issue of interpersonal comparability, but at the costs of making the new interpretation incompatible with natural selection interpretations of EGT. To the extent that social scientists seek such a natural selection interpretation, they face a dilemma: either face the challenge that interpersonal comparisons pose, or give up on the natural selection interpretation. By identifying these tensions, my analysis pleas for greater awareness of the specific purposes of EGT modelling in the social sciences, and for greater sensitivity to the underlying microstructure on which the evolutionary dynamics and other EGT solution concepts supervene. (shrink)

To a practitioner in the social sciences, game theory primarily helps to identify situations in which interdependent decisions are somehow problematic; solutions often require venturing into the social sciences. Game theory is usually about anticipating each other's choices; it can also cope with influencing other's choices. To a social scientist the great contribution of game theory is probably the payoff matrix, an accounting device comparable to the equals sign in algebra.

Solution concepts for game play implicitly assume what information is relevant for choosing moves. Maximin and Eliminating Dominated Strategies use payoff order; mixed strategies and Harsanyi's risk dominance use payoff values. "Cooperative" strategies use previous choices, ignoring payoffs altogether. We first define the 12 symmetric 2 × 2 games as a continuous payoff space then use this space to evaluate strategies based on different types of information. Strategic success is shown to be sensitive to actual payoffs and seldom (...) consistent for all games of an ordinally defined category such as Chicken. A new hybrid strategy using both payoff and choice information is introduced and shown to produce efficient outcomes in all symmetric 2×2 games when employed by both players. It does well in evolutionary tournaments against strategies of other types, especially in the difficult distribution games including Battle-of-the-Sexes. (shrink)

The game theoretic notion of best-response reasoning is sometimes criticized when its application produces multiple solutions of games, some of which seem less compelling than others. The recent development of the theory of team reasoning addresses this by suggesting that interacting players in games may sometimes reason as members of a team – a group of individuals who act together in the attainment of some common goal. A number of properties have been suggested for team-reasoning decision-makers’ goals to (...) satisfy, but a few formal representations have been discussed. In this paper we suggest a possible representation of these goals based on the notion of mutual advantage. We propose a method for measuring extents of individual and mutual advantage to the interacting decision-makers, and define team interests as the attainment of outcomes associated with maximum mutual advantage in the games they play. (shrink)