We analyze extensive games as interactive process models, using modallanguages plus matching notions of bisimulation as varieties of gameequivalences. Our technical results show how to fit existing modalnotions into this new setting.

We show that for solvable games, the calculation of the strategies which survive iterative elimination of dominated strategies in normal games is equivalent to the calculation of the backward induction outcome of some extensive game. However, whereas the normal game form does not provide information on how to carry out the elimination, the corresponding extensive game does. As a by-product, we conclude that implementation using a subgame perfect equilibrium of an extensive game with perfect information (...) is equivalent to implementation through a solution concept which we call guided iteratively elimination of dominated strategies which requires a uniform order of elimination. Journal of Economic Literature Classification Number: C72. (shrink)

We show that for solvable games, the calculation of the strategies which survive iterative elimination of dominated strategies in normal games is equivalent to the calculation of the backward induction outcome of some extensive game. However, whereas the normal game form does not provide information on how to carry out the elimination, the corresponding extensive game does. As a by-product, we conclude that implementation using a subgame perfect equilibrium of an extensive game with perfect information (...) is equivalent to implementation through a solution concept which we call guided iteratively elimination of dominated strategies which requires a uniform order of elimination. Journal of Economic Literature Classifica-. (shrink)

In certain finite extensive games with perfect information, Cristina Bicchieri (1989) derives a logical contradiction from the assumptions that players are rational and that they have common knowledge of the theory of the game. She argues that this may account for play outside the Nash equilibrium. She also claims that no inconsistency arises if the players have the minimal beliefs necessary to perform backward induction. We here show that another contradiction can be derived even with minimal beliefs, so (...) there is no paradox of common knowledge specifically. These inconsistencies do not make play outside Nash equilibrium plausible, but rather indicate that the epistemic specification must incorporate a system for belief revision. Whether rationality is common knowledge is not the issue. (shrink)

This paper suggests a way of formalizing the amount of information that can be conveyed to each player along every possible play of an extensive game. The information given to each player i when the play of the game reaches node x is expressed as a subset of the set of terminal nodes. Two definitions are put forward, one expressing the minimum amount of information and the other the maximum amount of information that can be conveyed without violating the (...) constraint represented by the information sets. Our definitions provide intuitive characterizations of such notions as perfect recall, perfect information and simultanetty. (shrink)

We develop a logical system that captures two different interpretations of what extensive games model, and we apply this to a long-standing debate in game theory between those who defend the claim that common knowledge of rationality leads to backward induction or subgame perfect (Nash) equilibria and those who reject this claim. We show that a defense of the claim à la Aumann (1995) rests on a conception of extensive game playing as a one-shot event in combination (...) with a principle of rationality that is incompatible with it, while a rejection of the claim à la Reny (1988) assumes a temporally extended, many-moment interpretation of extensive games in combination with implausible belief revision policies. In addition, the logical system provides an original inductive and implicit axiomatization of rationality in extensive games based on relations of dominance rather than the usual direct axiomatization of rationality as maximization of expected utility. (shrink)

The notion of perfect recall in extensive games was introduced by Kuhn (1953), who interpreted it as "equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves''. We provide a characterization and axiomatization of perfect recall based on two notions of memory: (1) memory of past knowledge and (2) memory of past actions.

Restricting attention to the class of extensive games defined by von Neumann and Morgenstern with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct (...) a particular information partition for each player and show that it captures the notion of maximum information in the sense that it is the finest within the class of information partitions that satisfy four natural properties. Using this notion of “maximum information” we are able to provide an alternative characterization of the meet of the information partitions. (shrink)

The multilinear extension of a cooperative game was introduced by Owen in 1972. In this contribution we study the Lovász extension for cooperative games by using the marginal worth vectors and the dividends. First, we prove a formula for the marginal worth vectors with respect to compatible orderings. Next, we consider the direct market generated by a game. This model of utility function, proposed by Shapley and Shubik in 1969, is the concave biconjugate extension of the game. Then we (...) obtain the following characterization: The utility function of a market game is the Lovász extension of the game if and only if the market game is supermodular. Finally, we present some preliminary problems about the relationship between cooperative games and combinatorial optimization. (shrink)

The model of incomplete cooperative games incorporates uncertainty into the classical model of cooperative games by considering a partial characteristic function. Thus the values for some of the coalitions are not known. The main focus of this paper is 1-convexity under this framework. We are interested in two heavily intertwined questions. First, given an incomplete game, how can we fill in the missing values to obtain a complete 1-convex game? Second, how to determine in a rational, fair, and (...) efficient way the payoffs of players based only on the known values of coalitions? We illustrate the analysis with two classes of incomplete games—minimal incomplete games and incomplete games with defined upper vector. To answer the first question, for both classes, we provide a description of the set of 1-convex extensions in terms of its extreme points and extreme rays. Based on the description of the set of 1-convex extensions, we introduce generalisations of three solution concepts for complete games, namely the τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-value, the Shapley value and the nucleolus. For minimal incomplete games, we show that all of the generalised values coincide. We call it the average value and provide different axiomatisations. For incomplete games with defined upper vector, we show that the generalised values do not coincide in general. This highlights the importance and also the difficulty of considering more general classes of incomplete games. (shrink)

In this note we introduce the notion of K–player additive extension of a symmetric two-player game and prove a result relating the equilibria in mixed strategies in the two games. Then we apply the result to the Borda electoral competition game.

In this note we introduce the notion of K–player additive extension of a symmetric two-player game and prove a result relating the equilibria in mixed strategies in the two games. Then we apply the result to the Borda electoral competition game.

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)

It would be useful to have a category of extensive-form games whose isomorphisms specify equivalences between games. Since working with entire games is too large a project for a single paper, I begin here with preforms, where a “preform” is a rooted tree together with choices and information sets. In particular, this paper first defines the category \, whose objects are “functioned trees”, which are specially designed to be incorporated into preforms. I show that \ is (...) isomorphic to the full subcategory of \ whose objects are converging arborescences. Then the paper defines the category \, whose objects are “node-and-choice preforms”, each of which consists of a node set, a choice set, and an operator mapping node-choice pairs to nodes. I characterize the \ isomorphisms, define a forgetful functor from \ to \, and show that \ is equivalent to the full subcategory of \ whose objects are perfect-information preforms. The paper also shows that many game-theoretic entities can be derived from preforms, and that these entities are well-behaved with respect to \ morphisms and isomorphisms. (shrink)

The Monty Hall game is one of the most discussed decision problems, but where a convincing behavioral explanation of the systematic deviations from probability theory is still lacking. Most people not changing their initial choice, when this is beneficial under information updating, demands further explanation. Not only trust and the incentive of interestingly prolonging the game for the audience can explain this kind of behavior, but the strategic setting can be modeled more sophisticatedly. When aiming to increase the odds of (...) winning, while Monty’s incentives are unknown, then not to switch doors can be considered as the most secure strategy and avoids a sure loss when Monty’s guiding aim is not to give away the prize. Understanding and modeling the Monty Hall game can be regarded as an ideal teaching example for fundamental statistic understandings. (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 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)

If semantic consequence is analyzed with extensive games, logical reasoning can be accounted for by looking at how players solve entailment games. However, earlier approaches to game semantics cannot achieve this reduction, by want of explicitly dened preferences for players. Moreover, although entailment games can naturally translate the idea of argumentation about a common ground, a cognitive interpretation is undermined by the complexity of strategic reasoning. We thus describe a class of semantic extensive entailment game (...) with algorithmic players, who have preferences for parsimonious spending of computational resources and thus compute partial strategies under qualitative uncertainty about future histories. We prove the existence of local preferences for moves and of strategic fixpoints that allow to map game-trees to tableaux proofs, and exhibit a strategy prole that solves the fixpoint selection problem, and can be mapped to systematic constructions of semantic trees, yielding a completeness result by translation. We then discuss the correspondence between proof heuristics and strategies in our games, the relations of our games to gts, and possible extensions to other entailment relations. We conclude that the main interest of our result lies in the possibility to bridge argumentative and cognitive models of logical reasoning, rather than in new meta-theoretic results. All proofs are given in appendix. (shrink)

This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there is a hierarchy of logics. The limit case is an infinitary predicate extension of modal propositional logic KD4, and is of special interest in applications. In Part I, (...) we develop the basic framework, and show some applications: an epistemic axiomatization of Nash equilibrium and formal undecidability on the playability of a game. To show the formal undecidability, we use a term existence theorem, which will be proved in Part II. (shrink)

Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational principle: if two generic programs, viewed as terms of type , are equal at any given instance A[T], then they are equal at all instances. They proved that this rule is admissible in a certain extension of System F, but finding a semantically (...) motivated model satisfying this principle remained an open problem.In the present paper, we construct a categorical model of polymorphism, based on game semantics, which contains a large collection of generic types. This model builds on two novel constructions:•A direct interpretation of variable types as games, with a natural notion of substitution of games. This allows moves in games A[T] to be decomposed into the generic part from A, and the part pertaining to the instance T. This leads to a simple and natural notion of generic strategy.•A “relative polymorphic product” which expresses quantification over the type variable Xi in the variable type A with respect to a “universe” which is explicitly given as an additional parameter B. We then solve a recursive equation involving this relative product to obtain a universe in a suitably “absolute” sense.Full Completeness for ML types is proved for this model. (shrink)

The prelims comprise: Strategic Interaction Nash Equilibrium Normal‐form Refinements Games in Extensive Form Extensive‐form Refinements Selection by Evolution Notes.

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)

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 argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme. The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this in (...) terms of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory.Keywords: Epistemic Programme; Game theory; Interactive epistemology; Mathematisation; Nash equilibrium. (shrink)

As a common social network, the SNEM plays an important role in emergency management. Magnitude emergencies are characterized by high complexity and uncertainty, and it is impossible to rely on the government for emergency management alone. We should absorb multiple subjects to build the SNEM and carry out extensive emergency mobilization in the whole society. The SNEM can integrate resources, gather consensus, promote participation, and reduce risks. The analysis of the types, generation mechanism, subject behavior, and strategy selection of (...) the SNEM aid in adopting appropriate mobilization strategy based on magnitude emergencies, achieving the adaptation of the SNEM and emergency scenarios. By constructing the evolutionary game model of the SNEM for magnitude emergencies, taking China as an empirical sample, this paper explores the behavior evolution law and stable strategy of the government, social organizations, and the public. The results showed that the symbiotic SNEM with a positive response of social organizations and the public under the path of high-intensity mobilization by the government is the best strategy combination, and it is conducive to maximizing the emergency joint force. (shrink)

The 2010 Commonwealth Games was Delhi's and India's biggest sporting event ever. In the immediate aftermath of the Games, this paper sets out to analyse the story of the Games' legacy- its politics, economic impact and to what extent was it successful in transforming Delhi into a global city and India into a sporting force to reckon with. Having already documented the history and politics of the Commonwealth Games with a focus on Delhi, , this paper (...) is an extension in trying to place Delhi 2010 in perspective, understand its long term meaning and explain its lasting legacy. (shrink)

The concept of an infinite game played on a finite graph is perhaps novel in the context of an rather extensive recent literature in which infinite games are generally played on an infinite game tree. We claim two advantages for our model, which is admittedly more restrictive. First, our games have a more apparent resemblance to ordinary parlor games in spite of their infinite duration. Second, by distinguishing those nodes of the graph that determine the winning (...) and losing of the game , we are able to offer a complexity analysis that is useful in computer science applications. (shrink)

Game-theoretic reasoning pervades economic theory and is used widely in other social and behavioural sciences. An Introduction to Game Theory International Edition, by Martin J. Osborne, presents the main principles of game theory and shows how they can be used to understand economics, social, political, and biological phenomena. The book introduces in an accessible manner the main ideas behind the theory rather than their mathematical expression. All concepts are defined precisely, and logical reasoning is used throughout. The book requires an (...) understanding of basic mathematics but assumes no specific knowledge of economics, political science, or other social or behavioural sciences. Coverage includes the fundamental concepts of strategic games, extensive games with perfect information, and coalitional games; the more advanced subjects of Bayesian games and extensive games with imperfect information; and the topics of repeated games, bargaining theory, evolutionary equilibrium, rationalizability, and maxminimization. The book offers a wide variety of illustrations from the social and behavioural sciences. Each topic features examples that highlight theoretical points and illustrations that demonstrate how the theory may be used. (shrink)

This paper aims to provide an ethical assessment of the shooting of animals for sport. In particular, it discusses the use of partridges and pheasants for shooting. While opposition to hunting and shooting large wild mammals is strong, game birds have often taken a back seat in everyday animal welfare concerns. However, the practice of raising game birds for sport poses significant ethical issues. Most birds shot are raised in factory-farming conditions, and there is a considerable amount of evidence to (...) show that these birds endure extensive suffering on these farms. Considering the fact that birds do have interests, including interests in life and not suffering, what are the ethical implications of using them for blood sports? Indeed, in the light of the suffering that game birds endure in factory farms, it may be that shooting such birds for sport is more morally problematic than other types of hunting and shooting which many people are often fiercely opposed to, for while it seems plausible to say that some animals may be harmed more by death than others (due to, say, their greater capacities), there may be harms that are worse than death (such as a life of intolerable suffering). The objective of this paper is to assess the ethics of shooting animals for sport, and in particular the practice of raising game birds for use in blood sports, by applying principles commonly used in ethics; specifically the principle of non-maleficence and equal consideration of (like) interests. (shrink)

The sense of agency – the subjective feeling of being in control of our own actions – is one central aspect of the phenomenology of action. Computational models provided important contributions toward unveiling the mechanisms underlying the sense of agency in individual action. In particular, the sense of agency is believed to be related to the match between the actual and predicted consequences of our own actions. In the study of joint action, models are even more necessary to understand the (...) mechanisms underlying the development of coordination strategies and how the subjective experiences of control emerge during the interaction. In a joint action, we not only need to predict the consequences of our own actions; we also need to predict the actions and intentions of our partner, and to integrate these predictions to infer their joint consequences. Understanding our partner and developing mutually satisfactory coordination strategies are key components of joint action and in the development of the sense of joint agency. Here we discuss a computational architecture which addresses the sense of agency during intentional, real-time joint action. We first reformulate previous accounts of the sense of agency in probabilistic terms, as the combination of prior beliefs about the action goals and constraints, and the likelihood of the predicted movement outcomes. To look at the sense of joint agency, we extend classical computational motor control concepts - optimal estimation and optimal control. Regarding estimation, we argue that in joint action the players not only need to predict the consequences of their own actions, but also need to predict partner’s actions and intentions and to integrate these predictions to infer their joint consequences. As regards action selection, we use differential game theory – in which actions develop in continuous space and time - to formulate the problem of establishing a stable form of coordination and as a natural extension of optimal control to joint action. The resulting model posits two concurrent observer-controller loops, accounting for ‘joint’ and ‘self’ action control. The two observers quantify the likelihoods of being in control alone or jointly. Combined with prior beliefs, they provide weighing signals which are used to modulate the ‘joint’ and ‘self’ motor commands. We argue that these signals can be interpreted as the subjective sense of joint and self agency. We demonstrate the model predictions by simulating a sensorimotor interactive task where two players are mechanically coupled and are instructed to perform planar movements to reach a shared final target by crossing two differently located intermediate targets. In particular, we explore the relation between self and joint agency and the information available to each player about their partner. The proposed model provides a coherent picture of the inter-relation of prediction, control, and the sense of agency in a broader range of joint actions. (shrink)

We consider an extension of signaling games to the case of prediction, where one agent perceives the current state of the world and sends a signal. The second agent perceives this signal, and makes a prediction about the next state of the world. We suggest that such games may be the basis of a model for the evolution of successful theorizing about the world.

Understanding human behaviour involves "why"'s as well as "how"'s. Rational people have good reasons for acting, but it can be hard to find out what these were and how they worked. In this Note, we discuss a few ways in which actions, preferences, and expectations are intermingled. This mixture is especially clear with the well-known solution procedure for extensive games called 'Backward Induction'. In particular, we discuss three scenarios for analyzing behaviour in a game. One can rationalize given (...) moves as revealing agents' preferences, one can also rationalize them as revealing agents' beliefs about others, but one can also change a predicted pattern of behaviour by making promises. All three scenarios transform given games to new ones, and we prove some results about their scope. A more general view of relevant game transformations would involve dynamic and epistemic game logics. Finally, our analysis describes and disentangles matters: but it will not tell you what to do! (shrink)

Denotational semantics of logic programming and its extensions have been studied thoroughly for many years. In 1998, a game semantics was given to definite logic programs by Di Cosmo, Loddo, and Nicolet, and a few years later it was extended to deal with negation by Rondogiannis and Wadge. Both approaches were proven equivalent to the traditional semantics. In this paper we define a game semantics for disjunctive logic programs and prove soundness and completeness with respect to the minimal model semantics (...) of Minker. The overall development has been influenced by the games studied for PCF and functional programming in general, in the styles of Abramsky–Jagadeesan–Malacaria and Hyland–Ong–Nickau. (shrink)

Two-player, zero-sum, non-cooperative, blindfold games in extensive form with incomplete information are considered in this paper. Any information about past moves which players played is stored in a database, and each player can access the database. A polynomial game is a game in which, at each step, all players withdraw at most a polynomial amount of previous information from the database. We show resource-bounded determinacy of some kinds of finite, zero-sum, polynomial games whose pay-off sets are computable (...) by non-deterministic polynomial-time function-oracle Turing machines. We call a pay-off set -determined if, for any polynomial game G associated with the given pay-off set, either player has a winning strategy which is in for any subgames of G. We show that there exists an FP-strongly-determined pay-off set which is computed by an exponential-time oracle Turing machine, where FP is the set of polynomial-time computable functions. We also discuss several relationships between the determinacy of polynomial games and recursion-theoretic properties for the classes co-NP and co-NEXP. We show that the polynomial version of the axiom of choice holds under some assumption of polynomial determinacy for a pay-off set which is polynomial-time computable with parallel queries. This principle of choice implies that co-NP has the separation property. (shrink)

The Shapley value is a well-known solution concept for TU games. The Maschler–Owen value and the NTU Shapley value are two well-known extensions of the Shapley value to NTU games. A hyperplane game is an NTU game in which the feasible set for each coalition is a hyperplane. On the domain of monotonic hyperplane games, the Maschler–Owen value is axiomatized. Although the domain of hyperplane game is a very interesting class of games to study, unfortunately, on (...) this domain, the NTU Shapley value is not well-defined, namely, it assigns an empty set to some hyperplane games. A prize game is an NTU game that can be obtained by “truncating” a hyperplane game. As such, a prize game describes essentially the same situation as the corresponding hyperplane game. It turns out that, on the domain of monotonic prize games, the NTU Shapley value is well-defined. Thus, one can define a value which is well-defined on the domain of monotonic hyperplane games as follows: given a monotonic hyperplane game, first, transform it into a prize game, and then apply the NTU Shapley value to it. We refer to the resulting value as the “generalized Shapley value” and compare the axiomatic properties of it with those of the Maschler–Owen value on the union of the class of monotonic hyperplane games and that of monotonic prize games. We also provide axiomatizations of the Maschler–Owen value and the generalized Shapley value on that domain. (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)

In this paper, we study the structural optimization of community governance in smart cities and optimize the structure based on the game analysis of dynamic planning evolution. Theoretically, the connotation and extension of the concept of “self-organization” are cleared, and the environment and conditions of community self-organization formation, the formation process of community self-organization, and the types of community self-organization are discussed. The so-called “self-organization” is a process of spontaneously moving from disorder to order, and the environment and conditions of (...) community self-organization are mainly the openness, nonequilibrium state, and nonlinearity of the system. The key parameters of the contract with the change of the values of each factor make up for the inability to collect data for the empirical study in this paper; then, it presents four linear stages along with the cause such as self-creation, self-expansion, self-maintenance, and self-degeneration, respectively. The types of community self-organization mainly include community self-organization with random aggregation, socialized community self-organization, and stable community self-organization with autonomy orientation. By systematically sorting out the relationship between community self-organization and government, while confirming the positive significance of community self-organization to community cultural governance, various complex conflicts and game relationships will deeply affect the actual effectiveness of cultural governance and provide useful knowledge reference for future community cultural governance. (shrink)

Nick Dyer-Witheford and Greig de Peuter. Games of Empire: Global Capitalism and Video Games . Minneapolis: University of Minnesota Press. 2009. 320pp. pbk. $19.95 ISBN-13: 978-0816666119. In Games of Empire , Nick Dyer-Witheford and Greig de Peuter expand an earlier study of “the video game industry as an aspect of an emerging postindustrial, post-Fordist capitalism” (xxix) to argue that videogames are “exemplary media of Empire” (xxix). Their notion of “Empire” is based on Michael Hardt and Antonio Negri’s (...) Empire (2000), which characterizes the contemporary world order as a decentralized system of global economic, political, and economic power that transcends national boundaries. In the view of the authors, Hardt and Negri’s account sets itself apart from other analyses of international politics by offering a “comprehensive account of conditions of work, forms of subjectivity, and types of struggle in contemporary capital” (xx). Dyer-Witheford and de Peuter thus divide Games of Empire into three sections to reflect each of these aspects of Empire ’s argument, seeing their work as the first account to explore “virtual games within a system of global ownership, privatized property, coercive class relations, military operations, and radical struggle” (xxix). Books in the University of Minnesota Press’s Electronic Mediations series “explore the humanistic and social implications” of new technologies that spark “significant changes in society and culture, politics and economics, thinking and being.” That’s an abstract goal, and one that Games of Empire surely meets. Yet at times it can be difficult to understand exactly which specific intervention this book seeks to make. It is unclear whether the authors of Games of Empire see their work as an indictment of game scholars’ lack of attention to political economy, or whether it’s a work of political theory hoping to show that other disciplines should be paying more attention to the production and play of videogames. Because Dyer-Witheford and de Peuter don’t directly criticize previous political critiques of gaming—such as Edward Castronova’s exploration of the “porous membrane” allowing two-way traffic between virtual economies and those of the real world, or Alexander Galloway’s unraveling of control protocols in algorithmic design, or Ian Bogost’s idea of political procedural rhetoric—they sometimes leave the reader wondering how to situate the book in the broader discourse on games and politics, either separately or together. Thus, Games of Empire might best be seen as an introduction to the writings of Hardt and Negri for game players and designers, rather than as a text for communicating the basic concepts of game studies and design. It is neither a truly new theory of games or digital media, nor is it a new theory of Empire—and that’s not a criticism. It is instead an introduction to Empire through popular culture, as Zizek does for Lacan in Looking Awry . If one were teaching an introductory course on contemporary political theory, this book would offer obvious inroads into Negri and Hardt’s thinking for a number of reasons. Despite its radical ideological bent, the book isn’t off-putting to readers who don’t necessarily share the authors’ politics. It synthesizes complex ideas from difficult thinkers like Marx, Foucault, and Guattari while integrating modifications and critiques of Empire theory itself. And although the book is dense, sometimes feeling longer than it actually is (just over 200 pages), Games of Empire maintains a breezy readability by tightly coupling core concepts of Empire theory to well-known games and widely-publicized conflicts within the videogame industry. The first section of the book focuses on immaterial labor, the accumulation of “cognitive capital,” and the global process of manufacturing videogame consoles. It is significant for the authors that videogames began as hacker experiments within research institutes of the military industrial complex, programmed on stolen time, before becoming a commodity (7). This is the first in a string of examples showing how creative dissidence and conflict fuel the continuing evolution of Empire’s control. Dyer-Witheford and de Peuter explain that the videogame industry now constitutes an international production apparatus dominating both creative work in developed nations and manual labor in developing ones. Because game industries in the United States, Western Europe, and Japan are predominately non-unionized, they serve as an exemplary system for analyzing how global capital exploits contemporary intellectual work—including an excellent analysis of the “EA Spouse” scandal of 2004. On the side of the consumer, the authors argue that rabid “console races” that drive the industry forward from a technological perspective serve to structure gamer identity and combat piracy; later in the book, these machines offer a window into the worlds of Congolese coltan mining and electronic waste (222-224). In the second section, Dyer-Witheford and de Peuter move on to deep case studies of individual games to show how the most popular game genres embed imperial assumptions about conflict, exchange, and urban life. First they argue that military training games such as Full Spectrum Warrior —co-developed by university researchers, industry developers, and military contractors—contribute to the “banalization” of war, a subjective state wherein perpetual preparedness for war is accepted as a part of everyday life (100). Chapter five covers Michel Foucalt’s notion of “biopower,” the extension of capital accumulation to life itself. The authors argue that virtual worlds such as World of Warcraft , which take market capitalism as a given and force players into essentialist roles and racial antagonisms, are organized to maximize control and profit (often on the backs of virtual currency “farmers” in China and southeast Asia). Finally, they criticize the naïve assumption that humor and cynicism in the popular sandbox game franchise Grand Theft Auto offer any remedy to its racialized, violent content. Instead, such games indulge and normalize the fantasy of getting rich at any cost by keeping the realities of contemporary urban life and corporate greed at a safe distance (181). Part three of Games of Empire focuses on “games of multitude,” a preliminary attempt to escape from Empire’s order through alternate modes of videogame development and play. Multitude is defined dialectically, as “the engine and the enemy” of Empire (187). This is the most important, yet also most contradictory section of the text. It lays bare the process by which Empire and its media feed our creative and intellectual development to overabundance. At a certain point, the force of the multitude reaches such a level that it threatens the stability of Empire; however, instead of following Hardt and Negri’s utopian assumptions about the radical potential of the multitude, the authors here follow Paolo Virno’s warning that Empire is “very good at adopting apparently iconoclastic practices and utopian ideas as management techniques and revenue sources” (188). At every turn, advances in player configurative power provide new sources of revenue and advertising angles for the game industry. A disappointing shortcoming of these latter pages is the lack of truly new examples for radical resistance within game development. Instead, it turns out that the radical left seems satisfied with the same mild successes that the left-of-center also has celebrated: artist’s mods, virtual world activism, and critical counterplay within strategy- and wargames. Having been frequently cited by many authors before Dyer-Witheford and de Peuter, this idea of subversion or resistance through play feels tired and unpersuasive. It is unclear if the authors believe it is possible to embrace game design itself as a way of pursuing what they call “exodus” from Empire, or if an all-too-fashionable subversion is the only workable strategy. While the book does explore how the earliest independent game studios were eventually subverted and incorporated into the game industry proper, it doesn’t affirm or critique more recent non-commercial, DIY game development projects such as Klik-of-the-Month Club and Ludum Dare. Dyer-Witheford and de Peuter’s analysis of so-called “tactical games,” including the editorial works of La Molleindustria, leads to an even more ambivalent take on the contemporary design ecology. At the conclusion of his essay on “Countergaming,” Galloway asserts that avant-garde videogame artists “should create new grammars of action […] should create alternative algorithms” (Galloway 125). Yet Dyer-Witheford and de Peuter characterize works such as McDonald’s Video Game and Oiligarchy as didactic, suggesting that the role of radical political games might be “limited to that of agitprop” (199). They are concerned that games like those of Molleindustria rigidly structure the activities of their players in order to prove a point. Yet, despite their repeated assertion that the equation of greater interactivity with democratic digital liberation is flawed, the authors see potential in policy simulators that “allow players to edit or tweak” (202) their parameters in response to what Bogost has called simulation fever , the simultaneous drive toward and fear of simulation (Bogost 108). The possibility of practicing radical design is bucked, and early attempts at critical game development like those of Molleindustria’s seem to be relegated to the status of exceptions that prove the rule for player-centered exodus. Overall, there is one glaring question Games of Empire leaves unanswered: how exactly are videogames the “exemplary media” of Empire, and what are the implications of videogames being exemplary in this way? Presumably Dyer-Witheford and de Peuter want to avoid essentialist claims, so they’re not keen on following Wark’s desire to mark “the game’s difference from [legacy media] as something that speaks to changes in the overall structure of social and technical relations” (Wark 225). It is also unclear how the production apparatuses, labor standards, and subjectivizing processes involved in the creation and use of other any other kind of digital media would fail to justify their equally exemplary status. Even the book’s concluding paragraph holds that virtual games “are one molecular component of this undecidable collective mutation” (Dyer-Witheford and de Peuter 229) of intellect, labor, and daily life. In the end, the authors seem to back away from their focus on games as exemplary to bring their work in line with broader theories of the gradual digitization of the everyday, in line with Galloway and Manovich. Despite these flaws, there is an undeniable elegance to Games of Empire ’s contrasting of gaming’s overwhelmingly imperial content with its multitudinous form . And its ambivalence about the potential of independent or political game development might be seen by scholars of Empire as a strength rather than a weakness, an acceptance that every new expression of multitude offers another opportunity for the expansion of Empire. The book also functions as a strong, all-encompassing call to greater responsibility on the part of mainstream game developers to be more conscious of the ideologies they embed in their work, of the way their intellectual property is used and manipulated by those who employ them, and of the material impact their industry has on the world at large. For players it offers a toolbox of concepts for radical examinations of their own play activities, asking them to be more cognizant of the consequences of their consumption of digital media and the ways in which their virtual lives interface with the real. REFERENCES Bogost, Ian. Unit Operations: An Approach to Videogame Criticism . Cambridge, Mass.: MIT Press, 2006. Castranova, Edward. Synthetic Worlds: The Business and Culture of Online Games . Chicago, Illinois: University of Chicago Press, 2006. Dyer-Witheford, Nick and de Peuter, Greig. Games of Empire: Global Capitalism and Video Games . Minneapolis, Minnesota: University of Minnesota Press, 2009. Galloway, Alexander. Gaming: Essays on Algorithmic Culture . Minneapolis, Minnesota: University of Minnesota Press, 2006). Wark, McKenzie. Gamer Theory . Cambridge, Mass.: Harvard University Press, 2007. (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)

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)

This paper consists of two parts. First, I shall consider two defences of Quine´s polemical Thesis of the Inscrutability of Reference put forward by Hookway, and Calvo Garzón, respectively. Then, I shall consider an extension of Quine´s succinct behavioural criteria of Radical Translationsuggested by Hintikka´s Game-Theoretical Semantics. I shall argue that Hintikka´s semantics suggest behavioural criteria which we can use to constrain perverse semantic theories. In particular, I shall try to show that whilst Hintikka´s behavioural data tells against Hookway´s proposal, (...) it reveals, nonetheless, a reason as to why my proposed perverse semantic theory enjoys the same priviledged status that a standard semantic theory is supposed toenjoy. (shrink)