In this paper I explain how to play and administer a game that helps teach students a lesson about the value of cooperation and the role of ethics and the law in obtaining the conditions under which cooperating is reason­able. I also discuss several applications of this Cooperation Game, primarily in courses in social and political philosophy, introductory ethics, and the philosophy of law. The game can usefully be played with a range of groups of students from small tutorial sections (...) to large sections of over one hundred, and the game and post-game analysis can be completed in one or two classes. (shrink)

We consider a class of games, which we call “groups’ games”, in which players are partitioned into classes within which players may be considered indistinguishable. We compute explicit formulas for some of the principal values restricted to these games. This is particularly useful for dealing with games with a large number of players where the usual formulas would be impractical to compute. We give several examples that illustrate how this idea may be applied to concrete situations.

Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided (...) in terms of game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed. (shrink)

Groups of people perform acts that are subject to standards of rationality. A committee may sensibly award fellowships, or may irrationally award them in violation of its own policies. A theory of collective rationality defines collective acts that are evaluable for rationality and formulates principles for their evaluation. This book argues that a group's act is evaluable for rationality if it is the products of acts its members fully control. It also argues that such an act is collectively rational if (...) the acts of the group's members are rational. Efficiency is a goal of collective rationality, but not a requirement, except in cases where conditions are ideal for joint action and agents have rationally prepared for joint action.The people engaged in a game of strategy form a group, and the combination of their acts yields a collective act. If their collective act is rational, it constitutes a solution to their game. A theory of collective rationality yields principles concerning solutions to games. One principle requires that a solution constitute an equilibrium among the incentives of the agents in the game. In a cooperative game some agents are coalitions of individuals, and it may be impossible for all agents to pursue all incentives. Because rationality is attainable, the appropriate equilibrium standard for cooperative games requires that agents pursue only incentives that provide sufficient reasons to act. The book's theory of collective rationality supports an attainable equilibrium-standard for solutions to cooperative games and shows that its realization follows from individuals' rational acts.By extending the theory of rationality to groups, this book reveals the characteristics that make an act evaluable for rationality and the way rationality's evaluation of an act responds to the type of control its agent exercises over the act. The book's theory of collective rationality contributes to philosophical projects such as contractarian ethics and to practical projects such as the design of social institutions. (shrink)

During a cultural festival, artists and theaters act as a cartel by agreeing on pricing decisions that maximize the groups’ profit as a whole. We model the problem of sharing the profit created by a festival among organizing theaters as a cooperative game. In such a game, the worth of a coalition is defined as the theaters’ profit from the optimal fixation of prices. We show that this class of games is convex and we axiomatically characterize the Shapley (...) value for this class of games. We also provide an axiomatic basis for the downstream incremental solution. Finally, we apply this model to the NEXT festival, for which we have collected data. We propose an approach to derive the games’ vector from the data and we compute the different solutions. (shrink)

We introduce a solution concept for cooperative games with transferable utility and a coalition structure that is proportional for two-player games. Our value is obtained from generalizing a proportional value for cooperative games with transferable utility in a way that parallels the extension of the Shapley value to the Owen value. We provide two characterizations of our solution concept, one that employs a property that can be seen as the proportional analog to Myerson’s balanced contribution (...) property; and a second one that relies on a consistency property. (shrink)

A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In (...) this paper we consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing properties. (shrink)

Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided (...) in terms of game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed. (shrink)

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal (...) analogy between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation. (shrink)

Australasian Journal of Philosophy, Volume 90, Issue 1, Page 205, March 2012.

By focusing on players’ relative contributions, we study some properties for values in positive cooperative games with transferable utilities. The well-known properties of symmetry (also known as “equal treatment of equals”) and marginality are based on players’ marginal contributions to coalitions. Both Myerson’s balanced contributions property and its generalization of the balanced cycle contributions property (Kamijo and Kongo Int J of Game Theory 39:563–571, 2010; BCC) are based on players’ marginal contributions to other players. We define relative versions (...) of marginality and BCC by replacing marginal contributions with relative contributions, and examine efficient values satisfying each of the two properties. On the class of positive games, a relative variation of marginality is incompatible with efficiency, and together with efficiency and the invariance property with respect to the payoffs of players under a player deletion, a relative variation of BCC characterizes the proportional value and egalitarian value in a unified manner. (shrink)

Virtual bargaining theory suggests that social agents aim to resolve non-cooperative games by identifying the strategy profile which they would agree to play if they could openly bargain. The theory thus offers an explanation of how social agents resolve games with multiple Nash equilibria. One of the main questions pertaining to this theory is how the principles of the bargaining theory could be applied in the analysis of hypothetical bargaining in non-cooperative games. I propose a (...) bargaining model based on the benefit-equilibrating bargaining solution concept for non-cooperative games, broadly in line with the principles underlying Conley and Wilkie's ordinal egalitarian solution for Pareto optimal point selection problems with finite choice sets. I provide formal characterizations of the ordinal and the cardinal versions of BES, discuss their application to n-player games, and compare model's theoretical predictions with the data available from several experiments involving `pie games'. (shrink)

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim of (...) this thesis is to enrich the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden, and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions. (shrink)

Provides the reader who has not studied game theory a brief and non‐technical introduction to the main categories of models and forms of analysis: strategic‐ form games; extensive‐form games; dominance; and Nash equilibrium.

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 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)

The quality of service of a user in user-centric unmanned aerial vehicle group is degraded by complex cochannel interference; hence, a cooperative game power control algorithm in UUAVG is proposed. The algorithm helps to establish a downlink power control model of the UUAVG, construct a product of the signal to interference noise ratio function of each user as a utility function of the cooperative game, and deduce the optimal power control scheme using the Lagrange function. This scheme reduces (...) the interference of the service unmanned aerial vehicle to edge users and improves the communication quality of all the users as well as the throughput of the entire system. Simulation results show that the average throughput of the CGPC algorithm improved by 10.32% compared with the traditional Stackelberg Game based Nonunified Pricing Power Control algorithm. This shows that the CGPC algorithm can effectively reduce the transmission power of the cooperative UAV and enhance the capacity of the entire system, ensuring communication quality. (shrink)

Coall & Hertwig (C&H) demonstrate the importance of grandparents to children, even in low fertility societies. We suggest policy-makers interested in reproductive timing in such contexts should be alerted to the practical applications of this cooperative breeding framework. The presence or absence of a supportive kin network could help explain why some women begin their reproductive careers or.

The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', 'self-evident', and 'justifiable'. I (...) also construct in modal operator logic a paradox involving reflexive empirical reasoning. Unlike the paradox of the Liar, the paradox of reflexive reasoning does not depend on self-reference. ;I consider various solutions to the Liar paradox and evaluate how well these solutions cope with the paradox of reflexive reasoning. I then formalize the solution to the paradoxes which I favor: the indexical-hierarchical approach, first sketched out by Charles Parsons and Tyler Burge. In this solution, occurrences of the predicate 'true' in sentence-tokens are contextually relativized to levels of a hierarchy. Drawing also on some brief remarks of Bertrand Russell and Charles Parsons, I develop an account of the kind of schematic generality needed for this theory to be statable. ;Finally, I demonstrate that the principles shown to be paradoxical are in fact presupposed by contemporary game theorists in their reliance on the notion of common knowledge or, more precisely, mutual belief. I create novel analyses of and corresponding solutions to several recalcitrant puzzles within game theory, including the "chain-store paradox". (shrink)

Ender's tortured conscience is an illustration of the moral importance of following principles of just war theory—the “unspoken rules of manly warfare”—and their apparent tension with the demands of war and survival. This chapter talks about the ethics of conflict in Ender's various games—his battles and wars. It asks, was justice served in the Third Invasion and destruction of the bugger worlds, the event that came to be called the xenocide. Ender's life is actually a testimony to the just (...) war axiom that all people desire peace. In the tradition of just war theory, there are five principles that lay out the requirements of jus ad bellum, or how to go to war in an ethical way. They include just cause, legitimate authority, right intention, probability of success, and last resort. Ender's strategy is always to use devastating force to incapacitate the enemy. (shrink)

The central premise of the book draws on the familiar observation that sport and state based legal systems are both rule governed practices that share a great deal in common: as the authors put it,...

I explore a connection between Robert Nozick's account of decision value/symbolic utility in The Nature of Rationality and F. P. Ramsey's discussion of ethically neutral propositions in his 1926 essay , a discussion that Brian Skyrms in Choice and Chance credits with disclosing deeper foundations for expected utility than the celebrated Theory of Games and Economic Behavior of von Neumann and Morgenstern. Ramsey's recognition of ethically non-neutral propositions is essential to his foundational work, and the similarity of these propositions (...) to symbolic utility helps make the case that the latter belongs to the apparatus that constructs expected utility, rather than being reducible to it or being part of a proposal that can be cheerfully ignored. I conclude that decision value replaces expected utility as the central idea in (normative) decision theory. Expected utility becomes an approximation that is good enough when symbolic utility is not at stake. (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)

Major construction projects have a great influence on the national economy and society, wherein cooperative relationship between construction suppliers plays an increasingly significant role in the overall supply chain system. However, the relationships between suppliers are noncontractual, multistage, dynamic, and complicated. To gain a deeper insight into the suppliers’ cooperative relationships, an evolutionary game model is developed to explore the cooperation tendency of multisuppliers. A replicator dynamic system is further formulated to investigate the evolutionary stable strategies of multisuppliers. (...) Then, fourteen “when-then” type scenarios are concluded and classified into six different evolutionary tracks. Meanwhile, the critical influencing factors are identified. The results show that the suppliers’ production capacity, owner-supplier contract, and the owner’s incentive mechanism influence the cooperation tendency of suppliers directly. The managerial implications contribute to insightful references for a more stable cooperative relationship between the owner and suppliers. (shrink)

Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality but also common (...) knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological game theory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; game theory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (shrink)

Evolutionary game theory is ethically neutral: its assumption of ‘rationality’ has nothing to do with selfishness but is in fact entirely compatible with altruism. If altruism has an evolutionary explanation then this fact is of no theological relevance: in particular it is not any sort of evidence of a divine plan etc.

Packed with ideas designed to help children learn to sing, this booklet offers criteria for selecting songs, strategies to bring out the best in children's voices, and suggestions for games, ideas, and resources.

The game theoretical approach to R&D cooperation does not investigate the role of trust in the initiation and success of R&D cooperation: it either assumes that firms are non-opportunists or that the R&D cooperation is supported by an incentive mechanism that eliminates opportunism. In contrast, the present paper focuses on these issues by introducing incomplete information and two types of firms: opportunist and non-opportunist. Defining trust as the belief of each firm that its potential collaborator will respect the contract, it (...) identifies the trust conditions under which firms initiate R&D alliances and contribute to their success. The higher the spillovers, the higher the level of trust required to initiate R&D cooperation for non-opportunists, while the inverse holds for opportunists. (shrink)

This paper explores the cooperation mechanisms for the prisoner’s dilemma game, a canonical example for studying cooperation mechanisms, with Bayesian games. By the approach allowing simultaneous moves with the assumption that the players might be self-interested or norm-following, we establish four possible Bayesian game models, all of which are cooperation mechanisms for the prisoner’s dilemma game except for the model in which one of the two players must be self-interested.

Talk of ‘robustness’ remains vague, despite the fact that it is clearly an important parameter in evaluating models in general and game-theoretic results in particular. Here we want to make it a bit less vague by offering a graphic measure for a particular kind of robustness— ‘matrix robustness’— using a three dimensional display of the universe of 2 x 2 game theory. In a display of this form, familiar games such as the Prisoner’s Dilemma, Stag Hunt, Chicken and Deadlock (...) appear as volumes, making comparison easy regarding the extent of different game-theoretic effects. We illustrate such a comparison in robustness between the triumph of Tit for Tat in a spatialized environment (Grim 1995, Grim, Mar, and St. Denis 1998) and a spatialized modeling of the Contact Hypothesis regarding prejudice reduction (Grim, et. al 2005a, 2005b). The geometrical representation of relative robustness also offers a possibility for links between geometrical theorems and results regarding robustness in game theory. (shrink)

The partial cooperation displayed by subjects in the Centipede Game deviates radically from the predictions of traditional game theory. Even standard, infinite population, evolutionary settings have failed to provide an explanation for this behavior. However, recent work in finite population evolutionary models has shown that such settings can produce radically different results from the standard models. This paper examines the evolution of partial cooperation in finite populations. The results reveal a new possible explanation that is not open to the standard (...) models and gives us reason to be cautious when employing these otherwise helpful idealizations. *Received January 2007; revised November 2007. †To contact the author, please write to: Department of Logic and Philosophy of Science, University of California, 3151 Social Science Plaza A, Irvine, CA 92697-5100; e-mail: [email protected]. (shrink)

The essays from prominent public intellectuals collected in this volume reflect an array of perspectives on the spectrum of conflict, competition, and cooperation, as well as a wealth of expertise on how games manifest in the world, how they operate, and how social animals behave inside them. They include previously unpublished material by former Cabinet minister Sayeeda Warsi, the philosopher A. C. Grayling, legal scholar Nicola Padfield, cycling coach David Brailsford, former military intelligence officer Frank Ledwidge, neuro-psychologist Barbara J. (...) Sahakian, zoological ecologist Nicholas B. Davies, and the final work of the late Nobel laureate Thomas C. Schelling. This is a must-read for anyone interested in the history, nature, and dynamics of games. (shrink)

In the literature on logics of imperfect information it is often stated, incorrectly, that the Game-Theoretical Semantics of Independence-Friendly quantifiers captures the idea that the players of semantical games are forced to make some moves without knowledge of the moves of other players. We survey here the alternative semantics for IF logic that have been suggested in order to enforce this “epistemic reading” of sentences. We introduce some new proposals, and a more general logical language which distinguishes between “independence (...) from actions” and “independence from strategies”. New semantics for IF logic can be obtained by choosing embeddings of the set of IF sentences into this larger language. We compare all the semantics proposed and their purported game-theoretical justifications, and disprove a few claims that have been made in the literature. (shrink)

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

It is widely agreed that humans have specific abilities for cooperation and culture that evolved since their split with their last common ancestor with chimpanzees. Many uncertainties remain, however, about the exact moment in the human lineage when these abilities evolved. This article argues that cooperation and culture did not evolve in one step in the human lineage and that the capacity to stick to long-term and risky cooperative arrangements evolved before properly modern culture. I present evidence that Homo (...) heidelbergensis became increasingly able to secure contributions form others in two demanding Paleolithic public good games (PPGGs): cooperative feeding and cooperative breeding. I argue that the temptation to defect is high in these PPGGs and that the evolution of human cooperation in Homo heidelberngensis is best explained by the emergence of modern-like abilities for inhibitory control and goal maintenance. These executive functions are localized in the prefrontal cortex and allow humans to stick to social norms in the face of competing motivations. This scenario is consistent with data on brain evolution that indicate that the largest growth of the prefrontal cortex in human evolution occurred in Homo heidelbergensis and was followed by relative stasis in this part of the brain. One implication of this argument is that subsequent behavioral innovations, including the evolution of symbolism, art, and properly cumulative culture in modern Homo sapiens , are unlikely to be related to a reorganization of the prefrontal cortex, despite frequent claims to the contrary in the literature on the evolution of human culture and cognition. (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)