In cooperative Cournot oligopoly games, it is known that the β-core is equal to the α-core, and both are non-empty if every individual profit function is continuous and concave (Zhao, Games Econ Behav 27:153–168, 1999b). Following Chander and Tulkens (Int J Game Theory 26:379–401, 1997), we assume that firms react to a deviating coalition by choosing individual best reply strategies. We deal with the problem of the non-emptiness of the induced core, the γ-core, by two different approaches. The (...) first establishes that the associated Cournot oligopoly Transferable Utility (TU)-games are balanced if the inverse demand function is differentiable and every individual profit function is continuous and concave on the set of strategy profiles, which is a step forward beyond Zhao’s core existence result for this class of games. The second approach, restricted to the class of Cournot oligopoly TU-games with linear cost functions, provides a single-valued allocation rule in the γ-core called Nash Pro rata (NP)-value. This result generalizes Funaki and Yamato’s (Int J Game Theory 28:157–171, 1999) core existence result from no capacity constraint to asymmetric capacity constraints. Moreover, we provide an axiomatic characterization of this solution by means of four properties: efficiency, null firm, monotonicity, and non-cooperative fairness. (shrink)

A new class of values combining marginalistic and egalitarian principles is introduced for cooperative TU-games. It includes some modes of solidarity among the players by taking the collective contribution of some coalitions to the grand coalition into account. Relationships with other class of values such as the Egalitarian Shapley values and the Procedural values are discussed. We propose a strategic implementation of our class of values in subgame perfect Nash equilibrium. Two axiomatic characterizations are provided: one of the whole (...) class of values, and one of each of its extreme points. (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)

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)

A solution for cooperative games with transferable utility, or simply TU-games, assigns a payoff vector to every TU-game. In this paper we discuss two classes of equal surplus sharing solutions. The first class consists of all convex combinations of the equal division solution and the center-of-gravity of the imputation-set value. The second class is the dual class consisting of all convex combinations of the equal division solution and the egalitarian non-separable contribution value. We provide characterizations of the two (...) classes of solutions using either population solidarity or a reduced game consistency in addition to other standard properties. (shrink)

In the framework of transferable utility games, we modify the 2-person Davis–Maschler reduced game to ensure non-emptiness of the imputation set of the adapted 2-person reduced game. Based on the modification, we propose two new axioms: reduced game monotonicity and reduced dominance. Using RGM, RD, NE, Covariance under strategic equivalence, Equal treatment property and Pareto optimality, we are able to characterize the kernel.

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 (...) class='Hi'>game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed. (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 (...) class='Hi'>game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed. (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)

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)

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)

Motivated by Hoff and Stiglitz’s :753–763, 2004) theory, we examine empirically how the creation of “rules of the game” affect the behavior of economic agents in a transition economy. Using a sample of Chinese state-owned enterprises in which controlling ownership was transferred to private acquirers between 1994 and 2006, we find that the post-privatization performance of firms depends on institutional factors. Before 2003, we observe severe post-privatization tunneling behaviors by acquirers and worse PPP. However, from 2003, when the State (...) issued regulations against tunneling and strengthened enforcement, the incidence of tunneling behaviors declined, and PPP improved. We find that better implementation of ownership transfer and longer prior experience of private acquirers are key factors that contribute to the improvement. (shrink)

We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion and we add a new modal variant to that class of logics. We also discuss the relative expressive power of the proposed logic in comparison to the standard (...) modal counterparts. (shrink)

We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion with respect to such a language extension, and we add a new modal variant to that class. We discuss the relative expressive power of the proposed logic in (...) comparison to the standard modal counterparts. We prove that the model checking problem for the resulting logic is \(\textsf{P}\) -complete. In addition, by exploring the connection with related product logics, we gain more insight towards having a better understanding of the subtleties of the proposed framework. (shrink)

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)

It is known that peer group games are a special class of games with a permission structure. However, peer group games are also a special class of digraph games. To be specific, they are digraph games in which the digraph is the transitive closure of a rooted tree. In this paper we first argue that some known results on solutions for peer group games hold more general for digraph games. Second, we generalize both digraph games as well as games with (...) a permission structure into a model called games with a local permission structure, where every player needs permission from its predecessors only to generate worth, but does not need its predecessors to give permission to its own successors. We introduce and axiomatize a Shapley value-type solution for these games, generalizing the conjunctive permission value for games with a permission structure and the β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-measure for weighted digraphs. (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,...

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.

We introduce values for rooted-tree and sink-tree digraph games axiomatically and provide their explicit formula representation. These values may be considered as natural extensions of the lower equivalent and upper equivalent solutions for line-graph games studied in van den Brink et al. (Econ Theory 33:349–349, 2007). We study the distribution of Harsanyi dividends. We show that the problem of sharing a river with a delta or with multiple sources among different agents located at different levels along the riverbed can be (...) embedded into the framework of a rooted-tree or sink-tree digraph game correspondingly. (shrink)

This article discusses the set of Harsanyi payoff vectors of a cooperative TU-game, also known as the Selectope. We reconsider some results on Harsanyi payoff vectors within a more general framework. First, an intuitive approach is used, showing that the set of Harsanyi payoff vectors is the core of an associated convex game. Next, the set of individual rational Harsanyi payoff vectors, the Harsanyi imputations in short, is considered. Existence conditions are provided, and if non-empty, we provide (...) a description as the core of a well-defined convex game, and show that it is an externally stable set. (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)

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)

This article discusses the set of Harsanyi payoff vectors of a cooperative TU-game, also known as the Selectope. We reconsider some results on Harsanyi payoff vectors within a more general framework. First, an intuitive approach is used, showing that the set of Harsanyi payoff vectors is the core of an associated convex game. Next, the set of individual rational Harsanyi payoff vectors, the Harsanyi imputations in short, is considered. Existence conditions are provided, and if non-empty, we provide (...) a description as the core of a well-defined convex game, and show that it is an externally stable set. (shrink)

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)

Considerable work during the past two decades has focused on modeling the structure of semantic memory, although the performance of these models in complex and unconstrained semantic tasks remains relatively understudied. We introduce a two‐player cooperative word game, Connector (based on the boardgame Codenames), and investigate whether similarity metrics derived from two large databases of human free association norms, the University of South Florida norms and the Small World of Words norms, and two distributional semantic models based on (...) large language corpora (word2vec and GloVe) predict performance in this game. Participant dyads were presented with 20‐item word boards with word pairs of varying relatedness. The speaker received a word pair from the board (e.g., exam‐algebra) and generated a one‐word semantic clue (e.g., math), which was used by the guesser to identify the word pair on the board across three attempts. Response times to generate the clue, as well as accuracy and latencies for the guessed word pair, were strongly predicted by the cosine similarity between word pairs and clues in random walk‐based associative models, and to a lesser degree by the distributional models, suggesting that conceptual representations activated during free association were better able to capture search and retrieval processes in the game. Further, the speaker adjusted subsequent clues based on the first attempt by the guesser, who in turn benefited from the adjustment in clues, suggesting a cooperative influence in the game that was effectively captured by both associative and distributional models. These results indicate that both associative and distributional models can capture relatively unconstrained search processes in a cooperative game setting, and Connector is particularly suited to examine communication and semantic search processes. (shrink)

We present experimental data on a simple market game. Several solution concepts from cooperative game theory are applied to predict the observed payoff distributions. Notably, a recently introduced solution concept meant to capture the influence of outside options on the payoff distribution within groups fares better than most other solution concepts under consideration. Our results shed some light on the effects of scarcity relations on markets on bargaining outcomes within negotiating dyads.

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)

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)

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.

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)

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)

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.

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)

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)

Inspired by Scarf, Zhao, Sandholm and Yang and Zhang, we introduce the model of coalitional population games with infinitely many pure strategies, and define the notions of NTU core and TU core for coalitional population games. We next prove the existence results for NTU cores and TU cores. Furthermore, as an extension of the NTU core, we introduce the notion of strong equilibria and prove the existence theorem of strong equilibria.

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)