Structural relations of symmetry among players in strategic games

The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to define partial symmetries in payoff matrices. With this purpose, we introduce the notion of the role a player plays with respect to another one, and combinatorial relations between roles are studied. Building on them, we define relations directly between players, which provide yet another characterization of structural symmetries in the payoff matrices of strategic games.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Economía; ArgentinaFil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

HedN Game, a Relational Framework for Network Based Cooperation

This paper proposes a new framework for cooperative games based on mathematical relations. Here cooperation is defined as a supportive partnerships represented by a directed network between players (aka hedonic relation). We examine in a specific context, modeled by abstract games how a change of supports induces a modification of strategic interactions between players. Two levels of description are considered: the first one describes the support network formation whereas the second one models the strategic interactions between players. Both are described in a unified formalism, namely CP~game. Stability conditions are stated, emphasizing the connection between these two levels. We also stress the interaction between updates of supports and their impact on the evolution of the context.Cooperative Game, Network, Stability, Hedonic Relation

Learning from failure

We study decentralized learning in organizations. Decentralization is captured through a symmetry constraint on agents’ strategies. Among such attainable strategies, we solve for optimal and equilibrium strategies. We model the organization as a repeated game with imperfectly observable actions. A fixed but unknown subset of action profiles are successes and all other action profiles are failures. The game is played until either there is a success or the time horizon is reached. For any time horizon, including infinity, we demonstrate existence of optimal attainable strategies and show that they are Nash equilibria. For some time horizons, we can solve explicitly for the optimal attainable strategies and show uniqueness. The solution connects the learning behavior of agents to the fundamentals that characterize the organization: Agents in the organization respond more slowly to failure as the future becomes more important, the size of the organization increases and the probability of success decreases.Game theory

International Environmental Agreements under Uncertainty: Does the Veil of Uncertainty Help?

Na and Shin (1998) showed that the veil of uncertainty can be conducive to the success of self-enforcing international environmental agreements. Later papers confirmed this negative conclusion about the role of learning. In the light of intensified research efforts worldwide to reduce uncertainty about the environmental impact of emissions and the cost of reducing them, this conclusion is intriguing. The purpose of this paper is threefold. First, we analyze whether the result carries over to a more general setting without restriction on the number of players and which considers not only no and full learning but also partial learning. Second, we test whether the conclusion also holds if there is uncertainty about abatement costs instead of uncertainty about the benefits from global abatement. Third, we propose a transfer scheme that mitigates the possible negative effect of learning and which may even transform it into a positive effect.transnational cooperation, self-enforcing international environmental agreements, uncertainty, learning

Learning from failure

We study decentralized learning in organizations. Decentralization is captured through a symmetry constraint on agents’ strategies. Among such attainable strategies, we solve for optimal and equilibrium strategies. We model the organization as a repeated game with imperfectly observable actions. A fixed but unknown subset of action profiles are successes and all other action profiles are failures. The game is played until either there is a success or the time horizon is reached. For any time horizon, including infinity, we demonstrate existence of optimal attainable strategies and show that they are Nash equilibria. For some time horizons, we can solve explicitly for the optimal attainable strategies and show uniqueness. The solution connects the learning behavior of agents to the fundamentals that characterize the organization: Agents in the organization respond more slowly to failure as the future becomes more important, the size of the organization increases and the probability of success decreases.Game theory

Coordination and Learning with a Partial Language

This paper explores how efficiency promotes the use of structure in language. It starts from the premise that one of language’s central characteristics is to provide a means for saying novel things about novel circumstances, its creativity. It is reasonable to expect that in a rich and changing environment, language will be incomplete. This encourages reliance on structure. It is shown how creative language use emerges form common knowledge structures, even if those structures are consistent with an a priori absence of a common language. ZUSAMMENFASSUNG - (Koordination und Lernen mit einer Partialsprache) In diesem Beitrag wird die Anwendung von Strukturen in einer Sprache aus Effizienzsicht begründet. Der Artikel geht davon aus, daß eines der wichtigsten Merkmale der Sprache in ihrer Kreativität zu sehen ist, d. h. als Mittel, um Neues über neue Sachverhalte auszusagen. Es ist deshalb zu erwarten, daß in einer vielfältigen und sich verändernden Umwelt die Sprache unvollständig bleiben wird. Dies fördert die Anwendung von Strukturen. Es wird gezeigt, wie die kreative Sprachanwendung aus allgemeinen Wissensstrukturen entsteht, auch dann, wenn diese Strukturen a priori noch keine gemeinsame Sprache bilden.Language; Coordination; Optimal Learning; Common Knowledge

Evolutionary games on multilayer networks: A colloquium

Networks form the backbone of many complex systems, ranging from the Internet to human societies. Accordingly, not only is the range of our interactions limited and thus best described and modeled by networks, it is also a fact that the networks that are an integral part of such models are often interdependent or even interconnected. Networks of networks or multilayer networks are therefore a more apt description of social systems. This colloquium is devoted to evolutionary games on multilayer networks, and in particular to the evolution of cooperation as one of the main pillars of modern human societies. We first give an overview of the most significant conceptual differences between single-layer and multilayer networks, and we provide basic definitions and a classification of the most commonly used terms. Subsequently, we review fascinating and counterintuitive evolutionary outcomes that emerge due to different types of interdependencies between otherwise independent populations. The focus is on coupling through the utilities of players, through the flow of information, as well as through the popularity of different strategies on different network layers. The colloquium highlights the importance of pattern formation and collective behavior for the promotion of cooperation under adverse conditions, as well as the synergies between network science and evolutionary game theory.Comment: 14 two-column pages, 8 figures; accepted for publication in European Physical Journal

On the Strategic Advantage of Negatively Interdependent Preferences

We study certain classes of supermodular and submodular games which are symmetric with respect to material payoffs but in which not all players seek to maximize their material payoffs. Specifically, a subset of players have negatively interdependent preferences and care not only about their own material payoffs but also about their payoffs relative to others. We identify sufficient conditions under which members of the latter group have a strategic advantage in the following sense: at all intragroup symmetric equilibria of the game, they earn strictly higher material payoffs than do players who seek to maximize their material payoffs. We show that these conditions are satisfied by a number of games of economic importance, and discuss the implications of these findings for the evolutionary theory of preference formation and the theory of Cournot competition.Interdependent Preferences, Submodular and Supermodular Games, Relative Profits, Cournot Oligopoly