The Existence of a Coalition-Proof Nash Equilibrium
The Existence of a Coalition-Proof Nash Equilibrium

Author: Sang-Seung Yi

Publisher:

Published: 1998

Total Pages: 0

ISBN-13:

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I provide two simple sufficient conditions under which the Pareto frontier of the Nash equilibrium set is coalition-proof. My first condition states there exists a pure-strategy Nash equilibrium which Pareto dominates all other serially undominated strategies. Under this condition, the Pareto-efficient Nash equilibrium is uniquely coalition- proof. I show that games with ordinal strategic complementarities which satisfy "ordinal monotone externalities" also satisfy the above condition. My second condition applies to games with strategic substitutabilities in equilibrium. Suppose that (1) the game has three players, or, a player's payoff depends only on his own strategy and the sum (but not the composition) of the opponents' strategies; and (2) the game has either positive externalities or negative externalities. Then the Pareto-efficient frontier of Nash equilibria is coalition-proof. Hence, under these two conditions, the common practice of the Pareto dominance refinement yields the same outcome as the coalition-proof Nash equilibrium refinement.

Computational Aspects of Cooperative Game Theory
Computational Aspects of Cooperative Game Theory

Author: Georgios Chalkiadakis

Publisher: Morgan & Claypool Publishers

Published: 2012

Total Pages: 171

ISBN-13: 1608456528

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Cooperative game theory is a branch of (micro-)economics that studies the behavior of self-interested agents in strategic settings where binding agreements among agents are possible. Our aim in this book is to present a survey of work on the computational aspects of cooperative game theory. We begin by formally defining transferable utility games in characteristic function form, and introducing key solution concepts such as the core and the Shapley value. We then discuss two major issues that arise when considering such games from a computational perspective: identifying compact representations for games, and the closely related problem of efficiently computing solution concepts for games. We survey several formalisms for cooperative games that have been proposed in the literature, including, for example, cooperative games defined on networks, as well as general compact representation schemes such as MC-nets and skill games. As a detailed case study, we consider weighted voting games: a widely-used and practically important class of cooperative games that inherently have a natural compact representation. We investigate the complexity of solution concepts for such games, and generalizations of them. We briefly discuss games with non-transferable utility and partition function games. We then overview algorithms for identifying welfare-maximizing coalition structures and methods used by rational agents to form coalitions (even under uncertainty), including bargaining algorithms. We conclude by considering some developing topics, applications, and future research directions.

Computational Aspects of Cooperative Game Theory
Computational Aspects of Cooperative Game Theory

Author: Georgios Raedt

Publisher: Springer Nature

Published: 2022-05-31

Total Pages: 150

ISBN-13: 3031015584

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Cooperative game theory is a branch of (micro-)economics that studies the behavior of self-interested agents in strategic settings where binding agreements among agents are possible. Our aim in this book is to present a survey of work on the computational aspects of cooperative game theory. We begin by formally defining transferable utility games in characteristic function form, and introducing key solution concepts such as the core and the Shapley value. We then discuss two major issues that arise when considering such games from a computational perspective: identifying compact representations for games, and the closely related problem of efficiently computing solution concepts for games. We survey several formalisms for cooperative games that have been proposed in the literature, including, for example, cooperative games defined on networks, as well as general compact representation schemes such as MC-nets and skill games. As a detailed case study, we consider weighted voting games: a widely-used and practically important class of cooperative games that inherently have a natural compact representation. We investigate the complexity of solution concepts for such games, and generalizations of them. We briefly discuss games with non-transferable utility and partition function games. We then overview algorithms for identifying welfare-maximizing coalition structures and methods used by rational agents to form coalitions (even under uncertainty), including bargaining algorithms. We conclude by considering some developing topics, applications, and future research directions.

A Game-Theoretic Perspective on Coalition Formation
A Game-Theoretic Perspective on Coalition Formation

Author: Debraj Ray

Publisher: Oxford University Press

Published: 2007-11

Total Pages: 336

ISBN-13: 019920795X

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Drawing upon and extending his inaugural Lipsey Lectures, Debraj Ray looks at coalition formation from the perspective of game theory. Ray brings together developments in both cooperative and noncooperative game theory to study the analytics of coalition formation and binding agreements.

Strictly Proper Mechanisms with Cooperating Players
Strictly Proper Mechanisms with Cooperating Players

Author: Sang In Chun

Publisher: Stanford University

Published: 2011

Total Pages: 94

ISBN-13:

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In order to obtain accurate information about the uncertainty in a decision situation, a decision maker may rely on the judgment of experts to obtain useful probabilistic forecasts. Strictly proper scoring rules have been shown to incentivize forecasters to provide truthful probabilistic forecasts and can be interpreted as a contract between a decision maker and a risk neutral forecaster rewarding greater expertise as well as truthful revelation. In recent years, prediction markets have been created to provide an efficient means to assess uncertain quantities from forecasters, and strictly proper scoring rules have been proposed for prediction markets, where the payment depends on the forecaster's score relative to others. However, we show that when those players can cooperate, these mechanisms can instead discourage them from reporting what they really believe. When players with different beliefs are able to cooperate and form a coalition, these mechanisms admit arbitrage and there is a report that will always pay coalition members more than their truthful forecasts. If the coalition were created by an intermediary, such as a web portal, the intermediary would be guaranteed a profit from this risk free surplus. Specifically, for the three most commonly used strictly proper scoring rules, we provide a cooperative report for coalition members and show the magnitude of the surplus from cooperation with numerical examples. We analyze the optimal behavior of coalition members within a coalition. Given a choice whether to participate in any coalition, players should participate. We show conditions under which coalition members should invite new members. We evaluate the optimal strategy of each coalition member under a set of simple assumptions including a quadratic scoring rule, and show that honest revelation within the coalition is a Bayesian Nash equilibrium. We show the consequence of players' cooperation to the decision maker receiving aggregated probabilities, and conclude with open challenges in the design and understanding of strictly proper mechanisms.

Existence and Stability of Nash Equilibrium
Existence and Stability of Nash Equilibrium

Author: Guilherme Carmona

Publisher: World Scientific

Published: 2013

Total Pages: 153

ISBN-13: 9814390658

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The book aims at describing the recent developments in the existence and stability of Nash equilibrium. The two topics are central to game theory and economics and have been extensively researched. Recent results on existence and stability of Nash equilibrium are scattered and the relationship between them has not been explained clearly. The book will make these results easily accessible and understandable to researchers in the field. Book jacket.