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Pure Nash Equilibria: Hard and Easy Games
"... In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NPhard, while deciding whether a game has a strong Nash equilibrium is Stcomplete. We then s ..."
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Cited by 64 (2 self)
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In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NPhard, while deciding whether a game has a strong Nash equilibrium is Stcomplete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each player's move depends on moves of other players. We say that a game has small neighborhood if the " utility function for each player depends only on (the actions of) a logarithmically small number of other players, The dependency structure of a game G can he expressed by a graph G(G) or by a hypergraph II(G). Among other results, we show that if jC has small neighborhood and if II(G) has botmdecl hypertree width (or if G(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFLcomplete and thus in the class _NC ~ of highly parallelizable problems. 1 Introduction and Overview of Results The theory of strategic games and Nash equilibria has important applications in economics and decision making [31, 2]. Determining whether Nash equilibria exist, and effectively computing
The theory of the firm as governance structure: From choice to contract
 JOURNAL OF ECONOMIC PERSPECTIVES
, 2002
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STRATEGIC EQUILIBRIUM
, 2000
"... An outcome in a noncooperative game is said to be selfenforcing, or a strategic equilibrium, if, whenever it is recommended to the players, no player has an incentive to deviate from it. This paper gives an overview of the concepts that have been proposed as formalizations of this requirement and o ..."
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Cited by 11 (0 self)
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An outcome in a noncooperative game is said to be selfenforcing, or a strategic equilibrium, if, whenever it is recommended to the players, no player has an incentive to deviate from it. This paper gives an overview of the concepts that have been proposed as formalizations of this requirement and of the properties and the applications of these concepts. In particular the paper discusses Nash equilibrium, together with its main coarsenings (correlated equilibrium, rationalizibility) and its main re…nements (sequential, perfect, proper, persistent and stable equilibria). There is also an extensive discussion on equilibrium selection.
An Operational Measure of Riskiness
, 2009
"... We propose a measure of riskiness of “gambles” (risky assets) that is objective: it depends only on the gamble and not on the decisionmaker. The measure is based on identifying for every gamble the critical wealth level below which it becomes “risky” to accept the gamble. ..."
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Cited by 11 (3 self)
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We propose a measure of riskiness of “gambles” (risky assets) that is objective: it depends only on the gamble and not on the decisionmaker. The measure is based on identifying for every gamble the critical wealth level below which it becomes “risky” to accept the gamble.
Algorithmic Rationality: Game Theory with Costly Computation
, 2007
"... We develop a general gametheoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional gametheoretic results (such as the existence of a Nash equilibrium) no longer hold. Nevertheless, we can use the framework to provide psycho ..."
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Cited by 10 (8 self)
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We develop a general gametheoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional gametheoretic results (such as the existence of a Nash equilibrium) no longer hold. Nevertheless, we can use the framework to provide psychologically appealing explanations to observed behavior in wellstudied games (such as finitely repeated prisoner’s dilemma and rockpaperscissors). Furthermore, we Consider the following game. You are given a random odd nbit number x and you are supposed to decide whether x is prime or composite. If you guess correctly you receive $2, if you guess incorrectly you instead have to pay a penalty of $1000. Additionally you have the choice of “playing safe” by giving up, in which case you receive $1. In traditional game theory, computation is considered
Modal logic and game theory: two alternative approaches, Risk Decision and Policy
, 2002
"... Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other’s rationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It i ..."
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Cited by 9 (1 self)
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Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other’s rationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It is shown that the same mathematical tool, namely modal logic, can be used to explicitly model both views. 1.
The Many Faces of Rationalizability,” The B.E
 Journal of Theoretical Economics (Topics
"... Abstract. The rationalizability concept was introduced in [7] and [19] to assess what can be inferred by rational players in a noncooperative game in the presence of common knowledge. However, this notion can be defined in a number of ways that differ in seemingly unimportant minor details. We shed ..."
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Cited by 7 (2 self)
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Abstract. The rationalizability concept was introduced in [7] and [19] to assess what can be inferred by rational players in a noncooperative game in the presence of common knowledge. However, this notion can be defined in a number of ways that differ in seemingly unimportant minor details. We shed light on these differences, explain their impact, and clarify for which games these definitions coincide. Also we apply the same analysis to explain the differences and similarities between various ways the iterated elimination of strictly dominated strategies was defined in the literature. This allows us to clarify the results of [12] and [11] and improve upon them. Our approach is based on a general study of the operators on complete lattices. We allow transfinite iterations of the considered operators and clarify the need for them. The advantage of such a general approach is that a number of results, including order independence for some of the notions of rationalizability and strict dominance, come for free. JEL classification: C72
Empirical microeconomics: Another perspective
 In M. Augier and J. March (Eds.), The Economics of Choice, Change and Organization: Essays in Memory of Richard M. Cyert
"... What was obvious to many of us at the time has become even more evident since: the ..."
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Cited by 5 (0 self)
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What was obvious to many of us at the time has become even more evident since: the