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319
Global Games: Theory and Applications
 IN “ADVANCES IN ECONOMICS AND ECONOMETRICS, THE EIGHTH WORLD CONGRESS”, DEWATRIPONT, HANSEN AND TURNOVSKY, EDS
, 2000
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Epistemic conditions for Nash equilibrium
, 1991
"... According to conventional wisdom, Nash equilibrium in a game “involves” common knowledge of the payoff functions, of the rationality of the players, and of the strategies played. The basis for this wisdom is explored, and it turns out that considerably weaker conditions suffice. First, note that if ..."
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Cited by 226 (6 self)
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According to conventional wisdom, Nash equilibrium in a game “involves” common knowledge of the payoff functions, of the rationality of the players, and of the strategies played. The basis for this wisdom is explored, and it turns out that considerably weaker conditions suffice. First, note that if each player is rational and knows his own payoff function, and the strategy choices of the players are mutually known, then these choices form a Nash equilibrium. The other two results treat the mixed strategies of a player not as conscious randomization of that player, but as conjectures of the other players about what he will do. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures yields Nash equilibrium. When n ≥ 3, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures yield Nash equilibrium when there is a common prior. Examples are provided showing these results to be sharp.
COMPUTATION OF EQUILIBRIA in Finite Games
, 1996
"... We review the current state of the art of methods for numerical computation of Nash equilibria for nitenperson games. Classical path following methods, such as the LemkeHowson algorithm for two person games, and Scarftype fixed point algorithms for nperson games provide globally convergent metho ..."
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Cited by 148 (1 self)
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We review the current state of the art of methods for numerical computation of Nash equilibria for nitenperson games. Classical path following methods, such as the LemkeHowson algorithm for two person games, and Scarftype fixed point algorithms for nperson games provide globally convergent methods for finding a sample equilibrium. For large problems, methods which are not globally convergent, such as sequential linear complementarity methods may be preferred on the grounds of speed. None of these methods are capable of characterizing the entire set of Nash equilibria. More computationally intensive methods, which derive from the theory of semialgebraic sets are required for finding all equilibria. These methods can also be applied to compute various equilibrium refinements.
Run the GAMUT: A comprehensive approach to evaluating gametheoretic algorithms
 In AAMAS04
, 2004
"... We present GAMUT 1, a suite of game generators designed for testing gametheoretic algorithms. We explain why such a generator is necessary, offer a way of visualizing relationships between the sets of games supported by GAMUT, and give an overview of GAMUT’s architecture. We highlight the importanc ..."
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Cited by 91 (10 self)
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(Show Context)
We present GAMUT 1, a suite of game generators designed for testing gametheoretic algorithms. We explain why such a generator is necessary, offer a way of visualizing relationships between the sets of games supported by GAMUT, and give an overview of GAMUT’s architecture. We highlight the importance of using comprehensive test data by benchmarking existing algorithms. We show surprisingly large variation in algorithm performance across different sets of games for two widelystudied problems: computing Nash equilibria and multiagent learning in repeated games. 2 1.
Sink equilibria and convergence
 IN FOCS
, 2005
"... We introduce the concept of a sink equilibrium. A sink equilibrium is a strongly connected component with no outgoing arcs in the strategy profile graph associated with a game. The strategy profile graph has a vertex set induced by the set of pure strategy profiles; its arc set corresponds to transi ..."
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Cited by 82 (12 self)
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We introduce the concept of a sink equilibrium. A sink equilibrium is a strongly connected component with no outgoing arcs in the strategy profile graph associated with a game. The strategy profile graph has a vertex set induced by the set of pure strategy profiles; its arc set corresponds to transitions between strategy profiles that occur with nonzero probability. (Here our focus will just be on the special case in which the strategy profile graph is actually a best response graph; that is, its arc set corresponds exactly to best response moves that result from myopic or greedy behaviour.) We argue that there is a natural convergence process to sink equilibria in games where agents use pure strategies. This leads to an alternative measure of the social cost of a lack of coordination, the price of sinking, which
Deterministic approximation of stochastic evolution in games
, 2002
"... This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The processes are Markov chains, and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied ..."
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Cited by 81 (5 self)
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This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The processes are Markov chains, and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the longrun behavior of the discrete stochastic process, for large populations, and its deterministic flow approximation. In particular, we provide probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow. We sharpen these results in the special case of ergodic processes.
EVOLUTIONARY DRIFT AND EQUILIBRIUM SELECTION
, 1996
"... This paper develops an approach to equilibrium selection in game theory based on studying the equilibriating process through which equilibrium is achieved. The differential equations derived from models of interactive learning typically have stationary states that are not isolated. Instead, Nash equ ..."
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Cited by 73 (2 self)
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This paper develops an approach to equilibrium selection in game theory based on studying the equilibriating process through which equilibrium is achieved. The differential equations derived from models of interactive learning typically have stationary states that are not isolated. Instead, Nash equilibria that specify the same behavior on the equilibrium path, but different outofequilibrium behavior, appear in connected components of stationary states. The stability properties of these components often depend critically on the perturbations to which the system is subjected. We argue that it is then important to incorporate such drift into the model. A su±cient condition is provided for drift to create stationary states with strong stability properties near a component of equilibria. This result is used to derive comparative static predictions concerning common questions raised in the literature on refinements of Nash equilibrium