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758
Complexity Results about Nash Equilibria
, 2002
"... Noncooperative game theory provides a normative framework for analyzing strategic interactions. ..."
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Cited by 134 (10 self)
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Noncooperative game theory provides a normative framework for analyzing strategic interactions.
A framework for sequential planning in multiagent settings
 Journal of Artificial Intelligence Research
, 2005
"... This paper extends the framework of partially observable Markov decision processes (POMDPs) to multiagent settings by incorporating the notion of agent models into the state space. Agents maintain beliefs over physical states of the environment and over models of other agents, and they use Bayesian ..."
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Cited by 129 (32 self)
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This paper extends the framework of partially observable Markov decision processes (POMDPs) to multiagent settings by incorporating the notion of agent models into the state space. Agents maintain beliefs over physical states of the environment and over models of other agents, and they use Bayesian update to maintain their beliefs over time. The solutions map belief states to actions. Models of other agents may include their belief states and are related to agent types considered in games of incomplete information. We express the agents ’ autonomy by postulating that their models are not directly manipulable or observable by other agents. We show that important properties of POMDPs, such as convergence of value iteration, the rate of convergence, and piecewise linearity and convexity of the value functions carry over to our framework. Our approach complements a more traditional approach to interactive settings which uses Nash equilibria as a solution paradigm. We seek to avoid some of the drawbacks of equilibria which may be nonunique and are not able to capture offequilibrium behaviors. We do so at the cost of having to represent, process and continually revise models of other agents. Since the agent’s beliefs may be arbitrarily nested the optimal solutions to decision making problems are only asymptotically computable. However, approximate belief updates and approximately optimal plans are computable. We illustrate our framework using a simple application domain, and we show examples of belief updates and value functions. 1.
A crash course in implementation theory
 SOC CHOICE WELFARE
, 2001
"... This paper is meant to familiarize the audience with some of the fundamental results in the theory of implementation and provide a quick progression to some open questions in the literature. ..."
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Cited by 116 (2 self)
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This paper is meant to familiarize the audience with some of the fundamental results in the theory of implementation and provide a quick progression to some open questions in the literature.
Robust mechanism design
 ECONOMETRICA
, 2005
"... The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces, with more higher order uncertainty. We study the "ex post equivalence" question: when is interim im ..."
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Cited by 111 (9 self)
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The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces, with more higher order uncertainty. We study the "ex post equivalence" question: when is interim implementation on all possible type spaces equivalent to requiring ex post implementation on the space of payoff types? We show that ex post equivalence holds when the social choice correspondence is a function and in simple quasilinear environments. When ex post equivalence holds, we identify how large the type space must be to obtain the equivalence. We also show that ex post equivalence fails in general, including in quasilinear environments with budget balance. For quasilinear environments, we provide an exact characterization of when interim implementation is possible in rich type spaces. In this environment, the planner can fully extract players’ belief types, so the incentive constraints reduce to conditions distinguishing types with the same beliefs about others’ types but different payoff types.
Maintaining a reputation when strategies are imperfectly observed
 Review of Economic Studies
, 1992
"... This paper studies reputation effects in games with a single longrun player whose choice of stagegame strategy is imperfectly observed by his opponents. We obtain lower and upper bounds on the longrun player's payoff in any Nash equilibrium of the game. If the longrun player's stagega ..."
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Cited by 106 (3 self)
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This paper studies reputation effects in games with a single longrun player whose choice of stagegame strategy is imperfectly observed by his opponents. We obtain lower and upper bounds on the longrun player's payoff in any Nash equilibrium of the game. If the longrun player's stagegame strategy is statistically identified by the observed outcomes, then for generic payoffs the upper and lower bounds both converge, as the discount factor tends to 1, to the longrun player's Stackelberg payoff, which is the most he could obtain by publicly committing himself to any strategy. 1.
The Bayesian Foundations of Solution Concepts of Games,” Working
 University of Chicago
, 1986
"... We transform a noncooperative game into a Bayesian decision problem for each player where the uncertainty faced by a player is the strategy choices of the other players, the priors of other players on the choice of other players, the priors over priors, and so on. We provide a complete characterizat ..."
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Cited by 103 (0 self)
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We transform a noncooperative game into a Bayesian decision problem for each player where the uncertainty faced by a player is the strategy choices of the other players, the priors of other players on the choice of other players, the priors over priors, and so on. We provide a complete characterization between the extent of knowledge about the rationality of players and their ability to successively eliminate strategies which are not best responses. This paper therefore provides the informational foundations of iteratively undominated strategies and rationalizable strategic behavior (B.D. Bernheim, Economefrica 52 (1984) 10071028; D. Pearce, Economefrica 52 (1984), 10291050). Sufficient conditions are also found for Nash equilibrium behavior and a result akin to R. J. Aumann (Econometrica 55 (1987) l18) on correlated equilibria, is derived with different hypotheses. Journal of
Population Uncertainty and Poisson Games
 International Journal of Game Theory
, 1997
"... A general class of models is developed for analyzing games with population uncertainty. Within this general class, a special class of Poisson games is defined. It is shown that Poisson games are uniquely characterized by properties of independent actions and environmental equivalence. The general de ..."
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Cited by 83 (5 self)
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A general class of models is developed for analyzing games with population uncertainty. Within this general class, a special class of Poisson games is defined. It is shown that Poisson games are uniquely characterized by properties of independent actions and environmental equivalence. The general definition of equilibrium for games with population uncertainty is formulated, and it is shown that the equilibria of Poisson games are invariant under payoffirrelevant type splitting. An example of a large voting game is discussed, to illustrate the advantages of using a Poisson game model for large games. Acknowledgments. I have benefited from many discussions on this topic with John Hillas and Dov Samet. Support from the National Science Foundation grant SES9308139 and from the Dispute Resolution Research Center is gratefully acknowledged. Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate * School of Management, Northwestern University, Evanston, IL 602082009. Email: myerson@nwu.edu 1 POPULATION UNCERTAINTY AND POISSON GAMES by Roger B. Myerson 1.
LARGE POPULATION STOCHASTIC DYNAMIC GAMES: CLOSEDLOOP MCKEANVLASOV SYSTEMS AND THE NASH Certainty Equivalence Principle
, 2006
"... We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the socalled Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control ..."
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Cited by 83 (7 self)
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We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the socalled Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis. The McKeanVlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent (or particle) at the microscopic level and the mass of individuals (or particles) at the macroscopic level. The overall game is decomposed into (i) an optimal control problem whose HamiltonJacobiBellman (HJB) equation determines the optimal control for each individual and which involves a measure corresponding to the mass effect, and (ii) a family of McKeanVlasov (MV) equations which also depend upon this measure. We designate the NCE Principle as the property that the resulting scheme is consistent (or soluble), i.e. the prescribed control laws produce sample paths which produce the mass effect measure. By construction, the overall closedloop behaviour is such that each agent’s behaviour is optimal with respect to all other agents in the game theoretic Nash sense.