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Knowledge and Common Knowledge in a Distributed Environment
 Journal of the ACM
, 1984
"... : Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system&apo ..."
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Cited by 578 (55 self)
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: Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system's state of knowledge. This paper presents a general framework for formalizing and reasoning about knowledge in distributed systems. We argue that states of knowledge of groups of processors are useful concepts for the design and analysis of distributed protocols. In particular, distributed knowledge corresponds to knowledge that is "distributed" among the members of the group, while common knowledge corresponds to a fact being "publicly known". The relationship between common knowledge and a variety of desirable actions in a distributed system is illustrated. Furthermore, it is shown that, formally speaking, in practical systems common knowledge cannot be attained. A number of weaker variants...
The Nash Bargaining Solution in Economic Modeling
 Rand Journal of Economics
, 1986
"... This article establishes the relationship between the static axiomatic theory of bargaining and the sequential strategic approach to bargaining. We consider two strategic models of alternating offers. The models differ in the source of the incentive of the bargaining parties to reach agreement: the ..."
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Cited by 563 (1 self)
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This article establishes the relationship between the static axiomatic theory of bargaining and the sequential strategic approach to bargaining. We consider two strategic models of alternating offers. The models differ in the source of the incentive of the bargaining parties to reach agreement: the bargainers ' time preference and the risk of breakdown of negotiation. Each of the models has a unique perfect equilibrium. When the motivation to reach agreement is made negligible, in each model the unique perfect equilibrium outcome approaches the Nash bargaining solution, with utilities that reflect the incentive to settle and with the proper disagreement jfoint chosen. The results provide a guide for the application of the Nash bargaining solution in economic modelling. 1.
Rationalizable Strategic Behavior and the Problem of Perfection
 ECONOMETRICA
, 1984
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Global Games: Theory and Applications,
 Advances in Economics and Econometrics (Proceedings of the Eighth World Congress of the Econometric Society),
, 2003
"... Abstract Global games are games of incomplete information whose type space is determined by the players each observing a noisy signal of the underlying state. With strategic complementarities, global games often have a unique, dominance solvable equilibrium, allowing analysis of a number of economi ..."
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Cited by 250 (19 self)
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Abstract Global games are games of incomplete information whose type space is determined by the players each observing a noisy signal of the underlying state. With strategic complementarities, global games often have a unique, dominance solvable equilibrium, allowing analysis of a number of economic models of coordination failure. For symmetric binary action global games, equilibrium strategies in the limit (as noise becomes negligible) are simple to characterize in terms of 'diffuse' beliefs over the actions of others. We describe a number of economic applications that fall in this category. We also explore the distinctive roles of public and private information in this setting, review results for general global games, discuss the relationship between global games and a literature on higher order beliefs in game theory * This paper was prepared for the Eighth World Congress of the Econometric Society (Seattle 2000). Section 3 incorporates work circulated earlier under the title "Private versus Public Information in Coordination Problems." We would like to thank Hans Carlsson, David Frankel, Josef Hofbauer, Jonathan Levin and Ady Pauzner for valuable comments on the paper, and Susan Athey for her insightful remarks as discussant at the Congress. Morris would like to record an important intellectual debt in this area to Atsushi Kajii, through joint research and long discussions. Morris is grateful for financial support from National Science Foundation grant #9709601. and describe the relationship to local interaction games and dynamic games with payoff shocks.
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 236 (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.
Incentives and Incomplete Information
 Journal of Public Economics, XI
, 1979
"... The problem of incentives for correct revelation in a collective decision model is presented as a game with incomplete information. Two approaches to incomplete information are used, a first where the individual beliefs are not introduced and a second where they are. In the first approach it is re ..."
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Cited by 192 (1 self)
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The problem of incentives for correct revelation in a collective decision model is presented as a game with incomplete information. Two approaches to incomplete information are used, a first where the individual beliefs are not introduced and a second where they are. In the first approach it is recalled that the mechanisms for which the solution to the incentive problem is in dominant strategies lead in general to a budgetary problem for the central agency. For these mechanisms a uniqueness property is demonstrated. In the second approach it is shown that if a compatibility condition is imposed on the individual beliefs and if a Bayesian solution is given to the incentive problem, then it is possible to avoid the budgetary problem. 1
Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation
 Journal of Prediction Markets
, 2002
"... In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. ..."
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Cited by 114 (5 self)
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In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals.
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 109 (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