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65
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 143 (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.
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 71 (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.
Persuasion bias, social influence, and unidimensional opinions. The Quarterly
 Journal of Economics
, 2003
"... We propose a boundedlyrational model of opinion formation in which individuals are subject to persuasion bias; that is, they fail to account for possible repetition in the information they receive. We show that persuasion bias implies the phenomenon of social influence, whereby one’s influence on g ..."
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Cited by 44 (0 self)
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We propose a boundedlyrational model of opinion formation in which individuals are subject to persuasion bias; that is, they fail to account for possible repetition in the information they receive. We show that persuasion bias implies the phenomenon of social influence, whereby one’s influence on group opinions depends not only on accuracy, but also on how wellconnected one is in the social network that determines communication. Persuasion bias also implies the phenomenon of unidimensional opinions; that is, individuals ’ opinions over a multidimensional set of issues converge to a single “leftright ” spectrum. We explore the implications of our model in several natural settings, including political science and marketing, and we obtain a number of novel empirical implications.
Reasoning about knowledge: An overview
 Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning About Knowledge
, 1986
"... Abstract: In this overview paper, I will attempt to identify and describe some of the common threads that tie together work in reasoning about knowledge in such diverse fields as philosophy, economics, linguistics, artificial intelligence, and theoretical computer sciencce. I will briefly discuss so ..."
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Cited by 31 (3 self)
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Abstract: In this overview paper, I will attempt to identify and describe some of the common threads that tie together work in reasoning about knowledge in such diverse fields as philosophy, economics, linguistics, artificial intelligence, and theoretical computer sciencce. I will briefly discuss some of the more recent work, particularly in computer science, and suggest some lines for future research.
Ignoring ignorance and agreeing to disagree
 J. of Economic Theory
, 1990
"... A model of information structure and common knowledge is presented which does not take states of the world as primitive. Rather, these states are constructed as sets of propositions, including propositions which describe knowledge. In this model information structure and measurability structure are ..."
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Cited by 30 (3 self)
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A model of information structure and common knowledge is presented which does not take states of the world as primitive. Rather, these states are constructed as sets of propositions, including propositions which describe knowledge. In this model information structure and measurability structure are endogenously defined in terms of the relation between the propositions. In particular, when agents are ignorant of their own ignorance, the information structure is not a partition of the state space. We show that Aumann’s (Ann. Statist. 4 (1976), 12361239) famous result on the impossibility of agreeing to disagree, which was proved for partitions, can be extended to such information structures. Journal of Economic Literature Classification Numbers: 021, 026. 0 1990 Academic press, hc. 1.
Dynamic interactive epistemology
, 2004
"... The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various gametheoretic solution concepts. Much of this work is based around the (static) Aumann structure model of interactive epistemology, but more recently dynamic models of interactive rea ..."
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Cited by 24 (1 self)
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The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various gametheoretic solution concepts. Much of this work is based around the (static) Aumann structure model of interactive epistemology, but more recently dynamic models of interactive reasoning have been developed, most notably by Stalnaker [Econ. Philos. 12 (1996) 133– 163] and Battigalli and Siniscalchi [J. Econ. Theory 88 (1999) 188–230], and used to analyze rational play in extensive form games. But while the properties of Aumann structures are well understood, without a formal language in which belief and belief revision statements can be expressed, it is unclear exactly what are the properties of these dynamic models. Here we investigate this question by defining such a language. A semantics and syntax are presented, with soundness and completeness theorems linking the two.
Computation in a Distributed Information Market
, 2003
"... According to economic theory, supported by empirical and laboratory evidence, the equilibrium price of a financial security reflects all of the information regarding the security's value. We investigate the dynamics of the computational process on the path toward equilibrium, where information dis ..."
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Cited by 22 (4 self)
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According to economic theory, supported by empirical and laboratory evidence, the equilibrium price of a financial security reflects all of the information regarding the security's value. We investigate the dynamics of the computational process on the path toward equilibrium, where information distributed among traders is revealed stepby step over time and incorporated into the market price. We develop a simplified model of an information market, along with trading strategies, in order to formalize the computational properties of the process. We show that securities whose payoffs cannot be expressed as a weighted threshold function of distributed input bits are not guaranteed to converge to the proper equilibrium predicted by economic theory. On the other hand, securities whose payoffs are threshold functions are guaranteed to converge, for all prior probability distributions. Moreover, these threshold securities converge in at most n rounds, where n is the number of bits of distributed information. We also prove a lower bound, showing a type of threshold security that requires at least n/2 rounds to converge in the worst case.
Information Aggregation in Dynamic Markets with Strategic Traders,” Working Paper
, 2009
"... This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a bounded time interval, and in every equilibrium, as ..."
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Cited by 21 (0 self)
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This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a bounded time interval, and in every equilibrium, as time approaches the end of the interval, the market price of a “separable” security converges in probability to its expected value conditional on the traders ’ pooled information. If the security is “nonseparable, ” then there exists a common prior over the states of the world and an equilibrium such that information does not get aggregated. The class of separable securities includes, among others, ArrowDebreu securities, whose value is one in one state of the world and zero in all others, and “additive ” securities, whose value can be interpreted as the sum of traders ’ signals.
Convergence and asymptotic agreement in distributed decision problems
 IEEE Trans. Automat. Contr
, 1984
"... AbstractWe consider a distributed team decision problem in nrhich A relatedand much more general situationis the subject of different agents obtain from the environment different stochastic measure this paper; we assume that the agents are not just interested in ments, possibly at different rand ..."
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Cited by 21 (2 self)
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AbstractWe consider a distributed team decision problem in nrhich A relatedand much more general situationis the subject of different agents obtain from the environment different stochastic measure this paper; we assume that the agents are not just interested in ments, possibly at different random times, related to the same uncertain obtaining an optimal estimate or a likelihood ratio, but their random vector. Each agent has the same objective function and prior objective is to try to minimize some common cost function, given probability distribution. We assume that each agent can compute an the available information. (Clearly, if each agent has a different optimal tentative decision based upon his om observation and that these cost function, no agreement is possible even if each agent had tentative decisions are communicated and received, possibly at random identical information.) In th~s setting. we assume that agents times, by a subset of other agents. Conditions for asymptotic convergence communicate to each other tentative decisions (which initially of each agent’s decision sequence and asymptotic agreement of all agents ’ will be different). That is, at any time, an agent computes an decisions are derived. optimal decision given the information he possesses and communicates it to other agents. Whenever an agent receives such a I.
Social software
 Synthese
, 2001
"... We suggest that the issue of constructing and verifying social procedures, which we suggestively call social software, be pursued as systematically as computer software is pursued by computer scientists. Certain complications do arise with social software which do not arise with computer software, b ..."
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Cited by 19 (4 self)
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We suggest that the issue of constructing and verifying social procedures, which we suggestively call social software, be pursued as systematically as computer software is pursued by computer scientists. Certain complications do arise with social software which do not arise with computer software, but the similarities are nonetheless strong, and tools already exist which would enable us to start work on this important project. We give a variety of suggestive examples and indicate some theoretical work which already exists. I send someone shopping. I give him a slip marked “five red apples”. He takes the slip to the shopkeeper who opens a drawer marked “apples”; then he looks up the word “red ” in a table and finds a colour sample opposite it; then he says the series of cardinal numbers – I assume he knows them by heart – up to the word “five ” and for each number he takes an apple of the same colour as the sample out of the drawer. “But what is the “meaning of the word ‘five’? ” No such thing was in question here, only how the word “five ” is used. In this passage from the Philosophical Investigations Wittgenstein is describing a social algorithm, albeit a simple one. He also introduces the notion of a data type (though not by that name) which is now quite important in computer algorithms. The words “apple”, “red”, “five ” belong to different data types and are used in very different ways. This variety forms a sharp contrast to the uniformity of objects in set theory, where everything, natural numbers, reals, etc. are constructed from the same basic material. But it does form a parallel to the variety we find in computer algorithms. In computer algorithms we also find integers, stacks, queues, and pointers which play different sorts of roles. Wittgenstein’s purpose in his example is to wean us away from the notion that there is just one kind of thing – meaning – which explains all different kinds of words, and he uses 1