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How canonical is the canonical model? A comment on Aumann's interactive epistemology

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Aumann (1989) argued that the natural partitions on the space of all maximally consistent sets of formulas in multi-player S5 logic are necessarily "commonly known" by the players. We show, however, that there are many other sets of partitions on this space that conform with the formulas that build the states - as many as there are subsets of th...

Aumann (1989) argued that the natural partitions on the space of all maximally consistent sets of formulas in multi-player S5 logic are necessarily "commonly known" by the players. We show, however, that there are many other sets of partitions on this space that conform with the formulas that build the states - as many as there are subsets of the continuum! Thus, assuming a set of partitions on this space is "common knowledge" is an informal but meaningful meta-assumption. ; Common knowledge · epistemic logic Minimize

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On the Evolutionary Emergence of Optimism

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Successful individuals were frequently found to be overly optimistic. This is puzzling because it might be thought that optimistic individuals who consistently overestimate their eventual payoffs will not do as well as realists who see the situation as it truly is and hence will not survive evolutionary pressures. We show that contrary to this i...

Successful individuals were frequently found to be overly optimistic. This is puzzling because it might be thought that optimistic individuals who consistently overestimate their eventual payoffs will not do as well as realists who see the situation as it truly is and hence will not survive evolutionary pressures. We show that contrary to this intuition, there is a large class of either competitive or cooperative strategic interactions between randomly matched pairs of individuals in the population, in which "cautiously" optimistic individuals not only survive but also prosper and take over the entire population. The reason for this result is that optimistic individuals who overestimate the impact of their actions on their payoffs, behave more aggressively than realists and pessimists. When the interactions between individuals involve negative externalities (the payoff of one player decreases with the actions taken by another player) and the actions are strategic substitutes, being aggressive induces the opponent to be softer, so optimists gain a strategic advantage that, for moderate levels of optimism, outweighs the loss from having the wrong perception of the environment. Likewise, when the interactions between individuals involve positive externalities and the actions are strategic complements, being aggressive triggers a favorable aggressive behavior from the opponent. Hence, in both cases, cautiously optimistic types fare better on average than other types of individuals. We show that if the initial distribution of types is sufficiently wide, then over time it will converge in distribution to a mass point on some level of cautious optimism. Minimize

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Topology-Free Typology of Beliefs

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In their seminal paper, Mertens and Zamir (1985) proved the existence of a universal Harsanyi type space which consists of all possible types. Their method of proof depends crucially on topological assumptions. Whether such assumptions are essential to the existence of a universal space remained an open problem. We answer it here by proving that...

In their seminal paper, Mertens and Zamir (1985) proved the existence of a universal Harsanyi type space which consists of all possible types. Their method of proof depends crucially on topological assumptions. Whether such assumptions are essential to the existence of a universal space remained an open problem. We answer it here by proving that a universal type space does exist even when spaces are defined in pure measure theoretic terms. Heifetz and Samet (1996) showed that coherent hierarchies of beliefs, in the measure theoretic case, do not necessarily describe types. Therefore, the universal space here differs from all previously studied ones, in that it does not necessarily consist of all coherent hierarchies of beliefs. ; Harsanyi types, Universal type spaces Minimize

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On the Generic (Im)possibility of Full Surplus Extraction in Mechanism Design

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A number of studies, most notably Cr?mer and McLean (1985, 1988), have shown that in Harsanyi type spaces of a fixed finite size, it is generically possible to design mechanisms that extract all the surplus from players, and as a consequence, implement any outcome as if the players’ private information were commonly known. In contrast, we show t...

A number of studies, most notably Cr?mer and McLean (1985, 1988), have shown that in Harsanyi type spaces of a fixed finite size, it is generically possible to design mechanisms that extract all the surplus from players, and as a consequence, implement any outcome as if the players’ private information were commonly known. In contrast, we show that within the set of common priors on the universal type space, the subset of priors that permit the extraction of the players’ full surplus is shy. Shyness is a notion of smallness for convex subsets of infinite-dimensional topological vector spaces (in our case, the set of common priors), which generalizes the usual notion of zero Lebesgue measure in finite-dimensional spaces. ; surplus extraction; information rents; mechanism design; private information; universal type space; genericity; prevalence Minimize

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On the Evolutionary Emergence of Optimism

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dispositions, evolution of preferences, selection dynamics, perception biases, interdependent preferences, imperfect observability

dispositions, evolution of preferences, selection dynamics, perception biases, interdependent preferences, imperfect observability Minimize

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Read My Lips, Watch for Leaps: Preference Equilibrium and Political Instability

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As norms and tastes adapt to the social conditions shaped by policy variables, voters' opinions about these policies may evolve as well. We show how this process can lead to political instability. Moreover, if a politician's platform is shaped opportunistically so as to gain the majority's support, once in office the politician should not implem...

As norms and tastes adapt to the social conditions shaped by policy variables, voters' opinions about these policies may evolve as well. We show how this process can lead to political instability. Moreover, if a politician's platform is shaped opportunistically so as to gain the majority's support, once in office the politician should not implement the promised policy in order to remain popular and get re-elected. Rather, the effective policy in this respect is the one which will be deemed optimal by most voters after the norms and opinions will adjust to that very policy. Copyright 2006 Royal Economic Society. Minimize

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Aspiration Traps

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Fundamental choices, like location or education, affect the attitudes and beliefs with which the individual will analyze future day to day decision problems. These effects cannot be assumed to be transparent to the individual. To restore methodological discipline in the analysis of such choices, we propose a solution concept based on an idea of ...

Fundamental choices, like location or education, affect the attitudes and beliefs with which the individual will analyze future day to day decision problems. These effects cannot be assumed to be transparent to the individual. To restore methodological discipline in the analysis of such choices, we propose a solution concept based on an idea of consistency: the individual should not regret her fundamental choices after her preferences and beliefs have adjusted thereof. We show that even single person decision problems admit multiple, Pareto-ranked solutions: the individual might be stuck in an aspiration trap. Minimize

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All in good time

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Issue-by-issue bargaining, Endogenous agenda, Asymmetric information, C78, D74, D80

Issue-by-issue bargaining, Endogenous agenda, Asymmetric information, C78, D74, D80 Minimize

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On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design

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A number of studies, most notably Crémer and McLean (1985, 1988), have shown that in generic type spaces that admit a common prior and are of a fixed finite size, an uninformed seller can design mechanisms that extract all the surplus from privately informed bidders. We show that this result hinges on the nonconvexity of such a family of priors....

A number of studies, most notably Crémer and McLean (1985, 1988), have shown that in generic type spaces that admit a common prior and are of a fixed finite size, an uninformed seller can design mechanisms that extract all the surplus from privately informed bidders. We show that this result hinges on the nonconvexity of such a family of priors. When the ambient family of priors is convex, generic priors do not allow for full surplus extraction provided that for at least one prior in this family, players' beliefs about other players' types do not pin down the players' own preferences. In particular, full surplus extraction is generically impossible in finite type spaces with a common prior. Similarly, generic priors on the universal type space do not allow for full surplus extraction. Copyright The Econometric Society 2006. Minimize

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Rationalizable Expectations

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Consider an exchange economy with asymmetric information. What is the set of outcomes that are consistent with common knowledge of rationality and market clearing? We propose the concept of CKRMC as an answer to this question. The set of price functions that are CKRMC is the maximal set F with the property that every f?F defi?nes prices that cle...

Consider an exchange economy with asymmetric information. What is the set of outcomes that are consistent with common knowledge of rationality and market clearing? We propose the concept of CKRMC as an answer to this question. The set of price functions that are CKRMC is the maximal set F with the property that every f?F defi?nes prices that clear the markets for demands that can be rationalized by some profile of subjective beliefs on F. Thus, the difference between CKRMC and Rational Expectations Equilibrium (REE) is that CKRMC allows for a situation where the agents do not know the true price function and furthermore may have different beliefs about it. We characterize CKRMC, study its properties, and apply it to a general class of economies with two commodities. CKRMC manifests intuitive properties that stand in contrast to the full revelation property of REE. In particular, we obtain that for a broad class of economies: (1) There is a whole range of prices that are CKRMC in every state. (2) The set of CKRMC outcomes is monotonic with the amount of information in the economy. Minimize

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