Categorization and correlation in a random-matching game

We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player is a best response to the distribution of actions of his opponents in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game.Random-matching game; Categorization; Correlated equilibrium

Pure self-confirming equilibrium

In a Self-Confirming Equilibrium (Fudenberg and Levine, 1993A) every player obtains partial information about other players' strategies and plays a best response to some conjecture which is consistent with his information. Two kinds of information structures are considered: In the first each player observes his own payoff while in the second the information is the distribution of players among the various actions. For each of these information structures we prove that pure Self-Confirming Equilibrium exists in some classes of games. Pure Nash equilibrium may fail to exist in these classes.Self-Confirming Equilibrium; Pure Equilibrium; Imperfect Monitoring

THE VALUE OF A STOCHASTIC INFORMATION STRUCTURE

Upon observing a signal, a Bayesian decision maker updates her probability distribution over the state space, chooses an action, and receives a payoff that depends on the state and the action taken. An information structure determines the set of possible signals and the probability of each signal given a state. For a fixed decision problem (consisting of a state space, action set and utility function) the value of an information structure is the maximal expected utility that the decision maker can get when the observed signals are governed by this structure. This note studies the functions defined over information structures that measure their value. It turns out that two conditions play a major role in the characterization of these functions: additive separability and convexity.Information structure, value of information, stochastic information

Cooperative investment games or population games

The model of a cooperative fuzzy game is interpreted as both a population game and a cooperative investment game. Three types of core- like solutions induced by these interpretations are introduced and investigated. The interpretation of a game as a population game allows us to define sub-games. We show that, unlike the well-known Shapley- Shubik theorem on market games (Shapley-Shubik) there might be a population game such that each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a population game needs to be also homogeneous. We also discuss some special classes of population games such as convex games, exact games, homogeneousgames and additive games.investment game, population game, fuzzy game, core-like solution, market game

Categorization generated by prototypes -- an axiomatic approach

We present a model of categorization based on prototypes. A prototype is an image or template of an idealized member of the category. Once a set of prototypes is defined, entities are sorted into categories on the basis of the prototypes they are closest to. We provide a characterization of those categorizations that are generated by prototypes.categorization, prototype, prototype-orineted decision making

On Concavification and Convex Games

We propose a new geometric approach for the analysis of cooperative games. A cooperative game is viewed as a real valued function $u$ defined on a finite set of points in the unit simplex. We define the \emph{concavification} of $u$ on the simplex as the minimal concave function on the simplex which is greater than or equal to $u$. The concavification of $u$ induces a game which is the \emph{totally balanced cover} of the game. The concavification of $u$ is used to characterize well-known classes of games, such as balanced, totally balanced, exact and convex games. As a consequence of the analysis it turns out that a game is convex if and only if each one of its sub-games is exact.concavification, convex games, core, totally balanced, exact games

Characterization of multidimensional spatial models of elections with a valence dimension

Spatial models of political competition are typically based on two assumptions. One is that all the voters identically perceive the platforms of the candidates and agree about their score on a "valence" dimension. The second is that each voter's preferences over policies are decreasing in the distance from that voter's ideal point, and that valence scores enter the utility function in an additively separable way. The goal of this paper is to examine the restrictions that these two assumptions impose, starting from a more primitive (and observable) data. Specifically, we consider the case where only the ideal point in the policy space and the ranking over candidates are known for each voter. We provide necessary and su±cient conditions for this collection of preference relations to be consistent with utility maximization as in the standard models described above. That is, we characterize the case where there are policies x1,...,xm for the m candidates and numbers v1,...,vm representing valence scores, such that a voter with an ideal policy y ranks the candidates according to vi-||xi-y||^2

Thinking categorically about others: A conjectural equilibrium approach

Inspired by the social psychology literature, we study the implications of categorical thinking on decision making in the context of a large normal form game. Every agent has a categorization (partition) of her opponents and can only observe the average behavior in each category. A strategy profile is a Conjectural Categorical Equilibrium (CCE) with respect to a given categorization profile if every player's strategy is a best response to some consistent conjecture about the strategies of her opponents. We show that, for a wide family of games and for a particular categorization profile, every CCE becomes almost Nash as the number of players grows. An equivalence of CCE and Nash equilibrium is achieved in the settings of a non-atomic game. This highlights the advantage of categorization as a simplifying mechanism in complex environments. With much less information in their hands agents behave as if they see the full picture. Some properties of CCE when players categorize `non-optimally' are also considered

Categorization and correlation in a random-matching game

We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player is a best response to the distribution of actions of his opponents in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game