Optimal Categorization

The importance of categorical reasoning in human cognition is well-established in psychology and cognitive science, and it is generally acknowledged that one of the most important functions of categorization is to facilitate prediction. This paper provides a model of optimal categorization. In the beginning of each period a subject observes a two-dimensional object in one dimension and wants to predict the object's value in the other dimension. The subject partitions the space of objects into categories. She has a data base of objects that were observed in both dimensions in the past. The subject determines what category the new object belongs to on the basis of observation of its first dimension. The average value in the second dimension, of objects in this category in the data base, is used as prediction for the object at hand. At the end of each period the second dimension is observed and the observation is stored in the data base. The main result is that the optimal number of categories is determined by a trade-off between (a) decreasing the size of categories in order to enhance category homogeneity, and (b) increasing the size of categories in order to enhance category sample size.Categorization; Priors; Prediction; Similarity-Based Reasoning.

Evolution of Theories of Mind

This paper studies the evolution of peoples' models of how other people think -- their theories of mind. First, this is formalized within the level-k model, which postulates a hierarchy of types, such that type k plays a k times iterated best response to the uniform distribution. It is found that, under plausible conditions, lower types co-exist with higher types. The results are extended to a model of learning, in which type k plays a k times iterated best response the average of past play. The results are also extended to the cognitive hierarchy model, and to the introduction of a type that plays a Nash equilibrium.Theory of Mind; Evolution; Learning; Level-k; Fictitious Play; Cognitive Hierarchy

Optimal categorization

The importance of categorical reasoning in human cognition is well-established in psychology and cognitive science, and it is generally acknowledged that one of the most important functions of categorization is to facilitate prediction. This paper provides a model of optimal categorization. In the beginning of each period a subject observes a two-dimensional object in one dimension and wants to predict the object's value in the other dimension. The subject partitions the space of objects into categories. She has a data base of objects that were observed in both dimensions in the past. The subject determines what category the new object belongs to on the basis of observation of its first dimension. The average value in the second dimension, of objects in this category in the data base, is used as prediction for the object at hand. At the end of each period the second dimension is observed and the observation is stored in the data base. The main result is that the optimal number of categories is determined by a trade-off between (a) decreasing the size of categories in order to enhance category homogeneity, and (b) increasing the size of categories in order to enhance category sample size

The Cry Wolf Effect in Evacuation: a Game-Theoretic Approach

In today's terrorism-prone and security-focused world, evacuation emergencies, drills, and false alarms are becoming more and more common. Compliance to an evacuation order made by an authority in case of emergency can play a key role in the outcome of an emergency. In case an evacuee experiences repeated emergency scenarios which may be a false alarm (e.g., an evacuation drill, a false bomb threat, etc.) or an actual threat, the Aesop's cry wolf effect (repeated false alarms decrease order compliance) can severely affect his/her likelihood to evacuate. To analyse this key unsolved issue of evacuation research, a game-theoretic approach is proposed. Game theory is used to explore mutual best responses of an evacuee and an authority. In the proposed model the authority obtains a signal of whether there is a threat or not and decides whether to order an evacuation or not. The evacuee, after receiving an evacuation order, subsequently decides whether to stay or leave based on posterior beliefs that have been updated in response to the authority's action. Best-responses are derived and Sequential equilibrium and Perfect Bayesian Equilibrium are used as solution concepts (refining equilibria with the intuitive criterion). Model results highlight the benefits of announced evacuation drills and suggest that improving the accuracy of threat detection can prevent large inefficiencies associated with the cry wolf effect.Comment: To be published in Physica

Social Learning and the Shadow of the Past

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are learning rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a learning rule for which the initial state has a lasting impact

Social Learning and the Shadow of the Past

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are learning rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a learning rule for which the initial state has a lasting impact

Observations on Cooperation

We study environments in which agents are randomly matched to play a game, and before the interaction begins each agent observes a limited amount of information about the partner's aggregate behavior. We develop a novel modeling approach for such environments and apply it to study the Prisoner's Dilemma. We first show that defection is evolutionarily stable for any level of observability and behavioral noise. Next we classify the Prisoner's Dilemma into four categories of games, and we fully characterize when cooperation is evolutionarily stable in each of them

Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli

We develop a framework in which individuals preferences co-evolve with their abilities to deceive others regarding their preferences and intentions. We show that a pure outcome is stable, essentially if and only if it is an efficient Nash equilibrium. All individuals have the same deception ability in such a stable state. In contrast, there are non-pure outcomes in which non-Nash outcomes are played, and different deception abilities co-exist. We extend our model to study preferences that depend also on the opponent's type

Stable Observable Behavior

We study stable behavior when players are randomly matched to play a game, and before the game begins each player may observe how his partner behaved in a few interactions in the past. We present a novel modeling approach and we show that strict Nash equilibria are always stable in such environments. We apply the model to study the Prisoner's Dilemma. We show that if players only observe past actions, then defection is the unique stable outcome. However, if players are able to observe past action profiles, then cooperation is also stable. Finally, we present extensions that study endogenous observation probabilities and the evolution of preferences

Unique Stationary Behavior

We study environments in which agents from a large population are randomly matched to play a one-shot game, and, before the interaction begins, each agent observes noisy information about the partner's aggregate behavior. Agents follow stationary strategies that depend on the observed signal. We show that every strategy distribution admits a unique behavior if each player observe on average less than action of his partner. On the other hand, if each player observes on average more than one action, we show that there exists a stationary strategy that admits multiple consistent outcomes