Paper # Author Title
There is a large repeated games literature illustrating how future interactions provide incentives for cooperation. Much of the earlier literature assumes public monitoring. Departures from public monitoring to private monitoring that incorporate differences in players’ observations may dramatically complicate coordination and the provision of incentives, with the consequence that equilibria with private monitoring often seem unrealistically complex or fragile. We set out a model in which players accomplish cooperation in an intuitively plausible fashion. Players process information via a mental system — a set of psychological states and a transition function between states depending on observations. Players restrict attention to a relatively small set of simple strategies, and consequently, might learn which perform well. Download Paper
Much of the repeated game literature is concerned with proving Folk Theorems. The logic of the exercise is to specify a particular game, and to explore for that game specification whether any given feasible (and individually rational) value vector can be an equilibrium outcome for some strategies when agents are sufficiently patient. A game specification includes a description of what agents observe at each stage. This is done by defining a monitoring structure, that is, a collection of probability distributions over the signals players receive (one distribution for each action profile players may play). Although this is simply meant to capture the fact that players don’t directly observe the actions chosen by others, constructed equilibria often depend on players precisely knowing these distributions, somewhat unrealistic in most problems of interest. We revisit the classic Folk Theorem for games with imperfect public monitoring, asking that incentive conditions hold not only for a precisely defined monitoring structure, but also for a ball of monitoring structures containing it. We show that efficiency and incentives are no longer compatible. Download Paper
The repeated game literature studies long run/repeated interactions, aiming to understand how repetition may foster cooperation. Conditioning future behavior on past play is crucial in this endeavor. For most situations of interest a given player does not directly observe the actions chosen by other players and must rely on noisy signals he receives about those actions. This is typically incorporated into models by defining a monitoring structure, that is, a collection of probability distributions over the signals each player receives (one distribution for each action profile players may play). Although this is simply meant to capture the fact that players don.t directly observe the actions chosen by others, constructed equilibria often depend on players precisely knowing the distributions, somewhat unrealistic in most problems of interest. This paper aims to show the fragility of belief free equilibrium constructions when one adds shocks to the monitoring structure in repeated games. Download Paper
Standard Bayesian models assume agents know and fully exploit prior distributions over types. We are interested in modeling agents who lack detailed knowledge of prior distributions. In auctions, that agents know priors has two consequences: (i) signals about own valuation come with precise inference about signals received by others; (ii) noisier estimates translate into more weight put on priors. We revisit classic questions in auction theory, exploring environments in which no such complex inferences are precluded. This is done in a parsimonious model of auctions in which agents are restricted to using simple strategies. Download Paper
There is a large repeated games literature illustrating how future interactions provide incentives for cooperation. Much of the earlier literature assumes public monitoring: players always observe precisely the same thing. Departures from public monitoring to private monitoring that incorporate differences in players’ observations may dramatically complicate coordination and the provision of incentives, with the consequence that equilibria with private monitoring often seem unrealistically complex. We set out a model in which players accomplish cooperation in an intuitively plausible fashion. Players process information via a mental system — a set of psychological states and a transition function between states depending on observations. Players restrict attention to a relatively small set of simple strategies, and consequently, might learn which perform well. Download Paper
Consider an agent who is unsure of the state of the world and faces computational bounds on mental processing. The agent receives a sequence of signals imperfectly correlated with the true state that he will use to take a single decision. The agent is assumed to have a finite number of "states of mind" that quantify his beliefs about the relative likelihood of the states, and uses the signals he receives to move from one state to another. At a random stopping time, the agent will be called upon to make a decision based solely on his mental state at that time. We show that under quite general conditions it is optimal that the agent ignore signals that are not very informative, that is, signals for which the likelihood of the states is nearly equal. This model provides a possible explanation of systematic inference mistakes people may make. Download Paper
There is a large repeated games literature illustrating how future interactions provide incentives for cooperation. Much of this literature assumes public monitoring: players always observe precisely the same thing. Even slight deviations from public monitoring to private monitoring that incorporate differences in players’ observations dramatically complicate coordination. Equilibria with private monitoring often seem unrealistically complex. We set out a model in which players accomplish cooperation in an intuitively plausible fashion. Players process information via a mental system — a set of psychological states and a transition function between states depending on observations. Players restrict attention to a relatively small set of simple strategies, and consequently, might learn which perform well. Download Paper
There is a large repeated games literature illustrating how future interactions provide incentives for cooperation. Much of this literature assumes public monitoring: players always observe precisely the same thing. Even slight deviations from public monitoring to private monitoring that incorporate differences in players’ observations dramatically complicate coordination. Equilibria with private monitoring often seem unrealistically complex. We set out a model in which players accomplish cooperation in an intuitively plausible fashion. Players process information via a mental system — a set of psychological states and a transition function between states depending on observations. Players restrict attention to a relatively small set of simple strategies, and consequently, might learn which perform well. Download Paper
Many important strategic problems are characterized by repeated interactions among agents. There is a large literature in game theory and economics illustrating how considerations of future interactions can provide incentives for cooperation that would not be possible in one-shot interactions. Much of the work in repeated games assumes public monitoring: players observe precisely the same thing at each stage of the game. It is well-understood that even slight deviations from public monitoring increase dramatically the difficulty the problems players face in coordinating their actions. Repeated games with private monitoring incorporate differences in what players observe at each stage. Equilibria in repeated games with private monitoring, however, often seem unrealistic; the equilibrium strategies may be highly complex and very sensitive to the fine details of the stochastic relationship between players’ actions and observations. Furthermore, there is no realistic story about how players might arrive at their equilibrium strategies.  We propose an alternative approach to understanding how people cooperate. Each player is endowed with a mental system that processes information: a mental system consists of a number of psychological states and a transition function between states that depends on observations made. In this world, a strategy is just a function from states to actions.  Our framework has the following desirable properties: (i) players restrict attention to a relatively small set of simple strategies. (ii) the number of strategies that players compare is small enough that players might ultimately learn which perform well. We find that some mental systems allow agents to cooperate under a broad set of parameters, while others are not conducive to cooperation. Download Paper
There is ample evidence that emotions affect performance. Positive emotions can improve performance, while negative ones may diminish it. For example, the fears induced by the possibility of failure or of negative evaluations have physiological consequences (shaking, loss of concentration) that may impair performance in sports, on stage or at school. There is also ample evidence that individuals have distorted recollection of past events, and distorted attributions of the causes of successes of failures. Recollection of good events or successes is typically easier than recollection of bad ones or failures. Successes tend to be attributed to intrinsic aptitudes or own effort, while failures are attributed to bad luck. In addition, these attributions are often reversed when judging the performance of others. The objective of this paper is to incorporate the first phenomenon above into an otherwise standard decision theoretic model, and show that in a world where performance depends on emotions, biases in information processing enhance welfare. Download Paper
There is ample evidence that emotions affect performance. Positive emotions can improve performance, while negative ones may diminish it. For example, the fears induced by the possibility of failure or of negative evaluations have physiological consequences (shaking, loss of concentration) that may impair performance in sports, on stage or at school. There is also ample evidence that individuals have distorted recollection of past events, and distorted attributions of the causes of successes of failures. Recollection of good events or successes is typically easier than recollection of bad ones or failures. Successes tend to be attributed to intrinsic aptitudes or own effort, while failures are attributed to bad luck. In addition, these attributions are often reversed when judging the performance of others. The objective of this paper is to incorporate the first phenomenon above into an otherwise standard decision theoretic model, and show that in a world where performance depends on emotions, biases in information processing enhance welfare. Download Paper
There is ample evidence that confidence can affect performance: confidence can improve performance, while a lack of confidence may diminish it. For example. the fears induced by the possibility of failure or of negative evaluations have physiological consequences (shaking, loss of concentration) that may impair performance in sports, on stage or at school. Download Paper