Person:

Fudenberg, Drew

This paper studies the set of equilibrium payoffs in repeated games with long- and short-run players and little discounting. Because the short-run players are unconcerned about the future, each equilibrium outcome is constrained to lie on their static reaction (best-response) curves. The natural extension of the folk theorem to games of this sort would simply include this constraint in the definitions of the feasible payoffs and minmax values. In fact, this extension does obtain under the assumption that each player's choice of a mixed strategy for the stage game is publicly observable but, in contrast to standard repeated games, the set of equilibrium payoffs is different if players can observe only their opponents' realized actions.

We examine games played by a single large player and a large number of opponents who are small, but not anonymous. If the play of the small players is observed with noise, and if the number of actions the large player controls is bounded as the number of small players grows, the equilibrium set converges to that of the game where there is a continuum of small players. This paper extends previous work on the negligibility of small players by dropping the assumption that small players' actions are “anonymous.” That is, we allow each small player's actions to be observed separately, instead of supposing that the small players' actions are only observed through their effect on an aggregate statistic.

We study a variation of fictitious play, in which the probability of each action is an exponential function of that action's utility against the historical frequency of opponents' play. Regardless of the opponents' strategies, the utility received by an agent using this rule is nearly the best that could be achieved against the historical frequency. Such rules are approximately optimal in i.i.d. environments, and guarantee nearly the minmax regardless of opponents' behavior. Fictitious play shares these properties provided it switches 'infrequently' between actions. We also study the long-run outcomes when all players use consistent and cautious rules.

In some experiments rational players who understand the structure of the game could improve their payoff. We bound the size of the observed losses in several such experiments. To do this, we suppose that observed play resembles an equilibrium because players learn about their opponents' play. Consequently, in an extensive-form game, some actions that are not optimal given the true distribution of opponents' play could be optimal given available information. We find that average losses are small: $0.03 to $0.64 per player with stakes between $2 and $30. In one of the three experiments we examine, this also implies a narrow range of outcome.

This paper studies the way that word-of-mouth communication aggregates the information of individual agents. We find that the structure of the communication process determines whether all agents end up making identical choices, with less communication making this conformity more likely. Despite the players' naive decision rules and the stochastic decision environment, word-of-mouth communication may lead all players to adopt the action that is on average superior. These socially efficient outcomes tend to occur when each agent samples only a few others.

In a self-confirming equilibrium, each player correctly forecasts the actions that opponents will take along the equilibrium path, but may be mistaken about the way that opponents would respond to deviations. This paper develops a refinement of self-confirming equilibrium in which players use information about opponents' payoffs in forming beliefs about the way that opponents play off of the equilibrium path. We show that this concept is robust to payoff uncertainty. We also discuss its relationship to other concepts and show that it is closely related to assuming almost common certainty of payoffs in an epistemic model with independent beliefs.

Forecasts are said to be calibrated if the frequency predictions are approximately correct. This is a refinement of an idea first introduced by David Blackwell in 1955. We show that “K-initialized myopic strategies” are approximately calibrated when K is large. These strategies first “initialize” by making each forecast exactly K times, and thereafter play, in each period t, the minmax strategy in a static game.

We present a general algorithm for computing the limit, as δ → 1, of the set of payoffs of perfect public equilibria of repeated games with long-run and short-run players, allowing for the possibility that the players′ actions are not observable by their opponents. We illustrate the algorithm with two economic examples. In a simple partnership we show how to compute the equilibrium payoffs when the folk theorem fails. In an investment game, we show that two competing capitalists subject to moral hazard may both become worse off if their firms are merged and they split the profits from the merger. Finally, we show that with short-run players each long-run player′s highest equilibrium payoff is generally greater when their realized actions are observed.

"Income smoothing" is the process of manipulating the time profile of earnings or earnings reports to make the reported income stream less variable. This paper builds a theory of income smoothing based on the managers' concern about keeping their position or avoiding interference, and on the idea that current performance receives more weight than past performance when one is assessing the future. When investment is added to the model, so that income reports and dividends can be set independently, we find that both dividends and income reports may be smoothed and that dividends may convey information not present in the income report.

This paper studies agents who consider the experiences of their neighbors in deciding which of two technologies to use. We analyze two learning environments, one in which the same technology is optimal for all players and another in which each technology is better for some of them. In both environments, players use exogenously specified rules of thumb that ignore historical data but may incorporate a tendency to use the more popular technology. In some cases these naive rules can lead to fairly efficient decisions in the long run, but adjustment can be slow when a superior technology is first introduced.