Minimizing Regret: The General Case

In repeated games with differential information on one side, the labelling "general case" refers to games in which the action of the informed player is not known to the uninformed, who can only observe a signal which is the random outcome of his and his opponent's action. Here we consider the problem of minimizing regret (in the sense first formulated by Hannan [8]) when the information available is of this type. We give a simple condition describing the approachable set.Minimize regret;differential information;approachability

Optimal Taxes Without Commitment.

In the problem of optimal taxation in an economy with two productive factors, labor and capital, the optimal solution when the government can commit to a sequence of tax rates, has the tax on capital tending to zero in the limit, with all the tax burden on labour. It is well known, however, that this solution is time inconsistent; so if the commitment power is not perfect, this second best tax plan will not be suitable. We model explicitly the tradeoff between the cost of revising the tax plan, and the benefit of the revision.FISCAL POLICY;CAPITAL;TAXES;TAXATION

Sophisticated Players and Sophisticated Agents

A sophisticated player is an individual who takes the action of the opponents, in a strategic situation, as determined by decision of rational opponents, and acts accordingly. A sophisticated agent is rational in the choice of his action, but ignores the fact that he is part of a strategic situation. We discuss a notion of equilibrium with sophisticated agents, we provide conditions for its existence, and argue that it differs systematically from the Nash equilibrium.Procedural rationality;sophisticated agents

Pay Enough - Or Don't Pay at All

Abstract: Economics seems largely based on the assumption that monetary incentives improve performance. By contrast, a large literature in psychology, including a rich tradition of experimental work, claims just the opposite. In this paper we present and discuss a set of experiments designed to test the effect of different monetary compensations on performance. In our experiments we find that whenever money is offered, a larger amount yields a higher performance. It is not true, however, that offering money always induces a higher performance: participants who were offered a small payoff gave a worse performance than those who were offered no compensation at all. These results suggest that the behavior of participants is influenced by their perception of the contract that is offered to them. When the contract offers money the environment is perceived as monetary, and participants respond in a qualitatively different way in monetary and non-monetary environments. In a different set of experiments we test subjects who, acting as principals, have to provide the appropriate incentive to agents. We show that principals do not anticipate the drastic difference in behavior. The vast majority of principals seem to think incorrectly that a larger compensation is unambiguously a better incentive.Monetary incentives;performance;motivation;principal-agent

Skill, Strategy and Passion: An Empirical Analysis of Soccer

zero sum games;motivation;rationality;natural experiments;sports;soccer

Sequential Common Agency

In a common agency game a set of principals promises monetary transfers to an agent which depend on the action he will take. The agent then chooses the action, and is paid the corresponding transfers. Principals announce their transfers simultaneously. This game has many equilibria; Bernheim and Whinston ([1]) prove that the action chosen in the coalition-proof equilibrium is e±cient. The coalition-proof equilibria have an alternative characterization as truthful equilibria. The other equilibria may be inefficient. Here we study the sequential formulation of the common agency game: principals announce their transfers sequentially. We prove that the set of equilibria is different in many important ways. The outcome is efficient in all the equilibria. The truthful equilibria still exist, but are no longer coalition-proof. Focal equilibria are now a different type of equilibria, that we call thrifty. In thrifty equilibria of the sequential games, principals are better off (and the agent worse off) than in the truthful equilibria of the simultaneous common agency. These results suggest that the sequential game is more desirable institution, because it does not have ine±cient equilibrium outcomes; but it is less likely to emerge when agents have the power to design the institution.Common agency;sequential games;principal agent games;political influence

Your Morals are Your Moods

We test the effect of players' moods on their behavior in a gift-exchange game.In the first stage of the game, player 1 chooses a transfer to player 2.In the second stage, player 2 chooses an effort level.Higher effort is more costly for player 2, but it increases player 1's payoff.We say that player 2 reciprocates if effort is increasing in the transfer received.Player 2 is generous if an effort is incurred even when no transfer is received.Subjects play this game in two different moods.To induce a `bad mood', subjects in the role of player 2 watched a sad movie before playing the game; to induce a `good mood', they watched a funny movie.Mood induction was effective: subjects who saw the funny movie reported a significantly better mood than those who saw the sad movie.These two moods lead to significant differences in player 2's behavior.We find that a bad mood implies more reciprocity while a good mood implies more generosity.Since high transfers are relatively more common, player 1 make more money when second movers are in a bad mood.rationality;motivation;game theory;emotions;reciprocity;gift giving

Learning to coordinate in a complex and non-stationary world

We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the Minority Game and using the replica formalism we show the existence of an equilibrium phase transition as a function of the ratio between the memory $\lambda$ and the learning rates $\Gamma$ of the agents. We show that, starting from a random configuration, a dynamic phase transition also exists, which prevents the system from reaching any Nash equilibria. Furthermore, in a non-stationary environment, we show by numerical simulations that agents with infinite memory play worst than others with less memory and that the dynamic transition naturally arises independently from the initial conditions.Comment: 4 pages, 3 figure

Sophisticated Players and Sophisticated Agents

A sophisticated player is an individual who takes the action of the opponents, in a strategic situation, as determined by decision of rational opponents, and acts accordingly. A sophisticated agent is rational in the choice of his action, but ignores the fact that he is part of a strategic situation. We discuss a notion of equilibrium with sophisticated agents, we provide conditions for its existence, and argue that it differs systematically from the Nash equilibrium