Imprecise Beliefs in a Principal Agent Model

This paper presents a principal-agent model where the agent has multiple, or imprecise, beliefs. We model this situation formally by assuming the agent's preferences are incomplete. One can interpret this multiplicity as an agent's limited knowledge of the surrounding environment. In this setting, incentives need to be robust to the agent's different beliefs. We study whether robustness implies simplicity. Under mild conditions, we show the unique optimal contract has a two-wage structure; a °at payment and bonus. That is, all output levels are divided into two groups, and the optimal incentive scheme pays the same amount for all output levels in each group. We also show that a two-state two-action framework can be thought of as a reduced form of the original model. We solve explicitly the principal's problem in this case, and discuss some implications of our model for firm ownership.

Automatic Generation of CHR Constraint Solvers

In this paper, we present a framework for automatic generation of CHR solvers given the logical specification of the constraints. This approach takes advantage of the power of tabled resolution for constraint logic programming, in order to check the validity of the rules. Compared to previous works where different methods for automatic generation of constraint solvers have been proposed, our approach enables the generation of more expressive rules (even recursive and splitting rules) that can be used directly as CHR solvers.Comment: to be published in Theory and Practice of Logic Programming, 16 pages, 2 figure

The Sport League's Dilemma: Competitive Balance versus Incentives to Win

We analyze a dynamic model of strategic interaction between a professional sport league that organizes a tournament, the teams competing to win it, and the broadcasters paying for the rights to televise it.Teams and broadcasters maximize expected profits, while the league's objective may be either to maximize the demand for the sport or to maximize the teams'joint profits.Demand depends positively on symmetry among teams (competitive balance) and how aggressively teams try to win (incentives to win).Revenue sharing increases competitive balance but decreases incentives to win.Under demand maximization, a performance-based reward scheme (used by European sport leagues) may be optimal. Under joint profit maximization, full revenue sharing (used by many US leagues) is always optimal.These results reflect institutional differences among European and American sports leagues.sport;competition;incentives;broadcasting industry;revenue sharing

The Sport League's Dilemma: Competitive Balance versus Incentives to Win

We analyze a dynamic model of strategic interaction between a professional sport league that organizes a tournament, the teams competing to win it, and the broadcasters paying for the rights to televise it. Teams and broadcasters maximize expected profits, while the league's objective may be either to maximize the demand for the sport or to maximize the teams' joint profits. Demand depends positively on symmetry among teams (competitive balance) and how aggressively teams try to win (incentives to win). Revenue sharing increases competitive balance but decreases incentives to win. Under demand maximization, a performance-based reward scheme (used by European sport leagues) may be optimal. Under joint profit maximization, full revenue sharing (used by many US leagues) is always optimal. These results reflect institutional differences among European and American sports leagues.

Uncertainty and Risk in Financial Markets

This paper considers a general equilibrium model in which the=20 distinction between un-certainty and risk is formalized by assuming agents= =20 have incomplete preferences over state-contingent consumption bundles, as=20 in Bewley (1986). Without completeness, individual decision making depends= =20 on a set of probability distributions over the state space. A bundle is=20 preferred to another if and only if it has larger expected utility for all= =20 probabilities in this set. When preferences are complete this set is a=20 singleton, and the model reduces to standard expected utility. In this=20 setting, we characterize Pareto optima and equilibria, and show that the=20 presence of uncertainty generates robust indeterminacies in equilibrium=20 prices and allocations for any speci=AFcation of initial endowments. We=20 derive comparative statics results linking the degree of uncertainty with=20 changes in equilibria. Despite the presence of robust indeterminacies, we=20 show that equilibrium prices and allocations vary continuously with=20 underlying fundamentals. Equilibria in a standard risk economy are thus=20 robust to adding small degrees of uncertainty. Finally, we give conditions= =20 under which some assets are not traded due to uncertainty aversion.

Skill, Strategy and Passion: An Empirical Analysis of Soccer

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

Skill, Strategy, and Passion: an Empirical Analysis of Soccer

Sports provide a natural experiment on individual choices in games with high stakes. We study soccer with a game-theoretic model of a match, and then evaluate the ability of this model to explain actual behavior with data from 2885 matches among professional teams. In our model, the strategy of a team depends on the current state of the game. When the game is tied, both teams attack. A losing team always attacks, while its winning opponent attacks early in the game, but it starts defending as the end of the match nears. We find that teams' skills, current score, and home field advantage are significant explanatory variables of the probability of scoring. We also find that a team which falls behind is relatively more likely to score. A team which is ahead, on the other hand, uses a conservative strategy very early in the match. These results support the main conclusions of our model. They indicate that soccer teams behave consistently with rationality and equilibrium. However, there is significant evidence that emotional factors are roughly as important as rational ones in determining the game's outcome, and they affect the strategic decisions of teams.

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 makes more money when second movers are in a bad mood.