Payoffs Of Other Players Research Articles

Identification of Non-Equilibrium Beliefs in Games of Incomplete Information Using Experimental Data

Abstract This paper studies the identification of players’ preferences and beliefs in discrete choice games using experimental data. The experiment comprises a set of games that differ in their matrices of monetary payoffs. The researcher is interested in the identification of preferences (utility of money) and beliefs on the opponents’ expected behavior, without imposing equilibrium restrictions or parametric assumptions on utility and belief functions. We show that the hypothesis of unbiased/rational beliefs is testable as long as the set of games in the experiment imply variation in monetary payoffs of other players, keeping the own monetary payoff constant. We present conditions for the full identification of utility and belief functions at the individual level – without restrictions on players’ heterogeneity in preferences or beliefs. We apply our method to data from two experiments: a matching pennies game, and a public good game.

Games of Love and Hate

A game of love and hate is one in which a player’s payoff is a function of her own action and the payoffs of other players. For each action profile, the associated payoff profile solves an interdependent utility system, and if that solution is bounded and unique for every profile we call the game coherent. Coherent games generate a standard normal form. Our central theorem states that every Nash equilibrium of such a game is Pareto optimal, in sharp contrast to the general prevalence of inefficient equilibria in the presence of externalities. While externalities in our model are restricted to flow only through payoffs there are no other constraints: they could be positive or negative, or of varying sign. We further show that our coherence and continuity requirements are tight.

From hierarchies to levels: new solutions for games with hierarchical structure

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict the players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the hierarchical structure relative to that player. To define each solution, we consider a certain mapping that transforms the hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley value to the class of games with levels structure. Such transformation mappings are studied by means of properties that relate a player’s position in both types of structure.

From Hierarchies to Levels: New Solutions for Games

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the structure relative to that player. To define each of these solutions, we consider a certain mapping that transforms any hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley Value to the class of games with levels structure. The transformations that map the set of hierarchical structures to the set of levels structures are also studied from an axiomatic viewpoint by means of properties that relate a player’s position in both types of structure.

From Hierarchies to Levels: New Solutions for Games with Hierarchical Structure

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the structure relative to that player. To define each of these solutions, we consider a certain mapping that transforms any hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley Value to the class of games with levels structure. The transformations that map the set of hierarchical structures to the set of levels structures are also studied from an axiomatic viewpoint by means of properties that relate a player’s position in both types of structure.

When Ignorance is Bliss - Information Asymmetries Enhance Prosocial Behavior in Dictator Games

In most laboratory experiments concerning prosocial behavior subjects are fully informed how their decision influences the payoff of other players. Outside the laboratory, however, individuals typically have to decide without such detailed knowledge. To assess the effect of information asymmetries on prosocial behavior, we conduct a laboratory experiment with a simple non-strategic interaction. A dictator has only limited knowledge about the benefits his prosocial action generates for a recipient. We observe subjects with heterogenous social preferences. While under symmetric information only individuals with the same type of preferences transfer, under asymmetric information different types transfer at the same time. As a consequence and the main finding of our experiment, uninformed dictators behave more prosocially than informed dictators.

Distributed Channel Selection in Time-Varying Radio Environment: Interference Mitigation Game With Uncoupled Stochastic Learning

This paper investigates the problem of distributed channel selection for interference mitigation in a time-varying radio environment without information exchange. Most existing algorithms, which were originally designed for static channels, are costly and inefficient in the presence of time-varying channels. First, we formulate this problem as a noncooperative game, in which the utility of each player is defined as a function of its experienced expected weighted interference. This game is proven to be an exact potential game with the considered network utility (the expected weighted aggregate interference) serving as the potential function. However, most game-theoretic algorithms are not suitable for the considered network, since they are coupled, i.e., the updating procedure is relying on the actions or payoffs of other players. Then, we propose a simple, completely distributed, and uncoupled stochastic learning algorithm, with which the users learn the desirable channel selections from their individual trial-payoff history. It is analytically shown that the proposed algorithm converges to pure strategy Nash equilibrium in time-varying radio environment; moreover, it achieves optimal channel selection profiles and makes the network interference-free for underloaded or equally loaded scenarios, while achieving, on average, near-optimal performance for overloaded scenarios.

Using Eyetracking to Study Learning in Games

We report results from an exploratory study using eye-tracking recording of information acquisition by players in a game theoretic learning paradigm. Eye-tracking is used to observe what information subjects look at in 4x4 normal-form games; the eye-tracking results favor sophisticated learning over adaptive learning and lend support to anticipatory or sophisticated models of learning in which subjects look at payoffs of other players to anticipate what those players might do. The decision data, however, are poorly fit by the simple anticipatory models we examine. We discuss how eye-tracking studies of information acquisition can fit into research agenda seeking to understand complex strategic behavior and consider methodological issues that must be addressed in order to maximize their potential.

Studying Learning in Games Using Eye-Tracking

We report results from an exploratory study using eye-tracking recording of information acquisition by players in a game theoretic learning paradigm. Eye-tracking is used to observe what information subjects look at in 4times4 normal-form games; the eye-tracking results favor sophisticated learning over adaptive learning and lend support to anticipatory or sophisticated models of learning in which subjects look at payoffs of other players to anticipate what those players might do. The decision data, however, are poorly fit by the simple anticipatory models we examine. We discuss how eye-tracking studies of information acquisition can fit into research agenda seeking to understand complex strategic behavior and consider methodological issues that must be addressed in order to maximize their potential.

On equilibrium in pure strategies in games with many players

We demonstrate that, if there are sufficiently many players, any Bayesian equilibrium of an incomplete information game can be “e-purified” . That is, close to any Bayesian equilibrium there is an approximate Bayesian equilibrium in pure strategies. Our main contribution is obtaining this result for games with a countable set of pure strategies. In order to do so we derive a mathematical result, in the spirit of the Shapley–Folkman Theorem, permitting countable strategy sets. Our main assumption is a “large game property,” dictating that the actions of relatively small subsets of players cannot have large affects on the payoffs of other players.

The role of utility interdependence in public good experiments

A popular approach to explain over-contribution in public good games is based on the assumption that people care (either positively or negatively) about the utility of other participants. Over-contribution then is an outcome of utility maximization where utility depends on subjects’ own payoffs as well as on the payoffs of other players. In this paper, I study to what extent this assumption of utility interdependence is responsible for over-contribution. I design three treatments where subjects’ decisions cannot affect opponents’ payoffs and thus utility interdependence cannot explain cooperative behavior. The main result is that while average contribution in these treatments is below the benchmark it nonetheless stays well above zero. Even when no one benefits from subjects’ generosity the average contributions are as high as one third of the endowment and are only 25% below those in the benchmark level. This suggests that utility interdependence is not the main factor responsible for over-contribution.

Stable bargained equilibria for assignment games without side payments

We consider NTU assignment games, which are generalizations of two-sided markets. Matched pairs bargain over feasible allocations; the disagreement outcome is endogenuously determined, taking in account outside options which are based on the current payoff of other players. An allocation is in equilibrium if and only if each pair is in equilibrium (no player wishes to rebargain). The set of equilibria is not empty and it naturally generalizes the intersection of the core and prekernel of TU assignment games. A set with similar properties does not exist for general NTU games. The main source of technical difficulties is the relatively complicated structure of the core in NTU games. We make a strong use of reduced games and consistency requirements. We generalize also the results obtained by Rochford (1984) for TU assignment games.