Common Interest Games Research Articles

Decentralized Learning for Optimality in Stochastic Dynamic Teams and Games With Local Control and Global State Information

Stochastic dynamic teams and games are rich models for decentralized systems and challenging testing grounds for multiagent learning. Previous work that guaranteed team optimality assumed stateless dynamics, or an explicit coordination mechanism, or joint-control sharing. In this article, we present an algorithm with guarantees of convergence to team optimal policies in teams and common interest games. The algorithm is a two-timescale method that uses a variant of Q-learning on the finer timescale to perform policy evaluation while exploring the policy space on the coarser timescale. Agents following this algorithm are “independent learners”: they use only local controls, local cost realizations, and global state information, without access to controls of other agents. The results presented here are the first, to the best of our knowledge, to give formal guarantees of convergence to team optimality using independent learners in stochastic dynamic teams and common interest games.

An Index of Competitiveness and Cooperativeness for Normal-Form Games

We develop an index of competitiveness and cooperativeness that is based on the primitives of a normal-form game, i.e., players, strategies and payoffs. The index relies on the unique decomposition of a given game into a zero-sum game and a common interest game. The index decreases in the distance to its zero-sum part and increases in common interest part. The comparative statics of our index coincide with economic intuition. The index also supports experimental findings in well-known classes of games in the sense that more cooperative and less competitive behavior correlates with lower values of the index. (JEL C71, C72)

Strategic gaze: an interactive eye-tracking study

We present an interactive eye-tracking study that explores the strategic use of gaze. We analyze gaze behavior in an experiment with four simple games. The game can either be a competitive (hide & seek) game in which players want to be unpredictable, or a game of common interest in which players want to be predictable. Gaze is transmitted either in real time to another subject, or it is not transmitted and therefore non-strategic. We find that subjects are able to interpret non-strategic gaze, obtaining substantially higher payoffs than subjects who do not see gaze. If gaze is transmitted in real time, gaze becomes more informative in the common interest games and players predominantly succeed to coordinate on efficient outcomes. In contrast, gaze becomes less informative in the competitive game.

Simple Characterizations of Potential Games and Zero-sum Equivalent Games

We provide several tests to determine whether a game is a potential game or whether it is a zero-sum equivalent game-a game which is strategically equivalent to a zero-sum game in the same way that a potential game is strategically equivalent to a common interest game. We present a unified framework applicable for both potential and zero-sum equivalent games by deriving a simple but useful characterization of these games. This allows us to re-derive known criteria for potential games, as well as obtain several new criteria. In particular, we prove (1) new integral tests for potential games and for zero-sum equivalent games, (2) a new derivative test for zero-sum equivalent games, and (3) a new representation characterization for zero-sum equivalent games.

The common-interest game between terrorists and the media: replication and extension

The findings of Rohner and Frey (Public Choice 133(1–2):129–145, 2007) suggest a positive Granger causality between media attention and terrorist attacks. We replicate and extend the empirical part of their study. Besides more periods which allow the circumventing of any possible far-reaching 9/11 effects, we add data from Fox News and use impulse response functions to analyse the persistence and magnitude of the effects. On the whole, we cannot confirm that there is a robust mutual Granger causal relationship between the media coverage and terrorism.

Measuring Competitiveness and Cooperativeness

We develop an index of competitiveness and cooperativeness which is based on the primitives of a normal-form game, i.e., players, strategies and payoffs. The index relies on a unique decomposition of a given game into a zero-sum game and a common-interest game. The index decreases in the distance to its zero-sum part and it increases in the distance to its common-interest part. Alternatively, the index increases if the share of variation in payoffs captured by the zero-sum part increases. We compute our index for well-known classes of games such as Prisoner's Dilemma, games with Strategic Complements and Substitutes, All-pay auctions, Tullock contests, and Public Goods games. The comparative statics of our index coincide with economic intuition. The index does well in explaining experimental findings in the sense that more cooperative and less competitive behavior correlates with lower values of the index.

Information Transmission in Revision Games

Revision games model a situation in which players can prepare their actions during a pre-play phase. We introduce one-sided incomplete information in two coordination games, one of common interest and one of opposing interest, and study how the pre-play phase affects coordination. We find that in the common interest game, the unique Bayesian equilibrium is such that the informed player will signal the state of the world through her prepared action, unless the pre-play phase is about to finish, in which case she seeks to coordinate with the other player. In the opposing interest game, the equilibrium is similar when the informed player is the one receiving less opportunity to revise her actions. When it is the uninformed player who receives less revision opportunities, we show that it is possible no information is revealed if both players are initially coordinated, but some information must be revealed if they are initially miscoordinated.

Cultural impediments to learning to cooperate: An experimental study of high- and low-caste men in rural India

We report experimental findings on how individuals from different cultures solve a repeated coordination game of common interest. The results overturn earlier findings that fixed pairs are almost assured to coordinate on an efficient and cooperative equilibrium. Subjects in the prior experiments were US university students, whereas the subjects in our study are men drawn from high and low castes in rural India. Most low-caste pairs quickly established an efficient and cooperative convention, but most high-caste pairs did not. The largest difference in behavior occurred when a player suffered a loss because he had tried to cooperate but his partner did not: In this situation, high-caste men were far less likely than low-caste men to continue trying to cooperate in the next period. Our interpretation is that for many high-caste men, the loss resulting from coordination failure triggered retaliation. Our results are robust to controls for education and wealth, and they hold by subcaste as well as by caste status. A survey we conducted supports the ethnographic evidence that more high-caste than low-caste men prefer to retaliate against a slight. We find no evidence that caste differences in trust or self-efficacy explain the caste gap in cooperation in our experiment. Our findings are of general interest because many societies throughout the world have cultures that lead individuals to (mis)perceive some actions as insults and to respond aggressively and dysfunctionally.

Team Reasoning and the Rational Choice of Payoff-Dominant Outcomes in Games

Standard game theory cannot explain the selection of payoff-dominant outcomes that are best for all players in common-interest games. Theories of team reasoning can explain why such mutualistic cooperation is rational. They propose that teams can be agents and that individuals in teams can adopt a distinctive mode of reasoning that enables them to do their part in achieving Pareto-dominant outcomes. We show that it can be rational to play payoff-dominant outcomes, given that an agent group identifies. We compare team reasoning to other theories that have been proposed to explain how people can achieve payoff-dominant outcomes, especially with respect to rationality. Some authors have hoped that it would be possible to develop an argument that it is rational to group identify. We identify some large—probably insuperable—problems with this project and sketch some more promising approaches, whereby the normativity of group identification rests on morality.

Team reasoning: Solving the puzzle of coordination

In many everyday activities, individuals have a common interest in coordinating their actions. Orthodox game theory cannot explain such intuitively obvious forms of coordination as the selection of an outcome that is best for all in a common-interest game. Theories of team reasoning provide a convincing solution by proposing that people are sometimes motivated to maximize the collective payoff of a group and that they adopt a distinctive mode of reasoning from preferences to decisions. This also offers a compelling explanation of cooperation in social dilemmas. A review of team reasoning and related theories suggests how team reasoning could be incorporated into psychological theories of group identification and social value orientation theory to provide a deeper understanding of these phenomena.

Expert information and majority decisions

This paper shows experimentally that hearing expert opinions can be a double-edged sword for collective decision making. We present a majoritarian voting game of common interest where committee members receive not only private information, but also expert information that is more accurate than private information and observed by all members. In theory, there are Bayesian Nash equilibria where the committee members' voting strategy incorporates both types of information and access to expert information enhances the efficiency of the majority decision. However, in the laboratory, expert information had excessive influence on the voting behaviour and prevented efficient aggregation of individual information. We find a large efficiency loss due to the presence of expert information especially when the committee size is large. Using an incentivized questionnaire, we find that many subjects severely underestimate the efficiency gain from information aggregation and they follow expert information much more frequently than efficiency requires. This suggests that those who understand the efficiency gain from information aggregation and perceive the game correctly might nonetheless be “stuck” in an inefficient outcome.

Common Interest and Signaling Games: A Dynamic Analysis

We present a dynamic model of the evolution of communication in a Lewis signaling game while systematically varying the degree of common interest between sender and receiver. We show that the level of common interest between sender and receiver is strongly predictive of the amount of information transferred between them. We also discuss a set of rare but interesting cases in which common interest is almost entirely absent, yet substantial information transfer persists in a “cheap talk” regime, and offer a diagnosis of how this may arise.

Quantum advice enhances social optimality in three-party conflicting interest games

Quantum pseudo-telepathy games are good examples of explaining the strangeness of quantum mechanics and demonstrating the advantage of quantum resources over classical resources. Most of the quantum pseudo-telepathy games are common interest games, nevertheless conflicting interest games are more widely used to model real world situations. Recently Pappa et al. (Phys. Rev. Lett. 114, 020401, 2015) proposed the first two-party conflicting interest game where quantum advice enhances social optimality. In the present paper we give two new three-party conflicting interest games and show that quantum advice can enhance social optimality in a three-party setting. The first game we propose is based on the famous GHZ game which is a common interest game. The second game we propose is related to the Svetlichny inequality which demonstrates quantum mechanics cannot be explained by the local hidden variable model in a three-party setting.

Two-player conflicting interest Bayesian games and Bell nonlocality

Nonlocality, one of the most remarkable aspects of quantum mechanics, is closely related to Bayesian game theory. Quantum mechanics can offer advantages to some Bayesian games, if the payoff functions are related to Bell inequalities in some way. Most of these Bayesian games that have been discussed are common interest games. Recently the first conflicting interest Bayesian game is proposed in Phys. Rev. Lett. 114, 020401 (2015). In the present paper we present three new conflicting interest Bayesian games where quantum mechanics offers advantages. The first game is linked with Cereceda inequalities, the second game is linked with a generalized Bell inequality with 3 possible measurement outcomes, and the third game is linked with a generalized Bell inequality with 3 possible measurement settings.

Circulant games

We study a class of two-player normal-form games with cyclical payoff structures. A game is called circulant if both players’ payoff matrices fulfill a rotational symmetry condition. The class of circulant games contains well-known examples such as Matching Pennies, Rock-Paper-Scissors, as well as subclasses of coordination and common interest games. The best response correspondences in circulant games induce a partition on each player’s set of pure strategies into equivalence classes. In any Nash Equilibrium, all strategies within one class are either played with strictly positive or with zero probability. We further show that, strikingly, a single parameter fully determines the exact number and the structure of all Nash equilibria (pure and mixed) in these games. The parameter itself only depends on the position of the largest payoff in the first row of one of the player’s payoff matrix.

Goals, Payoffs, and Classification of Games

This article shows that the conventional definition of pure conflict, pure common-interest and mixed-motive games based on the correlation of players’ payoffs, is inadequate. The reason is that payoffs do not always fully reflect potential complexity of players’ goals. I therefore generalize the standard model of strategic games by explicitly modeling players’ goals and propose a new definition of pure conflict, pure common-interest, and mixed-motive games based on mutual compatibility of players’ goals. I also show that the information about players’ goals can be useful for an analysis of various possibilities of how players can strategically modify the game to increase their equilibrium payoffs.

Asynchronicity and coordination in common and opposing interest games

We study games endowed with a pre-play phase in which players prepare the actions that will be implemented at a predetermined deadline. In the preparation phase, each player stochastically receives opportunities to revise her actions, and the finally-revised action is taken at the deadline. In 2-player \textquotedblleft common interest games, where there exists a best action profile for all players, this best action profile is the only equilibrium outcome of the dynamic game. In \textquotedblleft opposing interest games, which are $2\times 2$ games with Pareto-unranked strict Nash equilibria, the equilibrium outcome of the dynamic game is generically unique and corresponds to one of the stage-game strict Nash equilibria. Which equilibrium prevails depends on the payoff structure and on the relative frequency of the arrivals of revision opportunities for each of the players.

Strong Stackelberg reasoning in symmetric games: An experimental replication and extension

In common interest games in which players are motivated to coordinate their strategies to achieve a jointly optimal outcome, orthodox game theory provides no general reason or justification for choosing the required strategies. In the simplest cases, where the optimal strategies are intuitively obvious, human decision makers generally coordinate without difficulty, but how they achieve this is poorly understood. Most theories seeking to explain strategic coordination have limited applicability, or require changes to the game specification, or introduce implausible assumptions or radical departures from fundamental game-theoretic assumptions. The theory of strong Stackelberg reasoning, according to which players choose strategies that would maximize their own payoffs if their co-players could invariably anticipate any strategy and respond with a best reply to it, avoids these problems and explains strategic coordination in all dyadic common interest games. Previous experimental evidence has provided evidence for strong Stackelberg reasoning in asymmetric games. Here we report evidence from two experiments consistent with players being influenced by strong Stackelberg reasoning in a wide variety of symmetric 3 × 3 games but tending to revert to other choice criteria when strong Stackelberg reasoning generates small payoffs.

Multi-heuristic strategy choice: Response to Krueger.

Social projection cannot adequately explain coordination in common interest games, and nothing resembling social projection underlies team reasoning or strong Stackelberg reasoning. Although our experiments suggest that cognitive hierarchy Level-1 reasoning was most influential in the games that we investigated, strong Stackelberg reasoning and team reasoning were also used quite frequently by the players.

Explaining strategic coordination: Cognitive hierarchy theory, strong Stackelberg reasoning, and team reasoning.

In common interest games, players generally manage to coordinate their actions on mutually optimal outcomes, but orthodox game theory provides no reason for them to play their individual parts in these seemingly obvious solutions and no justification for choosing the corresponding strategies. A number of theories have been suggested to explain coordination, among the most prominent being versions of cognitive hierarchy theory, theories of team reasoning, and social projection theory (in symmetric games). Each of these theories provides a plausible explanation but is theoretically problematic. An improved theory of strong Stackelberg reasoning avoids these problems and explains coordination among players who care about their co-players’ payoffs and who act as though their co-players can anticipate their choices. Two experiments designed to test cognitive hierarchy, team reasoning, and strong Stackelberg theories against one another in games without obvious, payoff-dominant solutions suggest that each of the theories provides part of the explanation. Cognitive hierarchy Level-1 reasoning, facilitated by a heuristic of avoiding the worst payoff, tended to predominate, especially in more complicated games, but strong Stackelberg reasoning occurred quite frequently in the simpler games and team reasoning in both the simpler and the more complicated games. Most players considered two or more of these reasoning processes before choosing their strategies.