Common Payoffs Research Articles

Synchronization in evolving snowdrift game model

The interaction between the evolution of the game and the underlying network structure with evolving snowdrift game model is investigated. The constructed network follows a power-law degree distribution typically showing scale-free feature. The topological features of average path length, clustering coefficient, degree-degree correlations and the dynamical feature of synchronizability are studied. The synchronizability of the constructed networks changes by the interaction. It will converge to a certain value when sufficient new nodes are added. It is found that initial payoffs of nodes greatly affect the synchronizability. When initial payoffs for players are equal, low common initial payoffs may lead to more heterogeneity of the network and good synchronizability. When initial payoffs follow certain distributions, better synchronizability is obtained compared to equal initial payoff. The result is also true for phase synchronization of nonidentical oscillators.

Allocation of Cooperative Payoff in a Cooperative Game

In a cooperative game, there may be a series of coalitions which may lead to the coalition equilibrium of the game. There is a mixed coalition equilibrium under the principle of maximum allocation in a cooperative game. If the allocation process of the coalitions can satisfy the competitive allocation condition, that's to say, the allocation that a player gets from his coalition is more than his escape-payoff but less than his marginal contribution to his coalition, the coalition equilibrium under the principle of maximum allocation equals to the coalition equilibrium under the principle of minimum escape-payoff. The allocation process of the cooperative payoff of a coalition is actually the bargaining process of the coalition members, that is, the bargaining game for the allocation of cooperative payoff surplus. The bargaining game based on mutual threats among the allied members of a coalition for the allocation of cooperative payoff surplus is an uncooperative game, in which every coalition member sets up his threat-point, if his request on the cooperative payoff surplus is accepted by other bargaining rivals, he will join in the cooperative coalition, or he will implement his threat to withdraw from the coalition. The cooperative payoff surplus of a coalition can be divided into the common payoffs of all its subsets. The Nash equilibrium in the allied bargaining game about the allocation of the common payoff of a member set (a subset of member set of the coalition) is that each member in the member set will get an equal share of the common payoff. This allocation scheme decides the allocation rule of cooperative payoff surplus of a coalition. In an allied bargaining game about the allocation of cooperative payoff surplus of a coalition, members would be allied and set up a series of cooperative teams. In the equilibrium situation of the allied bargaining game, the allocation that a certain team gets from the common payoff of a team set (a subset of the team set that includes all the cooperative teams formed in the equilibrium situation in the allied bargaining game) is just the same as that of another team. The aggregate allocation of cooperative payoff of the coalition that a certain team gets is the sum of its allocations of common payoff that it gets from all the team sets which it belongs to.

Individual Behavior and Group Membership

People who are members of a group and identify with it behave differently from people who perceive themselves as isolated individuals. This difference depends on two main factors. First, preferences over outcomes change with the degree of identification with the group. Second, this identification depends on the saliency of the group structure. This paper tests these hypotheses and shows that group membership affects preferences over outcomes, and saliency of the group affects the perception of the environment. In two strategic environments, Battle of the Sexes and Prisoner's Dilemma, we create groups by allocating subjects to be Row or Column players. We manipulate the saliency of group membership by letting a player's own group watch as a passive audience as decisions are made, and by making part of the payoff common for members of the group. There is a strong and significant effect of group membership: It increases the aggressive stance of the hosts (people who have their group members in the audience), and reduces the one of the guests. The effect on outcomes depends on the game: In the Battle of the Sexes, the aggressiveness of hosts leads to more coordination; in the Prisoner's Dilemma, it leads to less cooperation. In the first case efficiency is increased, while in the second it is diminished. We also test for differences between in-group and out-group behavior in Prisoner's Dilemma games. In contrast to the minimal-group paradigm of the social-psychology literature, minimal groups do not affect behavior in our strategic environment. We see strong differences between in-group and out-group behavior only when we increase the saliency of group membership by having a degree of common payoffs.

Exact Superreplication Strategies for a Class of Derivative Assets

A superreplicating hedging strategy is commonly used when delta hedging is infeasible or is too expensive. This article provides an exact analytical solution to the superreplication problem for a class of derivative asset payoffs. The class contains common payoffs that are neither uniformly convex nor concave. A digital option, a bull spread, a bear spread, and some portfolios of bull spreads or bear spreads, are all included as special cases. The problem is approached by first solving for the transition density of a process that has a two‐valued volatility. Using this process to model the underlying asset and identifying the two volatility values as σmin and σmax, the value function for any derivative asset in the class is shown to solve the Black–Scholes–Barenblatt equation. The subreplication problem and several related extensions, such as option pricing with transaction costs, calculating superreplicating bounds, and superreplication with multiple risky assets, are also addressed.

Improvement paths in repeated pure coordination games

We apply the one-sided better reply dynamic and the idea of pure strategy profile improvement path to discounted, infinitely repeated pure coordination games (games with common payoffs). If the stage game is finite, starting from any finite complexity repeated game strategy profile, such improvement paths must exist and must be finite. Furthermore, maximal improvement paths always terminate in pure strategy subgame perfect Nash equilibria of the repeated game. Related to this, we conclude with some observations on infinitely repeated infinite pure coordination games.

A note on the complexity of determining optimal strategies in games with common payoffs

In a recent paper [Int J Game Theory (2001) 30:99–106], Chu and Halpern investigated the problem of finding optimal strategies in certain games with common payoffs. This short technical note answers a computational complexity question that was left open in their paper.

On the NP-completeness of finding an optimal strategy in games with common payoffs

Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of determining whether there exists a joint strategy where each player has an expected payoff of at least r is NP-complete as a function of the number of nodes in the extensive-form representation of the game.

Potential Games with Continuous Player Sets

We study potential games with continuous player sets, a class of games characterized by an externality symmetry condition. Examples of these games include random matching games with common payoffs and congestion games. We offer a simple description of equilibria which are locally stable under a broad class of evolutionary dynamics, and prove that behavior converges to Nash equilibrium from all initial conditions. We consider a subclass of potential games in which evolution leads to efficient play. Finally, we show that the games studied here are the limits of convergent sequences of the finite player potential games studied by Monderer and Shapley [22]. Journal of Economic Literature Classification Numbers: C72, C73, D62, R41.

On the number of pure strategy Nash equilibria in finite common payoffs games

In a two-person “random” common payoffs game, defined as a finite game in which the players receive the same payoff at each outcome, let X represent the number of pure strategy Nash equilibria occurring. Treating both the cases where players have strictly and weakly ordinal preferences over outcomes, we observe that the expected value of X approaches infinity as the sizes of the pure strategy sets of the players increase without bound. Furthermore, we show that for any fixed positive integer k, the probability that X exceeds k approaches one as pure strategy sets increase in size without bound.

The Game of Political Entry with Truly Effective Identical Players

This paper presents a general formal model for analyzing political entry decisions in strategic contexts. The model focuses on dichotomous entry decisions made by potential entrants in a full information setting. The players in the proposed entry game are truly effective equals. That is, they share common payoffs (their preferences are identical) and an individual's entry decision always affects his and the other players' payoffs. We illustrate the relevance and applicability of the model to the study of diverse issues such as voluntary contribution to the provision of public goods (e.g. private charitable contributions or individual participation in organizational decision-making) and the formation of exclusive and non-exclusive benefit groups (e.g. clubs, political parties, labor unions). Within the above-mentioned particular contexts two issues are of paramount significance. First, the characterization of the equilibrium and efficient entry (participation) levels. Second, the comparison between these levels. Both issues are briefly analyzed. It is shown that the equilibrium number of entrants can be efficient or inefficient depending on the specific form of the players' payoff functions. In particular, depending on the degree of excludability of non-entrants from the benefits accruing to entrants, on the degree of subtractability of the benefits, on whether the benefits are increasing or decreasing with the number of entrants and on the costs of entry.