International Game Theory Review

In this paper we introduce a new class of cooperative games. We define a characteristic function over the cycles of a digraph. We present a mathematical model for this situation and an axiomatic characterization of a solution for this class of cooperative games. This is introduced as a method to measure the importance of the nodes in a digraph, and can be related with the Shapley value of a game in characteristic function form. Also, we extend the modeling by applying coalitional structures for the nodes and r-efficient solutions, where the allocation amount is a real number r, showing axiomatic solutions in both cases.

The effects of uniting separated markets, each monopolized by a producer, into a globalized oligopolistic market, which is regarded as a noncooperative game, or as a Cournot oligopoly game, are investigated. The cases where such globalization degrades the profits of all producers coincidently, are examined. Linear demand and production functions are considered. It is shown that in complete symmetry, the degree of such coincident profit degradation is strongest (the worst-case ratio), where the degree means the most modest ratio of the profit degradation among all producers. The system is in complete symmetry when the values of parameters describing all producers and markets are identical. On the other hand, in producer symmetry, the degree of coincident consumer surplus improvement is highest (the best-case ratio), where the degree means the lowest of the ratios of consumer surplus improvement among all (previously separated) markets. The system is in producer symmetry when the values of parameters describing all producers are identical.

In context of the traditional Spence signaling model, the realization of a separating equilibrium ensures that each worker is allocated to the sector of the economy where they are most productive. Traditional analysis assumes, however, that the incremental returns to labor employment are constant across workers of any given type. This paper demonstrates that the efficiency properties of separating equilibria can be profoundly altered by the presence of nonlinear returns. In particular, we show that separating equilibria fail productive efficiency whenever production satisfies a weak form of diminishing returns. This separating equilibrium efficiency failure persists whether or not equilibrium wages are assumed to depend solely on distributions of worker productivity.

A sequential Colonel Blotto and rent seeking game with fixed and variable resources is analyzed. With fixed resources, which is the assumption in Colonel Blotto games, we show for the common ratio form contest success function that the second mover is never deterred. This stands in contrast to Powell's (Games and Economic Behavior67(2), 611–615) finding where the second mover can be deterred. With variable resources both players exert efforts in both sequential and simultaneous games, whereas fixed resources cause characteristics of all battlefields or rents to impact efforts for each battlefield. With variable resources only characteristics of a given battlefield impact efforts are to win that battlefield because of independence across battlefields. Fixed resources impact efforts and hence differences in unit effort costs are less important. In contrast, variable resources cause differences in unit effort costs to be important. The societal implication is that resource constrained opponents can be expected to engage in warfare, whereas an advantaged player with no resource constraints can prevent warfare.

In cooperative stochastic dynamic games a stringent condition — that of subgame consistency — is required for a dynamically stable cooperative solution. In particular, a cooperative solution is subgame consistent if an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior would remain optimal. This paper extends subgame consistent solutions to cooperative stochastic dynamic (discrete-time) games with random horizon. In the analysis new forms of the stochastic Bellman equation and the stochastic Isaacs–Bellman equation in discrete time are derived. Subgame consistent cooperative solutions are obtained for stochastic dynamic games. Analytically tractable payoff distribution mechanisms which lead to the realization of these solutions are developed. This is the first time that subgame consistent solutions for cooperative stochastic dynamic games with random horizon are presented.

This note provides a methodological contribution to the allocation of joint revenues obtained from passepartouts. In a passepartout system, a group of service providers offers a passepartout that allows its owners the use of specified services for an unlimited number of times during a fixed period of time. The corresponding allocation problem is, then, how to share the total joint revenues of the passepartout system adequately among the service providers. Arguments are provided to model a passepartout problem within the framework of bankruptcy and context-specific properties are considered in order to select an appropriate allocation rule.