International Game Theory Review

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝⁿ. This result is the first step for future work on differential games with lack of information.

New results on the variational stability of social Nash equilibria are obtained using the class of sequentially pseudocontinuous functions. This class of functions strictly includes the class of sequentially continuous functions and finds a natural motivation in the framework of Choice and Economic Theory since it characterizes the continuity of the preference relations on first countable topological spaces. We investigate the connections with previous results and we show that it is not possible to improve our results further on.

A class of nonzero-sum symmetric stochastic games of capital accumulation/resource extraction is considered. It is shown that Nash equilibria in the games with some natural constraints are also equilibrium solutions in unconstrained games and dominate in the Pareto sense an equilibrium leading to exhausting the entire resource stock in the first period of the game.

This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaidô-Isoda function is convex-concave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to design computational algorithms for finding such equilibria.

To comply with some freedom of individual choice the algorithms developed here are fairly decentralized. However, since coupling constraints must be enforced, repeated coordination is needed while underway towards equilibrium.

Particular instances include zero-sum, two-person games — or minimax problems — that are convex-concave and involve convex coupling constraints.

A concept of altruistic behavior (called friendly behavior) has been defined and used for equilibrium selection in some bargaining models in Rusinowska (2002), "Refinements of Nash Equilibria in view of Jealous and Friendly Behavior of Players", International Game Theory Review, 4, 281–299.

In this paper, the situation in which every player has friendly behavior is incorporated into the general context of normal form games by introducing a new refinement concept (called friendliness equilibrium). Existence, properties and connections with another refinement concept, introduced by the authors in a previous paper and which captures an idea of reciprocal altruism, are investigated. Examples and counterexamples are given illustrating concepts, results and links with other classical refinement concepts.

This paper develops a trade model for a technologically leading country and a developing country that exploits a renewable natural resource. Technology diffuses from the technological leader to the developing country through foreign direct investment (FDI). Alternatively, innovative activities can also be carried out in the developing economy. We prove the existence and uniqueness of an equilibrium path along which both countries grow at the same rate, maintaining the natural-resource stock at a constant level. The saddle-point property for this equilibrium is proved and a sensitivity analysis is carried out. The steady-state growth rate and consumption under both scenarios are compared and the effect of resource abundance analyzed.

Human carcinogenesis may be thought of as Darwinian evolution of cells within the body (somatic evolution). As such, it may be modeled using evolutionary game theory. Winners in this game proliferate while losers become extinct. Here evolutionary dynamics are proposed that model the rate of somatic evolution. The speed at which somatic evolution proceeds determines whether a clinically significant cancer will emerge in the lifetime of the individual. The underlying model has an associated adaptive landscape that illustrates the evolutionary potential of cells due to the selection forces and microenvironment. Normal cells have a novel adaptive landscape that permits both coexistence and invasion of mutant phenotypes. A mutant cellular population does not initially form a malignancy because of constraints resulting in limited growth and nonlethal coexistence. However this coexistence deforms the local adaptive landscape resulting in the potential for evolution to drive the mutant cells to an unoccupied fitness peak resulting in an evasive cancer. There are two factors that determine this evolutionary potential. The first factor involves a relaxation of proliferation constraints and the second involves an increase in nutrients thereby removing a barrier allowing the mutant cells to climb to an adaptive peak. One unfortunate consequence of the cancer reaching this peak is that it starts producing acid that further contributes to the demise of the normal cells.

The problem of comparing TU-cooperative game values is introduced and analyzed. The proposed method is based on multicriteria methodology and the ASPID (Analysis and Synthesis of Parameters under Information Deficiency) technique (Hovanov and Kolary (1998)). The Shapley value and the nucleolus are compared despite a lack of information about coalitional preferences.

Strategic behaviors of players depend crucially on the coalition structures of a game. A recursive sequence identifying the number of embedded coalitions in a n-player game is derived. The paper also derives a recursive sequence identifying the number of embedded coalitions in a n-player game where the position of the individual player in a partition counts.

This paper proposes a discrete analogue of concavity appropriate for potential games with discrete strategy sets. It guarantees that every Nash equilibrium maximizes a potential function.