Section: New Results

Game Theory

Participants : Eitan Altman, Konstantin Avrachenkov.

Dynamic potential games

In [11] K. Avrachenkov in collaboration with V. Mazalov and A. Rettieva (both from Petrozavodsk State Univ., Russia) treat discrete-time game-theoretic models of resource exploitation as dynamic potential games. The players (countries or firms) exploit a common stock on the infinite time horizon. The main aim is to obtain a potential for the linear-quadratic games of this type. The class of games where a potential can be constructed as a quadratic form is identified. As an example, the dynamic game of bioresource management is considered and the potentials are constructed in the case of symmetric and asymmetric players.

A Hawk and Dove game with infinite state space

In [16], E. Altman, in collaboration with A. Aradhye and R. El-Azouzi (UAPV) consider the Hawk-Dove game in which each of infinitely many individuals, involved with pairwise encounters with other individuals, can decide whether to act aggressively (Hawk) or peacefully (Dove). Each individual is characterized by its strength. The strength distribution among the population is assumed to be fixed and not to vary in time. If both individuals involved in an interaction are Hawks, there will be a fight, the result of which will be determined by the strength of each of the individuals involved. The larger the difference between the strength of the individuals is, the larger is the cost for the weaker player involved in the fight. The goal is to study the influence of the parameters (such as the strength level distribution) on the equilibrium of the game. The authors show that for some parameters there exists a threshold equilibrium policy while for other parameters there is no equilibrium policy at all.