The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular, using this perspective, we discuss the differences between two solution concepts for such games namely, those of Nash equilibrium and co-action equilibrium. For ...

effectiveness of the ultra-violet dose by the dose-independent factor q. This makes it possible to surmise that in our experiments the killing of the bacteria and the production of the mutants might be due to the same chemical effect produced by the ultra-violet irradiation. 1 Kelner, A., PROC. NATL. ACAD. ScI., 35, 73 (1949). 2 Dulbecco, R., Nature, 163, 949 (1949). 3 Witkin, E. M., Genetics, ...

versity of Minnesota. We are grateful to Bernhard von Stengel and an anonymous referee for helpful comments. Abstract The maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contrast to Keiding (1995), who arrives at this result by referring to the enumeration of Gr unbaum and Sreedharan (1967), our argument...

Melioration learning is an empirically well-grounded model of reinforcement learning. By means of computer simulations, this paper derives predictions for several repeatedly played two-person games from this model. The results indicate a likely convergence to a pure Nash equilibrium of the game. If no pure equilibrium exists, the relative frequencies of choice may approach the predictions of th...

Carlos Gracia-Lázaro 1, Luis Mario Floría 1,2 and Yamir Moreno 1,3,* 1 Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain; [email protected] (C.G.-L.); [email protected] (L.M.F.) 2 Departamento de Física de la Materia Condensada, University of Zaragoza, 50009 Zaragoza, Spain 3 Departamento de Física Teórica, Univer...

This paper is a self-contained survey of algorithms for computing Nash equilibria of two-person games given in normal form or extensive form. The classical Lemke{Howson algorithm for nding one equilibrium of a bimatrix game is presented graph-theoretically as well as algebraically in terms of complementary pivoting. Common deenitions of degenerate games are shown as equivalent. Enumeration of a...

The symmetrization method of Gale, Kuhn and Tucker for matrix games is extended for bimatrix games. It is shown that the equilibria of a bimatrix game and its symmetrization correspond two by two. A similar result is found with respect to quasi-strong, regular and perfect equilibria.

A model of taxation for cooperative n-person games is introduced where proper coalitions are taxed proportionally to their value. Games with non-empty core under taxation at rate e are a-balanced. Sharp bounds on e in matching games on (not necessarily bipartite) graphs are established. Upper and lower bounds on the smallest e in bin packing games are derived and euclidean random TSP games are ...

Innnite two-person games are a natural framework for the study of reactive nonterminating programs. The eeective construction of winning strategies in such games is an approach to the synthesis of reactive programs. We describe the automata theoretic setting of innnite games (given by \game graphs"), outline a new construction of winning strategies in nite-state games, and formulate some questi...