Two-person Finite Games Research Articles

On the IENBR-solvability of two-person finite games

Abstract We show that a two-person finite game is solved by the iterated elimination of never best responses (IENBR) if and only if it is best response acyclic and strongly solvable in the sense of Nash (1951). Thus the rationalizable strategies (Bernheim, 1984; Pearce, 1984) are equivalent to the Nash equilibrium strategies in two-person finite games if and only if the two conditions are met. We prove this for both mixed strategy games and pure strategy games.

Expectation-based learning in two-person finite games

Abstract Learning pure-strategy equilibrium of normal form bi-matrix games in the assumption of knowledge of own-payoffs and no knowledge of rival strategies is considered. An original learning algorithm based on mixed best-reply to expectations is proposed. Global convergence is ensured for a new class of games including but not restricted to potential games. Results of classic Linear-Reward Inaction schemes are significantly improved at the modest cost of knowledge of own payoffs.

Discovering theorems in game theory: Two-person games with unique pure Nash equilibrium payoffs

In this paper we provide a logical framework for two-person finite games in strategic form, and use it to design a computer program for discovering some classes of games that have unique pure Nash equilibrium payoffs. The classes of games that we consider are those that can be expressed by a conjunction of two binary clauses, and our program re-discovered Kats and Thisseʼs class of weakly unilaterally competitive two-person games, and came up with several other classes of games that have unique pure Nash equilibrium payoffs. It also came up with new classes of strict games that have unique pure Nash equilibria, where a game is strict if for both player different profiles have different payoffs.

Generalized correlated equilibrium for two-person games in extensive form with perfect information

A correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is applied for two-person finite games in extensive form with perfect information. Randomization by an umpire takes place over the leaves of the game tree. At every decision point players have the choice either to follow the recommendation of the umpire blindly or freely choose any other action except the one suggested. This scheme can lead to Pareto-improved outcomes of other correlated equilibria. Computational issues of maximizing a linear function over the set of soft correlated equilibria are considered and a linear-time algorithm in terms of the number of edges in the game tree is given for a special procedure called “subgame perfect optimization”.

On the relation between Nash equilibria and undominated strategies for two person, finite games

We show the equivalence between the existence of Nash equilibria for two-person finite games and sets of strategies being undominated relative to each other. An example shows that similar results will not be true for games with three or more players.

Solution concepts in two-person multicriteria games

In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.

Teorema de existencia de pares de equilibrio R−∈ para juegos finitos

R−∈ criterion is considered for two-person finite games. For each pair of pure strategies, each player have a lottery concerning basic arranged results.

Metodos de resolucion del criterio R−∈ para juegos

R−e criterion is considered for two-person finite games. For each pair of pure strategies, each player have a lottery concerning basic arranged results.