Nash equilibrium and generalized integration for infinite normal form games

In this paper, we investigate the existence of Berge–Zhukovskii equilibrium in general normal form games. We characterize its existence via the existence of a symmetric Nash equilibrium of some n-person subgame derived of the initial game. The significance of the obtained results is illustrated by two applications. One in economy with environmental externalities and the other in oligopoly markets.

Download Full-text

Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games

Topics in Theoretical Economics ◽

10.2202/1534-598x.1020 ◽

2004 ◽

Vol 4 (1) ◽

Cited By ~ 6

Author(s):

Eduardo Zambrano

Keyword(s):

Nash Equilibrium ◽

Normal Form ◽

Actual World ◽

Common Knowledge ◽

Counterfactual Reasoning ◽

Philosophical Literature ◽

Normal Form Games ◽

Normal Form Game ◽

The World ◽

Common Knowledge Of Rationality

When evaluating the rationality of a player in a game one has to examine counterfactuals such as "what would happen if the player were to do what he does not do?" In this paper I develop a model of a normal form game where counterfactuals of this sort are evaluated as in the philosophical literature (cf. Lewis, 1973; Stalnaker, 1968). According to this method one evaluates a statement like ``what would the player believe if he were to do what he does not do'' at the world that is closest to the actual world where the hypothetical deviation occurs. I show that in this model common knowledge of rationality need not lead to rationalizability. I also present assumptions that allow rationalizability to follow from common knowledge of rationality. These assumptions suggest that rationalizability may not rely on weaker assumptions about belief consistency than Nash equilibrium.

Download Full-text

Pessimistic Leader-Follower Equilibria with Multiple Followers

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/25 ◽

2017 ◽

Cited By ~ 3

Author(s):

Stefano Coniglio ◽

Nicola Gatti ◽

Alberto Marchesi

Keyword(s):

Nash Equilibrium ◽

Normal Form ◽

Scientific Literature ◽

Time Algorithm ◽

Exponential Time ◽

Normal Form Games ◽

Opposite Case ◽

Pure Strategies ◽

Multiple Followers ◽

Exponential Time Algorithm

The problem of computing the strategy to commit to has been widely investigated in the scientific literature for the case where a single-follower is present. In the multi-follower setting though, results are only sporadic. In this paper, we address the multi-follower case for normal-form games, assuming that, after observing the leader’s commitment, the followers play pure strategies and reach a Nash equilibrium. We focus on the pessimistic case where, among many equilibria, one minimizing the leader’s utility is chosen (the opposite case is computationally trivial). We show that the problem is NP-hard even with only two followers, and propose an exact exponential-time algorithm which, for any number of followers, either finds an equilibrium when the game admits a finite one or, if not, an α-approximation of the supremum of the leader’ utility, for any α > 0.

Download Full-text

Meta-Rationality in Normal Form Games

International Journal of Computers Communications & Control ◽

10.15837/ijccc.2010.5.2225 ◽

2010 ◽

Vol 5 (5) ◽

pp. 693

Author(s):

Dan Dumitru Dumitrescu ◽

Rodica Ioana Lung ◽

Tudor Dan Mihoc

Keyword(s):

Nash Equilibrium ◽

Normal Form ◽

Numerical Experiments ◽

Perfect Information ◽

Normal Form Games ◽

Different Types ◽

Evolutionary Technique ◽

Generalized Games

A new generative relation for Nash equilibrium is proposed. Different types of equilibria are considered in order to incorporate players different rationality types for finite non cooperative generalized games with perfect information. Proposed equilibria are characterized by use of several generative relations with respect to players rationality. An evolutionary technique for detecting approximations for equilibria is used. Numerical experiments show the potential of the method.

Download Full-text