BERGE–ZHUKOVSKII EQUILIBRIA: EXISTENCE AND CHARACTERIZATION

2014 ◽  
Vol 16 (04) ◽  
pp. 1450012 ◽  
Author(s):  
RABIA NESSAH ◽  
MOUSSA LARBANI
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
The Other ◽  
Environmental Externalities ◽  
Normal Form Games ◽  
Oligopoly Markets

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.

scholarly journals Non-altruistic Equilibria

2019 ◽  
Vol 67 (3-4) ◽  
pp. 185-195
Author(s):  
Kazuhiro Ohnishi
Keyword(s):  
Normal Form ◽  
Cooperative Games ◽  
The Other ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Normal Form Games ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria ◽  
Non Cooperative Games

Which choice will a player make if he can make one of two choices in which his own payoffs are equal, but his rival’s payoffs are not equal, that is, one with a large payoff for his rival and the other with a small payoff for his rival? This paper introduces non-altruistic equilibria for normal-form games and extensive-form non-altruistic equilibria for extensive-form games as equilibrium concepts of non-cooperative games by discussing such a problem and examines the connections between their equilibrium concepts and Nash and subgame perfect equilibria that are important and frequently encountered equilibrium concepts.

scholarly journals Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games

2004 ◽  
Vol 4 (1) ◽  
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.

scholarly journals Pessimistic Leader-Follower Equilibria with Multiple Followers

2017 ◽  
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.

Games with Unawareness

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yossi Feinberg
Keyword(s):  
Nash Equilibrium ◽  
Incomplete Information ◽  
Equilibrium Solution ◽  
Solution Concept ◽  
The Other ◽  
Extensive Form ◽  
Normal Form Games ◽  
Incomplete Information Games ◽  
Extended Nash Equilibrium ◽  
Information Games

AbstractWe provide a tool to model and solve strategic situations where players’ perceptions are limited, as well as situations where players realize that other players’ perceptions may be limited and so on. We define normal, repeated, incomplete information, and extensive form games with unawareness using a unified methodology. A game with unawareness is defined as a collection of standard games (of the corresponding form). The collection specifies how each player views the game, how she views the other players’ perceptions of the game and so on. The modeler’s description of perceptions, the players’ description of other players’ perceptions, etc. are shown to have consistent representations. We extend solution concepts such as rationalizability and Nash equilibrium to these games and study their properties. It is shown that while unawareness in normal form games can be mapped to incomplete information games, the extended Nash equilibrium solution is not mapped to a known solution concept in the equivalent incomplete information games, implying that games with unawareness generate novel types of behavior.

N-Player Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Security Policy ◽  
The Other ◽  
Security Level ◽  
Action Spaces

This chapter extends several of the concepts for two-player games to games with N-players. It begins by considering general games with N players P₁, P₂, . . ., P(subscript N), which are allowed to select policies within action spaces Γ‎₁, Γ‎₂, . . ., Γ‎(subscript N). Each player wants to minimize their own outcome, and does not care about the outcome of the other players. The chapter proceeds by discussing the security level, security policy, and Nash equilibrium for N-player games, pure N-player games in normal form, mixed policy for N-player games in normal form, and computation of the completely mixed Nash equilibrium for N-player games. A mixed Nash equilibrium is computed for a different game in which some (or all) players want to maximize instead of minimize the outcome.

scholarly journals Meta-Rationality in Normal Form Games

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.

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