Example of a Finite Game with No Berge Equilibria at All

Pykacz, Jarosław; Bytner, Pawel; Frąckiewicz, Piotr

doi:10.3390/g10010007

Cited by 30 publications

(6 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But this is not the case: Even though Berge equilibria are an intriguing concept, worthy of further investigations, sadly they are inappropriate as extensions of Kantian equilibria. First, there are three-player games [PBF19] admitting no mixed-strategy Berge equilibria, and deciding the existence of mixed-strategy Berge equilibria is NP-complete [NC18]. For two-player games Berge equilibria correspond [CKMT11] to the Nash equilibria of a modified games.…”

Section: Berge Equilibriamentioning

confidence: 99%

Game-theoretic Models of Moral and Other-Regarding Agents

Istrate

2020

Preprint

View full text Add to dashboard Cite

We investigate Kantian equilibria in finite normal form games, a class of non-Nashian, morally motivated courses of action that was recently proposed in the economics literature. We highlight a number of problems with such equilibria, including computational intractability, a high price of miscoordination, and expensive/problematic extension to general normal form games. We point out that such a proper generalization will likely involve the concept of program equilibrium. Finally we propose some general, intuitive, computationally tractable, other-regarding equilibria related to Kantian equilibria, as well as a class of courses of action that interpolates between purely self-regarding and Kantian behavior.

show abstract

Section: Berge Equilibriamentioning

confidence: 99%

Game-theoretic Models of Moral and Other-Regarding Agents

Istrate

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…So, the Berge equilibrium may not exist in a finite 3-person games. The example of this is given in [11]. The following example is taken from [11].…”

Section: Property 1 a Berge Equilibrium In Game (1) With N = = {1 2mentioning

confidence: 99%

“…Moreover, in N-person games (N ≥ 3) with a finite set of strategies, the Berge equilibrium may not exist in the class of mixed strategies. Such example was constructed, in particular, in [11]. The lack of Berge equilibrium might be caused by the fact that it is often impossible to follow the Golden Rule of morality in relation to all players at the same time.…”

Section: Introductionmentioning

confidence: 99%

Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

Kudryavtsev

Malkov

2020

Open Computer Science

View full text Add to dashboard Cite

The paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

show abstract

“…The paper introduces the Perfectly Transparent Equilibrium -the idea based on rounds elimination of strategy profiles that do not imply maximin payoffs. Another notion worth mentioning is Berge equilibrium [6,7,8]. The concept is based on altruism in the sense that each player's aim is to maximize the payoffs of the other players.…”

Section: Introductionmentioning

confidence: 99%

Kantian equilibria in classical and quantum symmetric games

Frąckiewicz¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

The aim of the paper is to examine the notion of simple Kantian equilibrium in 2 × 2 symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a result, we derive a formula that determines the reasonable strategies for any payoffs in the bimatrix game. This allowed us to compare the payoff results for classical and quantum way of playing the game. We showed that a very large part of 2 × 2 symmetric games have more beneficial Kantian equilibria when they are played with the use of quantum strategies.

show abstract

Example of a Finite Game with No Berge Equilibria at All

Abstract: The problem of the existence of Berge equilibria in the sense of Zhukovskii in normal form finite games in pure and in mixed strategies is studied. The example of a three-player game that has Berge equilibrium neither in pure nor in mixed strategies is given.

Cited by 30 publications

References 6 publications

Game-theoretic Models of Moral and Other-Regarding Agents

Game-theoretic Models of Moral and Other-Regarding Agents

Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

Kantian equilibria in classical and quantum symmetric games

Contact Info

Product

Resources

About