论文信息 - Unilateral support equilibria

Unilateral support equilibria

Abstract The concept of Berge equilibria is based on supportive behavior among the players: each player is supported by the group of all other players. In this paper, we consider individual support rather than group support. The main idea is to introduce individual support relations, modeled by derangements. In a derangement, every player supports exactly one other player and every player is supported by exactly one other player. A unilaterally supportive strategy combination with respect to every possible derangement is called a unilateral support equilibrium. Our main insight is that in a unilateral support equilibrium, every player is supported by every other player individually. This is reflected by the alternative formulation of a unilateral support equilibrium in terms of pay-off functions, instead of using derangements. Moreover, it is shown that every Berge equilibrium is also a unilateral support equilibrium and we provide an example in which there is no Berge equilibrium, while the set of unilateral support equilibria is non-empty. Finally, the relation between the set of unilateral support equilibria and the set of Nash equilibria is explored.

Peter Borm | Ruud Hendrickx | Jop Schouten

[1] H. Corley. A Mixed Cooperative Dual to the Nash Equilibrium , 2015 .

[2] J. Goodman. Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[3] Moussa Larbani,et al. A note on Berge equilibrium , 2007, Appl. Math. Lett..

[4] Antonin Pottier,et al. A New Theorem to Find Berge Equilibria , 2012, IGTR.

[5] Eric van Damme,et al. Non-Cooperative Games , 2000 .

[6] Moussa Larbani,et al. A note on the existence of Berge and Berge-Nash equilibria , 2008, Math. Soc. Sci..

[7] T. W. Körner,et al. Mutual support in games: Some properties of Berge equilibria , 2011 .

[8] M. M. Kostreva,et al. Equi-well-posed games , 1996 .

[9] C. Berge,et al. Théorie générale des jeux à $n$ personnes , 1957 .

[10] P. Courtois,et al. Existence and computation of Berge equilibrium and of two refinements , 2017 .

[11] D. Hausman,et al. Economics and Philosophy , 1992, Economics and Philosophy.

[12] J. Nash. Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[13] V. I. Zhukovskii,et al. Some Problems of Non-Antagonistic Differential Games , 1985 .

[14] Michael M. Kostreva,et al. Some existence theorems of Nash and Berge Equilibria , 2004, Appl. Math. Lett..

[15] Herbert W. Corley,et al. A Cooperative Dual to the Nash Equilibrium for Two-Person Prescriptive Games , 2014, J. Appl. Math..