### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | CentER, Center for Economic Research |

Number of pages | 14 |

Volume | 2018-011 |

Publication status | Published - 27 Mar 2018 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2018-011 |

### Fingerprint

### Keywords

- mutual support equilibria
- Berge equilibria
- unilateral support equilibria

### Cite this

*Unilateral Support Equilibria*. (CentER Discussion Paper; Vol. 2018-011). Tilburg: CentER, Center for Economic Research.

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**Unilateral Support Equilibria.** / Schouten, Jop; Borm, Peter; Hendrickx, Ruud.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Unilateral Support Equilibria

AU - Schouten, Jop

AU - Borm, Peter

AU - Hendrickx, Ruud

PY - 2018/3/27

Y1 - 2018/3/27

N2 - 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 extend this concept by maintaining the idea of supportive behavior among the players, but eliminating the underlying coordination issues. We suggest to consider individual support rather than group support. The main idea is to introduce 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. Subsequently, we dene a new equilibrium concept, called a unilateral support equilibrium, which is unilaterally supportive with respect to every possible derangement. We show that a unilateral support equilibrium can be characterized in terms of pay-offfunctions so that every player is supported by every other player individually. 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.

AB - 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 extend this concept by maintaining the idea of supportive behavior among the players, but eliminating the underlying coordination issues. We suggest to consider individual support rather than group support. The main idea is to introduce 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. Subsequently, we dene a new equilibrium concept, called a unilateral support equilibrium, which is unilaterally supportive with respect to every possible derangement. We show that a unilateral support equilibrium can be characterized in terms of pay-offfunctions so that every player is supported by every other player individually. 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.

KW - mutual support equilibria

KW - Berge equilibria

KW - unilateral support equilibria

M3 - Discussion paper

VL - 2018-011

T3 - CentER Discussion Paper

BT - Unilateral Support Equilibria

PB - CentER, Center for Economic Research

CY - Tilburg

ER -