Unilateral Support Equilibria

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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 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.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages14
Volume2018-011
Publication statusPublished - 27 Mar 2018

Publication series

NameCentER Discussion Paper
Volume2018-011

Fingerprint

Nash equilibrium

Keywords

  • mutual support equilibria
  • Berge equilibria
  • unilateral support equilibria

Cite this

Schouten, J., Borm, P., & Hendrickx, R. (2018). Unilateral Support Equilibria. (CentER Discussion Paper; Vol. 2018-011). Tilburg: CentER, Center for Economic Research.
Schouten, Jop ; Borm, Peter ; Hendrickx, Ruud. / Unilateral Support Equilibria. Tilburg : CentER, Center for Economic Research, 2018. (CentER Discussion Paper).
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Schouten, J, Borm, P & Hendrickx, R 2018 'Unilateral Support Equilibria' CentER Discussion Paper, vol. 2018-011, CentER, Center for Economic Research, Tilburg.

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

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

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Unilateral Support Equilibria

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AU - Hendrickx, Ruud

PY - 2018/3/27

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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.

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KW - Berge equilibria

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Schouten J, Borm P, Hendrickx R. Unilateral Support Equilibria. Tilburg: CentER, Center for Economic Research. 2018 Mar 27. (CentER Discussion Paper).