A Mixed Cooperative Dual to the Nash Equilibrium

Corley, H. W.

doi:10.1155/2015/647246

Cited by 20 publications

(16 citation statements)

References 18 publications

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“…The game shown in Table 1 is the normal form representation for the game in Figure 3. However, it was proven in [3] that an MBE does not exist for this game. We now consider the same game but with perfect information as shown in Figure 4.…”

Section: Examplesmentioning

confidence: 98%

The Mixed Berge Equilibrium in Extensive Form Games

Nahhas¹,

Corley²

2017

TEL

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In this paper we apply the concept of a mixed Berge equilibrium to finite n-person games in extensive form. We study the mixed Berge equilibrium in both perfect and imperfect information finite games. In addition, we define the notion of a subgame perfect mixed Berge equilibrium and show that for a 2-person game, there always exists a subgame perfect Berge equilibrium. Thus there exists a mixed Berge equilibrium for any 2-person game in extensive form. For games with 3 or more players, however, a mixed Berge equilibrium and a subgame perfect mixed Berge equilibrium may not exist. In summary, this paper extends extensive form games to include players acting altruistically.

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Section: Examplesmentioning

confidence: 98%

The Mixed Berge Equilibrium in Extensive Form Games

Nahhas¹,

Corley²

2017

TEL

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“…At first, the focus was to find existence theorems for a very general setting of non-cooperative games, but later on, the research also included results for more specific classes of games (in particular for mixed extensions of finite games) and related problems. We mention the papers of Radjef (1988), Abalo and Kostreva (2004), Nessah, Larbani, and Tazdaït (2007) and Larbani and Nessah (2008) for existence theorems, and Colman et al (2011), Musy, Pottier, and Tazdaït (2012), Corley and Kwain (2014) and Corley (2015), for research on mixed extensions of finite games. This paper builds on the ideas and concepts in the spirit of the last four papers.…”

Section: Introductionmentioning

confidence: 99%

“…In a Berge equilibrium, every player is supported by the group of all other players together and in that sense is reflecting the idea of mutual support. According to both Larbani and Nessah (2008) and Corley (2015), this can be seen as the idea of 'one for all, and all for one'. Indeed, every player supports (as part of a larger group) every other player and all other players support every single player.…”

Section: Introductionmentioning

confidence: 99%

Unilateral support equilibria

Schouten

Borm

Hendrickx

2019

Journal of Mathematical Psychology

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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 define 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-off functions 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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“…For a game with unselfish players invoking this Golden Rule rationale, a BE is thus an equilibrium since no unilateral change of strategy by any player can improve another player's payoff. Such mutual support has been studied in Colman [15], Corley and Kwain [16], Corley [17], and the references therein. The mixed BE is called a dual equilibrium to the NE in the latter two references because of the duality discussed there.…”

Section: Introductionmentioning

confidence: 99%

“…In the latter case, even a mixed BE may not exist (17 lected by the players. For example, a "rational" action profile could be one that gives each player a "fair" payoff relative to all the players.…”

Section: Introductionmentioning

confidence: 99%

Normative Utility Models for Pareto Scalar Equilibria in n-Person, Semi-Cooperative Games in Strategic Form

Corley¹

2017

TEL

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Semi-cooperative games in strategic form are considered in which either a negotiation among the n players determines their actions or else an arbitrator specifies them. Methods are presented for selecting such action profiles by using multiple-objective optimization techniques. In particular, a scalar equilibrium (SE) is an action profile for the n players that maximize a utility function over the acceptable joint actions. Thus the selection of "solutions" to the game involves the selection of an acceptable utility function. In a greedy SE, the goal is to assign individual actions giving each player the largest payoff jointly possible. In a compromise SE, the goal is to make individual player payoffs equitable, while a satisficing SE achieves a target payoff level while weighting each player for possible additional payoff. These SEs are formally defined and shown to be Pareto optimal over the acceptable joint actions of the players. The advantage of these SEs is that they involve only pure strategies that are easily computed. Examples are given, including some well-known coordination games, and the worst-case time complexity for obtaining these SEs is shown to be linear in the number of individual payoffs in the payoff matrix. Finally, the SEs of this paper are checked against some standard game-theoretic bargaining axioms.

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A Mixed Cooperative Dual to the Nash Equilibrium

Cited by 20 publications

References 18 publications

The Mixed Berge Equilibrium in Extensive Form Games

The Mixed Berge Equilibrium in Extensive Form Games

Unilateral support equilibria

Normative Utility Models for Pareto Scalar Equilibria in n-Person, Semi-Cooperative Games in Strategic Form

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