Arbeitspapier

On non-cooperative foundation and implementation of the Nash solution in subgame perfect equilibrium via Rubinstein's game

The alternating offers game due to Rubinstein (1982) had been used by Binmore (1980) and by Binmore et.al. (1986) to provide via its unique subgame perfect equilibrium an approximate non-cooperative support for the Nash bargaining solution of associated cooperative two-person bargaining games. These results had strengthened the prominent role of the Nash bargaining solution in cooperative axiomatic bargaining theory and its application, for instance in labor markets, and have often even be interpreted as a mechanism theoretical implementation of the Nash solution. Our results in the present paper provide exact non-cooperative foundations first, in our Proposition, via weakly subgame perfect equilibria of a game that is a modification of Rubinstein's game, then in our Theorem, via sub-game perfect equilibria of a game that is a further modification of our first game. Moreover, they provide a general rule how to transform approximate support results into exact ones. Finally, we discuss the relation of the above mentioned support results, including our present ones, with mechanism theoretic implementation in (weakly) subgame perfect equilibrium of the Nash solution. There we come to the conclusion that a sound interpretation as an implementation can hardly be found except in very rare cases of extremely restricted domains of players' preferences.

Language: Englisch

Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 550

Classification: Wirtschaft
Cooperative Games
Noncooperative Games
Stochastic and Dynamic Games; Evolutionary Games; Repeated Games

Subject: Nash program
Non-cooperative foundation
Implementation
Nash solution
Rubinstein game
Subgame perfect equilibrium

Event: Geistige Schöpfung

(who): Duman, Papatya
Trockel, Walter

Event: Veröffentlichung

(who): Bielefeld University, Center for Mathematical Economics (IMW)

(where): Bielefeld

(when): 2016

Handle: http://hdl.handle.net/10419/149007

URN: urn:nbn:de:0070-pub-29003840

Last update: 10.03.2025, 11:44 AM CET

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Object type

Arbeitspapier

Associated

Duman, Papatya
Trockel, Walter
Bielefeld University, Center for Mathematical Economics (IMW)

Time of origin

2016

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