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# On non-cooperative foundation and implementation of the Nash Solution in subgame perfect equilibrium via Rubinstein’s game

## Author

Listed:
• Duman, Papatya

(Center for Mathematical Economics, Bielefeld University)

• Trockel, Walter

(Center for Mathematical Economics, Bielefeld University)

## Abstract

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.

## Suggested Citation

• Duman, Papatya & Trockel, Walter, 2016. "On non-cooperative foundation and implementation of the Nash Solution in subgame perfect equilibrium via Rubinstein’s game," Center for Mathematical Economics Working Papers 550, Center for Mathematical Economics, Bielefeld University.
• Handle: RePEc:bie:wpaper:550
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File Function: First Version, 2016

## References listed on IDEAS

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## Citations

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Cited by:

1. Papatya Duman & Walter Trockel, 2020. "Nash Smoothing on the Test Bench: Ha-Essential Equilibria," Working Papers CIE 130, Paderborn University, CIE Center for International Economics.
2. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "A sequential bargaining protocol for land rental arrangements," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 65-99, June.
3. Duman, Papatya & Trockel, Walter, 2020. "Nash Smoothing on the Test Bench: $H_{\alpha}$ -Essential Equilibria," Center for Mathematical Economics Working Papers 632, Center for Mathematical Economics, Bielefeld University.

### Keywords

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

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