# original papers : Bargaining solutions with non-standard objectives

## Author

Listed:
• Peter B. Linhart

## Abstract

I examine the pure-strategy solutions of the sealed-bid bargaining game with incomplete information, when the buyer's and seller's objectives are other than the standard objective, namely maximization of expected profit. The motivation for this exploration lies in three problems of the standard formulation: the necessity of assuming common priors, the existence of uncountably many Nash equilibria, with no means for the players to coordinate on any one of them, and the uncertain relationship between these equilibria and observed behavior in bargaining experiments. Specifically, I consider two alternative objectives: minimization of maximum regret, and maximization of maximum profit. The solution concept here is not Nash equilibrium, but rather $\alpha$-individually rational strategy bundle. For that reason, I shall, where appropriate, use the word "solution" in place of "equilibrium." Yet we find that the notion of Nash Equilibrium reappears, in a sense to be explained. In the minimax-regret case I find (in contrast to the case of expected profit) a unique solution; this solution reduces, for priors with coincident support, to the linear equilibrium of Chatterjee-Samuelson. In the maximum-profit case there are many solutions; they turn out to be slight generalizations of the one-step equilibria of Leininger-Linhart-Radner.

## Suggested Citation

• Peter B. Linhart, 2001. "original papers : Bargaining solutions with non-standard objectives," Review of Economic Design, Springer;Society for Economic Design, vol. 6(2), pages 225-239.
• Handle: RePEc:spr:reecde:v:6:y:2001:i:2:p:225-239
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## Citations

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Cited by:

1. Lampros Boukas & Diogo Pinheiro & Alberto Pinto & Stylianos Xanthopoulos & Athanasios Yannacopoulos, 2009. "Behavioural and Dynamical Scenarios for Contingent Claims Valuation in Incomplete Markets," Papers 0903.3657, arXiv.org.
2. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
3. Rasch, Alexander & Wambach, Achim & Wiener, Kristina, 2012. "Bargaining and inequity aversion: On the efficiency of the double auction," Economics Letters, Elsevier, vol. 114(2), pages 178-181.

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