Saglam, Ismail (2016): An Alternative Characterization for Iterated KalaiSmorodinskyNash Compromise.

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Abstract
In this paper, we offer for twoperson games an alternative characterization of Iterated KalaiSmorodinskyNash Compromise (IKSNC), which was introduced and first characterized by Saglam (2016) for $n$person games. We present an axiom called GammaDecomposability, satisfied by any solution that is decomposable with respect to a given reference solution Gamma. We then show that the IKSNC solution is uniquely characterized by GammaDecomposability whenever Gamma satisfies the standard axioms of Independence of Equivalent Utility Representations and Symmetry, along with three additional axioms, namely Restricted Monotonicity of Individually Best Extensions, Weak Independence of Irrelevant Alternatives, and Weak Pareto Optimality under Symmetry.
Item Type:  MPRA Paper 

Original Title:  An Alternative Characterization for Iterated KalaiSmorodinskyNash Compromise 
English Title:  An Alternative Characterization for Iterated KalaiSmorodinskyNash Compromise 
Language:  English 
Keywords:  Cooperative bargaining; KalaiSmorodinsky solution; Nash solution 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C78  Bargaining Theory ; Matching Theory 
Item ID:  73564 
Depositing User:  Ismail Saglam 
Date Deposited:  07 Sep 2016 14:43 
Last Modified:  28 Sep 2019 12:53 
References:  Kalai, E. and Smorodinsky, M. (1975) Other solutions to Nash's bargaining problem, Econometrica 43, 513518. Kalai, E. (1977) Proportional solutions to bargaining situations: Interpersonal utility comparisons, Econometrica 45, 16231630. Nash, J. F. (1950) The bargaining problem, Econometrica 28, 155162. Rachmilevitch, S. (2012) Gradual negotiations and proportional solutions, Operations Research Letters 40, 459461. Rachmilevitch, S. (2014) Bridging the gap between the Nash and KalaiSmorod insky bargaining solutions, in Contributions to Game Theory and Management, Vol. 7, eds. Petrosyan, L. & Zenkevich, N. (St. Petersburg University), pp. 300312. Raiffa, H. (1953) Arbitration schemes for generalized twoperson games, in Contributions to the Theory of Games II, Annals of Mathematics Studies, No. 28, eds. Kuhn, H. W. & Tucker, A. W. (Princeton University Press), pp. 361387. Roth, A. E. (1979) An impossibility result concerning nperson bargaining games, International Journal of Game Theory 8, 129132. Saglam, I. (2014) A simple axiomatization of the egalitarian solution, International Game Theory Review 16, 145000811. Saglam, I. (2016) Iterated KalaiSmorodinskyNash compromise, MPRA Paper 70614, University Library of Munich, Germany. Salonen, H. (1988) Decomposable solutions for nperson bargaining games, European Journal of Political Economy 4, 333347. Thomson, W. (1983) The fair division of a fixed supply among a growing population, Mathematics of Operations Research 8, 319326. Thomson, W. and Lensberg, T. (1989) Axiomatic Theory of Bargaining with a Variable Number of Agents (Cambridge University Press). Trockel, W. (2014) Robustness of intermediate agreements for the discrete Raiffa solution, Games and Economic Behavior 85, 3236. Trockel, W. (2015) Axiomatization of the discrete Raiffa solution, Economic Theory Bulletin 3, 917. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/73564 