Kalai-Smorodinsky Bargaining Solution and Alternating Offers Game

ABSTRACT

This article presents an alternating offers game that supports a Kalai-Smorodinsky bargaining solution (KSS). It is well known that a solution to an alternating offers game has a breakdown point equivalent to a status quo that converges to its Nash bargaining solution because the probability of breakdown becomes negligible, whereas we show that a KSS is obtained if a breakdown gives everything to the player who rejects. The former option, which is adopted by many application papers may be suitable for*ex ante* production. However, the latter option should be more appropriate for *ex post* production, because players do not need to be concerned with cooperation.

This article presents an alternating offers game that supports a Kalai-Smorodinsky bargaining solution (KSS). It is well known that a solution to an alternating offers game has a breakdown point equivalent to a status quo that converges to its Nash bargaining solution because the probability of breakdown becomes negligible, whereas we show that a KSS is obtained if a breakdown gives everything to the player who rejects. The former option, which is adopted by many application papers may be suitable for

Cite this paper

Y. Nishihara, "Kalai-Smorodinsky Bargaining Solution and Alternating Offers Game,"*Theoretical Economics Letters*, Vol. 3 No. 1, 2013, pp. 78-79. doi: 10.4236/tel.2013.31012.

Y. Nishihara, "Kalai-Smorodinsky Bargaining Solution and Alternating Offers Game,"

References

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[2] J. Nash, “Two-Person Cooperative Games,” Econometrica, Vol. 21, No. 1, 1953, pp. 128-140. doi:10.2307/1906951

[3] A. Shaked and J. Sutton, “Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model,” Econometrica, Vol. 52, No. 6, 1984, pp. 1351-1364. doi:10.2307/1913509

[4] A. Rubinstein, “Perfect Equilibrium in a Bargaining Model,” Econometrica, Vol. 50, No. 1, 1982, pp. 97-109. doi:10.2307/1912531

[5] S. Rachmilevitch, “Cooperative Bargaining: Independence and Monotonicity Imply Disagreement,” Economics Letters, Vol. 118, No. 1, 2013, pp. 240-242. doi:10.1016/j.econlet.2012.10.024

[6] J. Nash, “The Bargaining Problem,” Econometrica, Vol. 18, No. 2, 1950, pp. 155-162. doi:10.2307/1907266

[7] N. Anbarci and J. H. Boyd III, “Nash Demand Game and the Kalai-Smorodinsky Solution,” Games and Economic Behavior, Vol. 71, No. 1, 2011, pp. 14-22. doi:10.1016/j.geb.2010.07.009

[8] J. V. Howard, “A Social Choice Rule and Its Implementation in Perfect Equilibrium,” Journal of Economic Theory, Vol. 56, No. 1, 1992, pp. 142-159. doi:10.1016/0022-0531(92)90073-Q

[9] H. Moulin, “Implementing the Kalai-Smorodinsky Bargaining Solution,” Journal of Economic Theory, Vol. 33, No. 1, 1984, pp. 32-45. doi:10.1016/0022-0531(84)90038-3

[10] J. Dubra, “An Asymmetric Kalai-Smorodinsky Solution,” Economics Letters, Vol. 73, No. 2, 2001, pp. 131-136. doi:10.1016/S0165-1765(01)00426-8

[11] I. Bozbay, F. Dietrich and H. Peters, “Bargaining with Endogenous Disagreement: The Extended Kalai-Smorodinsky Solution,” Games and Economic Behavior, Vol. 74, No. 1, 2012, pp. 407-417. doi:10.1016/j.geb.2011.06.007

[12] T. Anant, B. Mukherji and K. Basu, “Bargaining without Convexity: Generalizing the Kalai-Smorodinsky Solution,” Economics Letters, Vol. 30, No. 2, 1990, pp. 115-119. doi:10.1016/0165-1765(90)90155-T

[1] E. Kalai and M. Smorodinsky, “Other Solutions to Nash’s Bargaining Problem,” Econometrica, Vol. 43, No. 3, 1975, pp. 513-518. doi:10.2307/1914280

[2] J. Nash, “Two-Person Cooperative Games,” Econometrica, Vol. 21, No. 1, 1953, pp. 128-140. doi:10.2307/1906951

[3] A. Shaked and J. Sutton, “Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model,” Econometrica, Vol. 52, No. 6, 1984, pp. 1351-1364. doi:10.2307/1913509

[4] A. Rubinstein, “Perfect Equilibrium in a Bargaining Model,” Econometrica, Vol. 50, No. 1, 1982, pp. 97-109. doi:10.2307/1912531

[5] S. Rachmilevitch, “Cooperative Bargaining: Independence and Monotonicity Imply Disagreement,” Economics Letters, Vol. 118, No. 1, 2013, pp. 240-242. doi:10.1016/j.econlet.2012.10.024

[6] J. Nash, “The Bargaining Problem,” Econometrica, Vol. 18, No. 2, 1950, pp. 155-162. doi:10.2307/1907266

[7] N. Anbarci and J. H. Boyd III, “Nash Demand Game and the Kalai-Smorodinsky Solution,” Games and Economic Behavior, Vol. 71, No. 1, 2011, pp. 14-22. doi:10.1016/j.geb.2010.07.009

[8] J. V. Howard, “A Social Choice Rule and Its Implementation in Perfect Equilibrium,” Journal of Economic Theory, Vol. 56, No. 1, 1992, pp. 142-159. doi:10.1016/0022-0531(92)90073-Q

[9] H. Moulin, “Implementing the Kalai-Smorodinsky Bargaining Solution,” Journal of Economic Theory, Vol. 33, No. 1, 1984, pp. 32-45. doi:10.1016/0022-0531(84)90038-3

[10] J. Dubra, “An Asymmetric Kalai-Smorodinsky Solution,” Economics Letters, Vol. 73, No. 2, 2001, pp. 131-136. doi:10.1016/S0165-1765(01)00426-8

[11] I. Bozbay, F. Dietrich and H. Peters, “Bargaining with Endogenous Disagreement: The Extended Kalai-Smorodinsky Solution,” Games and Economic Behavior, Vol. 74, No. 1, 2012, pp. 407-417. doi:10.1016/j.geb.2011.06.007

[12] T. Anant, B. Mukherji and K. Basu, “Bargaining without Convexity: Generalizing the Kalai-Smorodinsky Solution,” Economics Letters, Vol. 30, No. 2, 1990, pp. 115-119. doi:10.1016/0165-1765(90)90155-T