Abstract
Abstract. This paper suggests variations to the baseline Nash cooperative solution that take into account the Kalai-Smorodinsky critique. One the one hand, a CES form of the maximand is proven to accommodate both the generalized two-person Nash and the Kalai-Smorodinsky - as other proportional - solutions as special cases. As an alternative, a Stone-Geary formulation is forwarded, weighing both the distances to the threat and to the ideal point, along with the corresponding CES generalization. Interpretations of the implied equilibrium solutions – generalizable to n-person cooperative games – are provided, arising as equations balancing geometric averages of measures of attitude towards (large) risk(s) of the players.
Keywords. Two-person cooperative games, Cooperative games maximands, Opportunism, Pessimism.
JEL. C71, H56, D74, J51, J52, D39.References
Aumann, R.J., & Kurz, H. (1977). Power and taxes, Econometrica, 45(5), 1137-1161. doi. 10.2307/1914063
Binmore, K., Rubinstein, A., & Wolinsky, A. (1986). The Nash solution in economic modelling, Rand Journal of Economics, 17(2), 176-188. doi. 10.2307/2555382
Blackorby, C., Bossert, W., & Donaldson, D. (1994). Generalized Ginis and cooperative bargaining solutions, Econometrica, 62(5), 1161-1178. doi. 10.2307/2951511
Boadway, R.W., & Bruce, N. (1984). Welfare Economics. Oxford, Basil Blackwell.
Cahuc, P., & Zylberberg, A. (2001). Le Marché du Travail. Bruxelles: De Boeck & Larcier.
Kalai, E. (1977). Proportional solutions to bargaining situations: Interpersonal utility comparisons, Econometrica, 45(7), 1623-1630. doi. 10.2307/1913954
Kalai, E. & Smorodinsky, M. (1975). Other solutions to Nash’s bargaining problem, Econometrica, 43(3), 513-518. doi. 10.2307/1914280
Manzini, P. (1998). Game theoretic models of wage bargaining, Journal of Economic Surveys, 12(1), 1-41. doi. 10.1111/1467-6419.00046
Nash, J. (1950). The bargaining problem, Econometrica, 18(1), 155-162. doi. 10.2307/1907266
Nash, J. (1953). Two-person cooperative games, Econometrica, 21(1), 128-140. doi. 10.2307/1906951
Osborne, M., & Rubinstein, A. (1990). Bargaining and Markets. Academic Press.
Riddell, W.C. (1981). Bargaining under uncertainty, American Economic Review, 71(4), 579-590.
Roth, A.E. (1977). Independence of irrelevant alternatives, and solutions to Nash’s bargaining problem, Journal of Economic Theory, 16(2), 247-251. doi. 10.1016/0022-0531(77)90008-4
Rubinstein, A. (1982). Perfect equilibrium in a bargaining model, Econometrica, 50(1), 97-109. doi. 10.2307/1912531
Svejnar, J. (1986). Bargaining power, fear of disagreement, and wage settlements: Theory and evidence from U.S. industry, Econometrica, 54(5), 1055-1078. doi. 10.2307/1912322
Verchenko, P.I. (2004). Multiplicative approach in efficiency characteristics estimation and risk pricing, In Proceedings of the Scientific School MA SR – 2004, St. Petersburg: p.368-373.
