Duersch, Peter and Oechssler, Joerg and Schipper, Burkhard C (2010): Pure Saddle Points and Symmetric Relative Payoff Games.
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It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of a finite population evolutionary stable strategies.
|Item Type:||MPRA Paper|
|Original Title:||Pure Saddle Points and Symmetric Relative Payoff Games|
|Keywords:||symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; finite population evolutionary stable strategy; increasing differences; decreasing differences; potentials; additive separability|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games
|Depositing User:||Burkhard C Schipper|
|Date Deposited:||22. Feb 2010 11:28|
|Last Modified:||01. Sep 2015 11:33|
Alos-Ferrer, C. and A.B. Ania (2005). The evolutionary stability of perfectly competitive behavior, Economic Theory 26, 497-516.
Ania, A. (2008). Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition, Journal of Economic Behavior and Organization 65, 472-488.
Branzei, R., Mallozzi, L., and S. Tijs (2003). Supermodular games and potential games, Journal of Mathematical Economics 39, 39-49.
Bryant, J. (1983). A simple rational expectations Keynes-type coordination model, Quartely Journal of Economics 98, 525-528.
Debreu, G. (1952). A social equilibrium existence theorem, Proceedings of the National Academy of Sciences 38, 886-893.
Duersch, P., Oechssler, J., and B.C. Schipper (2010). Unbeatable imitation, mimeo., University of Heidelberg and the University of California, Davis.
Hehenkamp, B., Leininger, W., and A. Possajennikov (2004). Evolutionary equilibrium in Tullock contests: Spite and overdissipation, European Journal of Political Economy 20, 1045-1057.
Hehenkamp, B., Possajennikov, A., and T. Guse (2010). On the equivalence of Nash and evolutionary equilibrium in finite populations, Journal of Economic Behavior and Organization 73, 254-258.
Leininger, W. (2006). Fending off one means fending off all: evolutionary stability in quasi-submodular games, Economic Theory 29, 713-719.
Matros, A., Temzilidis, T., and J. Duffy (2009). Competitive behavior in market games: Evidence and theory, mimeo.
Milgrom, P. and J. Roberts (1990). Rationalizability, learning, and equilibrium in games with strategic complementarities, Econometrica 58, 1255-1277.
Monderer, D. and L.S. Shapley (1996). Potential games, Games and Economic Behavior 14, 124-143.
Nash, J. (1953). Two--person cooperative games, Econometrica 21, 128-140.
Nash, J. (1951). Non-cooperative games, Annals of Mathematics 54, 286-295.
von Neumann, J. (1928). Zur Theorie der Gesellschaftsspiele, Mathematische Annalen 100, 295-320.
Nydegger, R.V. and G. Owen (1974). Two-person bargaining: An experimental test of the Nash axioms, International Journal of Game Theory 3, 239-249.
Osborne, M. (2004). An introduction to game theory, Oxford University Press.
Possajennikov, A. (2003). Evolutionary foundation of aggregative-taking behavior, Economic Theory 21, 921-928.
Radzik, T. (1991). Saddle point theorems, International Journal of Game Theory 20, 23-32.
Roth, A.E. and M.W.K. Malouf (1979). Game-theoretic models and the role of information in bargaining, Psychological Review 86, 574-594.
Schaffer, M.E. (1989). Are profit-maximizers the best survivors?, Journal of Economic Behavior and Organization 12, 29-45.
Schaffer, M.E. (1988). Evolutionary stable strategies for a finite population and a variable contest size, Journal of Theoretical Biology 132, 469-478.
Shapley, L.S. (1964). Some topics in two-person games, in: Dresher, M., Shapley, L.S. and A.W. Tucker (eds.), Advances in Game Theory, Annals of Mathematical Studies 52, 1-28.
Tanaka, Y. (2000). A finite population ESS and a long run equilibrium in an n-players coordination game, Mathematical Social Sciences 39, 195-206.
Topkis, D. M. (1998). Supermodularity and complementarity, Princeton, New Jersey: Princeton University Press.
Tullock, G. (1980). Effcient rent seeking, in: Buchanan, Tollison, Tullock (eds.), Towards a theory of the rent seeking society, Texas A & M University Press, 3-15.
Van Huyck, J., Battalio, R., and R. Beil (1990). Tacit coordination games, strategic uncertainty and coordination failure, American Economic Review 80, 234-248.
Vega-Redondo, F. (1997). The evolution of Walrasian behavior, Econometrica 65, 375-384.
Walker, J.M., Gardner, R., and E. Ostrom (1990). Rent dissipation in a limited-access Common-Pool resource: Experimental evidence, Journal of Environmental Economics and Management 19, 203-211.