Collaborative Dominance: When Doing Unto Others As You Would Have Them Do Unto You Is Reasonable.

Souza, Filipe and Rêgo, Leandro (2012): Collaborative Dominance: When Doing Unto Others As You Would Have Them Do Unto You Is Reasonable.

Abstract

In this article, we analyze how reasonable it is to play according to some Nash equilibria if players have a preference for one of their opponents’ strategies. For this, we propose the concepts of collaborative dominance and collaborative equilibrium. First we prove that, when the collaborative equilibrium exists it is always efficient, what can be seen as a focal property. Further we argue that a reason for players choosing not to collaborate is if they are focusing in security instead of efficiency, in which case they would prefer to play maximin strategies. This argument allows us to reduce the hall of reasonable equilibria for games where a collaborative equilibrium exists. Finally, we point out that two-player zero-sum games do not have collaborative equilibrium and, moreover, if there exists a strategy profile formed only by collaboratively dominated actions it is a Nash equilibrium in such kind of game.

• Item Type: MPRA Paper
• Language: English
• Keywords: Nash Equilibrium; Collaborative Dominance; Two-Players Zero-Sum Games
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory

References

[1] Aumann R J. 1974. Subjectivity and Correlation in Randomized Strategies. Journal of Mathematical Economics, 1: 67-96.

[2] Aumann R J. 1987. Correlated Equilibrium as an Expression of Bayesian Rationality. Econometrica, 55: 1-18.

[3] Aumann , R J.; Maschler, M. 1972. Some thoughts on the minimax principle. Management Science, 18: 54-63.

[4] Harsanyi, J C. 1973. Games with Randomly Disturbed Payoffs: A New Rationale for Mixed Strategy Equilibrium Points. International Journal of Game Theory, 2: 1-23.

[5] Harsanyi, J C.; Selten, R. 1988. A General Theory of Equilibrium Selection in Games. London: MIT Press.

[6] Kalai, E.; Samet, D. 1984. Persistente Equilibria. International Journal of Game Theory, 13: 129-144.

[7] Kuhn, H. W.; Tucker A. W. 1958. John von Neumann’s work in the theory of games and mathematical economics. Bulletin of the American Mathematical Society, 64:100-122.

[8] Leonard, R. J. 1995. From Parlor Games to Social Science: Von Neumann, Morgenstern, and the Creation of Game Theory, 1928-1994. Journal of Economic Literature, 33: 730-761. [9] Myerson, R. B. 1978. Refinements of the Nash Equilibrium Concept. International Journal of Game Theory, 7: 73-80.

[10] Nasar, S. 1998. A Beautiful Mind: A Biography of John Forbes Nash, Jr. New York: Simon.

[11] Nash, J F. 1951. Non-Cooperative Games. The Annals of Mathematics, 54: 286-295.

[12] Osborne, M. J.; Rubinstein, A. 1994. A Course in Game Theory. Cambridge Mass: MIT Press.

[13] Poundstone, W. 1992. Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb. Oxford: Oxford University Press.

[14] Pruzhansky, V. 2011. Some interesting properties of maximin strategies. International Journal of Game Theory, 40: 351-365.

[15] Selten, R. 1975. A reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4:25-55.