International Journal of Game Theory

, Volume 45, Issue 3, pp 719–729 | Cite as

Pure strategy equilibrium in finite weakly unilaterally competitive games

Original Paper
  • 256 Downloads

Abstract

We consider the finite version of the weakly unilaterally competitive game (Kats and Thisse, in Int J Game Theory 21:291–299, 1992) and show that this game possesses a pure strategy Nash equilibrium if it is symmetric and quasiconcave (or single-peaked). The first implication of this result is that unilaterally competitive or two-person weakly unilaterally competitive finite games are solvable in the sense of Nash, in pure strategies. We also characterize the set of equilibria of these finite games. The second implication is that there exists a finite population evolutionarily stable pure strategy equilibrium in a finite game, if it is symmetric, quasiconcave, and weakly unilaterally competitive.

Keywords

Weakly unilaterally competitive game Finite game Symmetric game Quasiconcave game Existence of a pure strategy equilibrium Solvable game 

JEL Classification

C72 (Noncooperative game) 

References

  1. Davey BA, Priestly HA (1990) Introduction to lattices and order. Cambridge University Press, CambridgeGoogle Scholar
  2. Duersch P, Oechssler J, Schipper BC (2012a) Pure strategy equilibria in symmetric two-player zero-sum games. Int J Game Theory 41:553–564Google Scholar
  3. Duersch P, Oechssler J, Schipper BC (2012b) Unbeatable imitation. Games Econ Behav 76:88–96Google Scholar
  4. Friedman JW (1983) On characterizing equilibrium points in two person strictly competitive games. Int J Game Theory 12:245–247CrossRefGoogle Scholar
  5. Friedman JW (1991) Game theory with applications to economics, 2nd edn. Oxford University Press, OxfordGoogle Scholar
  6. Hehenkamp B, Possajennikov A, Guse T (2010) On the equivalence of Nash and evolutionary equilibrium in finite populations. J Econ Behav Organ 73:254–258CrossRefGoogle Scholar
  7. Kats A, Thisse J-F (1992) Unilaterally competitive games. Int J Game Theory 21:291–299CrossRefGoogle Scholar
  8. Milgrom P, Roberts J (1990) Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58:1255–1277CrossRefGoogle Scholar
  9. Monderer D, Shapley LS (1996) Potential games. Games Econ Behav 14:124–143CrossRefGoogle Scholar
  10. Nash J (1951) Non-cooperative games. Ann Math 54:286–295CrossRefGoogle Scholar
  11. Schaffer ME (1988) Evolutionarily stable strategies for a finite population and a variable contest size. J Theor Biol 132:469–478CrossRefGoogle Scholar
  12. Schaffer ME (1989) Are profit-maximizers the best survivors?—A Darwinian model of economic natural selection. J Econ Behav Organ 12:29–45CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Business AdministrationTokyo Metropolitan UniversityTokyoJapan

Personalised recommendations