evolutionarily stable strategy

Definition

A mixed strategy x*x^* in a two-player symmetric game is an evolutionarily stable strategy (ESS) if for every mixed strategy xx that differs from x*x^* there exists ϵ0=ϵ0(x)>0\epsilon_0 = \epsilon_0(x) > 0 such that, for all ϵ∈(0,ϵ0)\epsilon \in (0,\epsilon_0), (1−ϵ)u1(x,x*)+ϵu1(x,x)<(1−ϵ)u1(x*,x*)+ϵu1(x*,x*)(1-\epsilon) u_1(x, x^*) + \epsilon u_1(x,x) < (1-\epsilon) u_1(x^*, x^*) + \epsilon u_1(x^*, x^*)

References

  1. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 190.
  2. Smith, J. M., & Price, G. R. (1973). The logic of animal conflict. Nature, 246(5427), 15-18. https://doi.org/10.1038/246015a0
  3. https://wiki.mbalib.com/wiki/%E8%BF%9B%E5%8C%96%E7%A8%B3%E5%AE%9A%E7%AD%96%E7%95%A5
  4. https://knowledgehive.github.io/Game-Theory/lecture%2012.html