Alice will not want to change strategies if
So q, Bob’s probability of playing hawk, is also 1/3. Consequently the Nash equilibrium in this payoff structure is to play hawk one-third of the time and dove two-thirds of the time.
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Siegfried, Tom "Appendix--Calculating a Nash Equilibrium."
A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature.
Washington, DC: The National Academies Press, 2006.
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