battle of the sexes game

#game_theory

Game

		Player II
		F	C
Player I	F	2, 2	0, 0
	C	0, 0	1, 2

game has three equilibria:

$(F, F)$ , payoff $(2,1)$
$(C,C)$ , payoff $(1,2)$
$([\frac{2}{3}(F),\frac{1}{3}(C)],[\frac{1}{3}(F),\frac{2}{3}(C)])$ , payoff $(\frac{2}{3}, \frac{2}{3})$

References

M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 301.