(Nash equilibrium in an asymmetric variant of Hawk-Dove) Let β be a mixed strategy that assigns positive probability only to the actions AA and PP in the game in Figure 294.1. Show that in order that AA and PP yield a player the same expected payoff when her opponent uses the strategy β, we need β to assign probability (V + v)/2c to AA. Show further that when her opponent uses this strategy β, a player obtains a higher expected payo? from the action AP than she does from the action AA, so that (β, β) is not a Nash equilibrium.