Strictly Perfect Equilibrium (a) Show that a completely mixed Nash equilibrium in a finite game G is strictly perfect. (b) Show that a strict Nash equilibrium in a game G is strictly perfect. (A Nash...

Strictly Perfect Equilibrium

(a) Show that a completely mixed Nash equilibrium in a finite game G is strictly perfect.

(b) Show that a strict Nash equilibrium in a game G is strictly perfect. (A Nash equilibrium is strict if any unilateral deviation of a player leads to a strictly lower payoff for that player.)

(c) Compute all Nash equilibria, perfect equilibria, proper equilibria, and strictly perfect equilibria in the following game, where ˛; ˇ > 0. (Conclude that strictly perfect equilibria may fail to exist.)