Consider the following game trees.

(a) Find all equilibria for the game tree on the left. Which of these are subgameperfect?

(b) In the game tree on the right, the payoffs \

(a,

b, c, d\) are positive real numbers. For each of the following statements (i), (ii), (iii), decide if it is true or false, justifying your answer with an argument or counterexample; you may refer to any standard results. For any \

(a,

b, c, d>0\), (i) the game always has a subgame-perfect equilibrium (SPE);
(ii) the payoff to player II in any SPE is always at least as high as her payoff in any equilibrium;
(iii) the payoff to player I in any SPE is always at least as high as his payoff in any equilibrium.

2 21 T B II 43 a b 0 0 T B II C 0 d 0