Consider the game of imperfect information with the following sequence of moves:
- nature determines whether payoffs are given by matrix I or II below, each being equally likely;
- player 1 (the row player) is informed about nature’s move (that is, he learns the actual payoffs), but player 2 is not;
- player 1 chooses U or D, and player 2 chooses L or R simultaneously;
- the payoffs are determined by the matrix drawn by nature.
Matrix I has the following payoffs: (U,L): (1,1) (U,R), (D,L), (D,R): (0,0)
Matrix II has the following payoffs: (U,L), (U,R), (D,L): (0,0) (D,R): (2,2)
(a) Draw the extensive-form tree of the game.
(b) Find all (pure or mixed strategy) sequential equilibria.
(c) Find all (pure or mixed strategy) trembling-hand perfect equilibria.