- Exercise 3 Consider The Three Player Game G With The Payoffs Given In Table 1 Player 1 Chooses One Table 1 Payoffs O 1 (254.32 KiB) Viewed 34 times
Exercise 3. Consider the three-player game G with the payoffs given in Table 1. (Player 1 chooses one Table 1: Payoffs of G W N E L R L R L R (3,3,3) (0,0,0) T B ( (4, 4, 4) (0, 4, 8) (4, 0,8) (0,0,0) ( (4,4,0) (4, 0,8) (0,4,8) (0, 0, 4)
( (0, 0, 0) (3,3,3) of the two rows T, B, player 2 chooses one of the two columns L, R, and player 3 chooses one of the three matrices W, N, E.) 1. Show that E is not the best response to any pair of mixed strategies of players 1 and 2. 2. Find all mixed Nash equilibria. 3. Find a belief of player 3 according to which E is the unique best response and show that E is not weakly dominated. 4. Describe explicitly a correlated equilibrium in which player 3 chooses B (for sure, with probability 1) and players 1 and 2 play (T, L) and (B, R) with equal probabilities.