- Consider The Three Player Game G With The Payoffs Given In Table 1 Player 1 May Choose Table 1 Payoffs Of G U D L R L 1 (280.43 KiB) Viewed 54 times
Consider the three-player game G with the payoffs given in Table 1. (Player 1 may choose Table 1: Payoffs of G U D L R L R N (2, 1, 2) (2, 1, 2) (0, 0, 0) (0,0,0) E (1,0,1) (1, 0, 1) (2, 1, 2) (2,1,2) W (2, 1, 2) (0, 0, 0) (2, 1, 2) (0, 0, 0) S (1,0, 1) (2, 1, 2) (1, 0, 1) (2,1,2) each of the rows N, E, W, S, Player 2 each of the columns L, R, and Player 3 each of the two matrices U, D.) Let (p, q, r, s), (y, 1-y), and (z, 1-z) be typical mixed strategies of Player 1, Player 2, and Player 3, respectively. Find and explicitly describe all mixed strategies of Player 1 such that both other players are indif- ferent. (Hint: Show that Player 2 (respectively 3) is indifferent if r and s (respectively p and q) are in a certain relation.)