Chapter 14.4, Problem 4P

Find the Nash equilibria, including any mixed strategy equilibria that might exist, for the following strategic-form games. 1. Curve Slider 1, 2 0,3 2,1 Fast Early 3,0 2,1 1, 2 2,1 1, 2 3,0 Mid Late 2. Nice Mean 0,3 1,1 Nice 3,3 3,0 Mean 3. Beef Fish Red 3,3 White 1,2 0,1 2,0 Fight х, 2 1,1 2, x Train Fight Train 0,0 4.

3. Consider the following n-person game. Each player picks an integer between 1 and m. If you pick k, and you are the only one that picks k, then you win Sk. Note: there can be multiple winners (or no winners) in a round of this game. (a) Find your expected payoff if you choose k, given that the other n -1 players are using strategy p = (P1. P2,....Pm). (b) Find the Nash equilibrium when n = 2 and m = 3. Note, this is just a simple 2-player non zero sum game, but be careful!

Consider the following sequential game. There are two players, Player 1 and Player 2, who alternate turns, Each turn, each player can choose one of two actions: Across (A) or Down (D). If either player chooses D on their turn, the game ends. Otherwise, it becomes the other player's turn, who may again play either A or D. The game ends after 100 turns for each player, if no player has played D previously. Payoffs in the game are represented by the following game tree, where nodes denote turns for each player, branches denote actions, and final payoffs are indicated at the end of each branch (Player 1's payoff is the first number, Player 2's payoff is the second): 100 100 ID D. D 98 98 97 100 99 99 98 101 Note that the sum of payoffs for each player is increasing by 1 each turn. However, a player claims a slightly larger payoff if the game ends on their turn, rather than their opponent's. Assuming that both players strictly apply the principle of backward induction, what payoffs will the…