question archive Consider a game with two players, each of whom can choose a number between 0 and 100, including O and 100
Consider a game with two players, each of whom can choose a number between 0 and 100, including O and 100
Subject:EconomicsPrice: Bought3
Consider a game with two players, each of whom can choose a number between 0 and 100, including O and 100. Let s1 and s2 be the respective strategies of players 1 and 2. Payoffs are determined by the following rules: • If 81 +82 < 100, player 1 receives si and player 2 receives 82. • If 81 +82 > 100, both players receive 0. 1. Find the pure strategies Nash equilibria of this game. (b) 2. Suppose now that players' choices are no longer constrained to values below 100, but they can choose zero or any positive number. What are the pure strategies Nash equilibria of this modified game? 3. Consider again a situation in which players choose a number between 0 and 100, but the payoffs are determined in a different way, which is: If 81 +82 < 100, player 1 receives s, and player 2 receives $1. • If 81 +82 > 100, both players receive 0. Find the new set of Nash equilibria in pure strategies.
