91影视

Let \(G\) be a strictly competitive game that has a Nash equilibrium. a. Show that if some of player 1's payoffs in \(G\) are increased in such a way that the resulting game \(G^{\prime}\) is strictly competitive then \(G^{\prime}\) has no equilibrium in which player 1 is worse off than she was in an equilibrium of \(G\). (Note that \(G^{\prime}\) may have no equilibrium at all.) b. Show that the game that results if player 1 is prohibited from using one of her actions in \(G\) does not have an equilibrium in which player 1 's payoff is higher than it is in an equilibrium of \(G\). c. Give examples to show that neither of the above properties necessarily holds for a game that is not strictly competitive.

(Guessing Morra) In the two-player game 鈥淕uessing Morra鈥�, each player simultaneously holds up one or two fingers and also guesses the total shown. If exactly one player guesses correctly then the other player pays her the amount of her guess (in $, say). If either both players guess correctly or neither does so then no payments are made.