Each of two players has two possible actions, Quiet and Fink; each action pair results in...

 

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Each of two players has two possible actions, Quiet and Fink; each action pair results in the players' receiving amounts of money equal to the numbers corresponding to that action pair in Figure 26.1. (For example, if player 1 chooses Quiet and player 2 chooses Fink, then player 1 receives nothing, whereas player 2 receives $3.) The players are not "selfish"; rather, the preferences of each player i are represented by the payoff function m; (a) + am; (a), where m; (a) is the amount of money received by player i when the action profile is a, j is the other player, and a is a given non- negative number. Player 1's payoff to the action pair (Quiet, Quiet), for example, is 2+2a. a. Formulate a strategic game that models this situation in the case a = 1. Is this game the Prisoner's Dilemma? b. Find the range of values of a for which the resulting game is the Prisoner's Dilemma. For values of a for which the game is not the Prisoner's Dilemma, find the Nash equilibria. Each of two players has two possible actions, Quiet and Fink; each action pair results in the players' receiving amounts of money equal to the numbers corresponding to that action pair in Figure 26.1. (For example, if player 1 chooses Quiet and player 2 chooses Fink, then player 1 receives nothing, whereas player 2 receives $3.) The players are not "selfish"; rather, the preferences of each player i are represented by the payoff function m; (a) + am; (a), where m; (a) is the amount of money received by player i when the action profile is a, j is the other player, and a is a given non- negative number. Player 1's payoff to the action pair (Quiet, Quiet), for example, is 2+2a. a. Formulate a strategic game that models this situation in the case a = 1. Is this game the Prisoner's Dilemma? b. Find the range of values of a for which the resulting game is the Prisoner's Dilemma. For values of a for which the game is not the Prisoner's Dilemma, find the Nash equilibria.