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4. Consider a game with two players deciding simultaneously how much to donate for the organization of a party. Let dį be the amount donated by player 1 and d2 the amount donated by player 2. Once the money is donated they cannot get it back, no matter whether they organize the party or not. They will be able to organize the party if and only if the sum of their donations is more than or equal to 150 dollars (i.e., dı+d2 > 150). If they organize the party their payoff is 71 = 100 – d, and 72 100 – d2 where 100 is their identical valuation of party. If they do not organize the party, their payoff is 111 = -dand 712 -d2. (a) Is there any Nash equilibrium in which the party is not organized? If yes, find one and verify that it is indeed a Nash equilibrium. If not, explain why. (b) Is there any Nash equilibrium in which the party is organized? If yes, find one and verify that it is indeed a Nash equilibrium. If not, explain why. (c) Suppose now that player 1 makes a donation first and player 2, observing the do- nation of player 1, decides how much to donate. Solve the game by backward induction. Explain what is the strategy profile and what are the resulting payoff for each player

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