Question 3. (25 pts.) Consider the following normal form game that involves a society composed of 3 individuals, each of

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Question 3 25 Pts Consider The Following Normal Form Game That Involves A Society Composed Of 3 Individuals Each Of 1 (80.46 KiB) Viewed 34 times

Question 3. (25 pts.) Consider the following normal form game that involves a society composed of 3 individuals, each of whom has an endowment of 1 of a perfectly divisible consumption good (which can be consumed only in non-negative amounts). Each of these players is choosing how much to contribute to the “public fund," and that choice (due to feasibility considerations) must be in (0,1). All players' contributions are summed, and the emerging surplus equals twice the total contributions into the public fund. Then, this surplus is distributed equally among the players (independent of the amount of contri- butions of specific individuals). That is, if the total contribution into the public fund equals y, then each player gets * returns from the public fund regardless of their contribution levels. The players care only about their total consumption of the consumption good. As a result, the utility (payoff) of a player who has contributed x € (0,1) amount of his consumption good to the public fund when the total contributions to the public fund is given by y equals 2y (1 - 1) +23 a. (10 pts.) Formulate this situation as a normal form game and provide its formal definition. b. (5 pts.) Identify players' utilities for the given action profile x = (11, 12, 13) = (1/2, 4/5, 1/3) where I; E [0, 1] denotes the contribution of player i into the public fund, i = 1,2,3. C. (10 pts.) Find the strict dominant strategy equilibrium of this game. Please show your work. We will not award full grades to correct answers that do not contain a detailed display of the steps needed.