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Question 2: Contributing to public goods Each player i = 1, 2 is given $100, and then asked to contribute an amount 392', to a common fund. Each player keeps the remainder 100 152-. Both players receive $0.75 of each dollar contributed to the common fund. (Note: The common fund is a public good). For simplicity, assume that cc;- can take only three values: 0,50, or 100. The payoffs for the players are as follows: 3 Player 1: (100 :31) + 1(31 +332) lm a:2| 3 Player 2: (100 2:2) + E0131 + 2:2) lm] 5172' Note that |a:1 3:2] is the absolute value of .151 .952. That is, if m] > :32, then |w1 3:2 2 9:1 x2 > 0. Also, if 3:1 0. (i) Write down the payoff matrix assuming ,8 = 0 and nd out all Nash equilibria of the game. (ii) Interpret [5' (> 0). (iii) Write down the payoff matrix assuming ,8 = % and nd out all Nash equilibria of the game. [Note: There are three strategies for each player contribute 100, contribute 50 or contribute nothing. Draw a 3 x 3 matrix. Calculate the payoffs. Find the Nash equilibria