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Consider the following game between four players. Each player i has an initial endowment of 20 units of money. This money can be split between a private account (xi) and a public account (yi). The payoff for each player consists of the amount she allocated to her private account plus 2 times the minimum of all contributions to the public account,
i.e., πi = xi + 2min(y1, y2, y3, y4)
a) What is the payoff function for player i = 1?
b) Find the pure strategy Nash equilibria under the assumption that all participants are fully rational and only interested in their own earnings.
c) Give a reason why one of the equilibrium may be a focal point for the players (you 2 must state which equilibrium you think is a focal point).
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