Question

Alice and Bob are each considering contributing to a public park which will be enjoyed by all. Alice has $9, of which she’ll contribute $a. Bob has $12 of which he’ll contribute $b. Alice’s payoff depends on the total contribution, a + b, the money she has left over to spend on other things, 9 – a, and an “interaction term” combining both of these terms, (9 – a)(a + b). Thus her payoff, x = a + b + 9 – a + (9 – a)(a + b) = b + 9 +(9 – a)(a + b). Similarly, Bob’s payoff is given by y = a + b + 12 – b + (12 – b)(a + b) = a + 12 +(12 – b)(a + b).

Find the Nash Equilibrium contributions. Are these contribution levels Pareto Efficient? If not, find the Pareto Efficient levels of contributions.

Can you explain it in graph?

Answer 1