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Two people are engaged in a joint project. If each person i puts in the effort xi, the outcome of the project is worth f(x1, x2). Each person's effort level xi is a number between [0,1], and effort costs c(xi). The worth of the project is split equally between the two people, regardless of their effort levels, so the net payoff of each player is
f(x1, x2)/2 - c(xi).
Draw the players Best Responses, and find the Nash equilibria when
(i) f(x1, x2) = 3x1x2 and c(xi) = xi
2, for i = 1, 2.
(ii) f(x1, x2) = 4x1x2 and c(xi) = xi, for i = 1, 2.
Provide a brief interpretation in each case.
P2 and P3 play with a penny. P1 picks between same (S) and different (D). After observing P1's choice, P2 and P3 get to picked Simultaneously independently either head (H) and tail
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