Three people choose whether to contribute a fixed amount toward the provision of
ID: 1228500 • Letter: T
Question
Three people choose whether to contribute a fixed amount toward the provision of a public good. This good is provided if and only if at least two of them contribute. If it is not provided, contributions are not refunded. Each person ranks outcomes from best to worst as follows: An outcome in which the good is provided and she does not contribute Any outcome in which the good is provided and she contributes Any outcome in which the good is not provided and she does not contribute Any outcome in which the good is not provided and she contributes Formulate this situation as a strategic game. Represent the game in the form of the payoff matrices and find any and all Nash Equilibrium. Show your logic.Explanation / Answer
In this case, we create two matwicies and players 1 and 2 will compare as usual in their respective coulmns. Player 3 will compare in the same cell corresposnding in both matricies. We will call our payoffs 1 2 3 4 for simplicity but they correspond to the entries in the question above.
P2
provide do not provide provide do not provide
provide 1,1,1 1,2,1 1,3,1 1,4,1
P1 do not provide 2,1,2 2,2,2 2,3,2 2,4,2
provide 3,1,3 3,2,3 3,3,3 3,4,3
do not provide 4,1 4 4,2,4 4,3,4 4,4,4
P3 Provide
P2
provide do not provide provide do not provide
provide 1,1,3 1,2,3 1,3,3 1,4,3
P1 do not provide 2,1,4 2,2,4 2,3,4 2,4,4
provide 3,1,1 3,2,1 3,3,1 3,4,1
do not provide 4,1 2 4,2,2 4,3,2 4,4,2
P3 Do not provide
Next we compare payoffs to find NE
In this case, the only NE is (provde,provide,provide)
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