Question

Question 2 Suppose you need to decide whether to make or not a donation to National Public Radio (NPR). To sinplify the analysis, assume that donations are the same fix amount (C =10) for everybody who decides to donate, and that private contributions are the only source of funding for the radio. The variety of programs that NPR is able to supply and therefore the utility of listeners depends on the number of individuals donating. If n individuals donated to NPR, the benefit of listening to the radio for those who donated is B(n) = 2n + 58, and 4n for those who did not donate. a. Write the payoff functions for an individual who is pondering whether to make a donation or not, assuming n of the other N - 1 individuals in the society are donnting. b. Draw the payoff functions on a graph, plotting the payoffs on the y-axis and the number of n partici- pants among the other N - 1 individuals on the x-axis. Is this an example of a prisoners' dilemma, a game of chicken, or an assurance game?

can someone help me set up and guide me through this problem.

Answer 1

(a) probability that the individual donates is 1/2 since there are only two strategies available to the individual in his action set. Therefore considering that N-1 people have donated, payoff to an individual if he chooses to donate would be = 2(N-1+1) +58) - 10 = 2n+48

If chooses not to donate (4(N-1)= 4n-4

(B) this game is similar to prisoner dillema

120 payoff 100 2n+58-10 -20 -10 10 20 30 40 50 60 n of N-1 participants