Y7

Two fishermen, Alan, and Brian must decide simultaneously on the number of hours to spend fishing on a particular day, which can be any number between 0 and 24. Let x_A denote the number of hours Alan fishes; x_B the number of hours Brian fishes; and X=x_A+x_B the total fishing time. The value of fish produced per hour of fishing is given by 60 2X, and the cost to each fisherman per hour of fishing is 4.

(a) Write down the payoff functions for the two fishermen and, explaining your reasoning, derive their reaction functions. Is this a game of positive or negative externalities? Does it exhibit strategic substitutes or strategic complements?

(b) Explain why in the Nash equilibrium of the game each fisherman fishes for x^*= 28/3 hours per day. What are the players' payoffs in equilibrium?

(c) A social planner, interested in maximising the sum of the two fishermen's' pay-offs, thinks that they can do better for themselves by each fishing for only 14/2 hours each day. If both players follow the planner's advice, what are their payoffs?

(d) Construct a game in which each player considers cooperating by following the social planner's advice or defecting on cooperation. What is the structure of this game, and what is the equilibrium if the game is played only once.