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An island has two reefs that are suitable for fishing, and there are twenty fishers who simultaneously and independently choose at which of the two reefs (1 or 2) to fish. Each fisher can fish at only one reef. The total number of fish harvested at a single reef depends on the number of fishers who choose to fish there. The total catch is equally divided between the fishers at the reef. At reef 1, the total harvest is given by f1(r1) = 8r1 - r12/2, where r1, is the number of fishers who select reef 1. For reef 2, the total catch is f2(r2) = 4r2, where r2 is the number of fishers who choose reef 2. Assume that each fisher wants to maximize the number of fish that he or she catches.
(a) Find the Nash equilibrium of this game. In equilibrium, what is the total number of fish caught?
(b) The chief of the island asks his economics advisor whether this arrangement is efficient (i.e., whether the equilibrium allocation of fishers among reefs maximizes the number of fish caught). What is the answer to the chief's question? What is the efficient number of fishers at each reef?
(c) The chief decides to require a fishing license for reef 1, which would require each fisher who fishes there to pay the chief x fish. Find the Nash equilibrium of the resulting location-choice game between the fishers. Is there a value of x such that the equilibrium choices of the fishers results in an efficient outcome? If so, what is this value of x?
Player 1 has the following set of strategies {A1;A2;A3;A4}; player 2’s set of strategies are {B1;B2;B3;B4}. Use the best-response approach to find all Nash equilibria.
A supplier and a buyer, who are both risk neutral, play the following game, The buyer’s payoff is q^'-s^', and the supplier’s payoff is s^'-C(q^'), where C() is a strictly convex cost function with C(0)=C’(0)=0. These payoffs are commonly known.
Pertaining to the matrix need simple and short answers, Find (a) the strategies of the firm (b) where will the firm end up in the matrix equilibrium (c) whether the firm face the prisoner’s dilemma.
Consider the two-period repeated game in which this stage game is played twice and the repeated-game payo s are simply the sum of the payo s in each of the two periods.
Two players, Ben and Diana, can choose strategy X or Y. If both Ben and Diana choose strategy X, every earns a payoff of $1000.
The market for olive oil in new York City is controlled by 2-families, Sopranos and Contraltos. Both families will ruthlessly eliminate any other family that attempts to enter New York City olive oil market.
Following is a payoff matrix for Intel and AMD. In each cell, 1st number refers to AMD's profit, while second is Intel's.
Determine the solution to the given advertising decision game between Coke and Pepsi, assuming the companies act independently.
Little Kona is a small coffee corporation that is planning entering a market dominated through Big Brew. Each corporation's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price.
Suppose you and your classmate are assigned a project on which you will earn one combined grade. You each wish to receive a good grade, but you also want to avoid hard work.
Consider trade relations in the United State and Mexico. Suppose that leaders of two countries believe the payoffs to alternative trade policies are as follows:
Use the given payoff matrix for a simultaneous move one shot game to answer the accompanying questions.
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