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You should be able to convince yourself that neither of these possibilities constitutes a Nash equilibrium. In both cases, one or both of the candidates would have an incentive to deviate. The case with three candidates is more complicated — there is an infinity of pure-strategy Nash equilibria.
She obviously has no incentive to deviate. It is true that she can increase her vote total by changing position but, given the positions of the other two candidates, there is no move she can make that will give her any chance of winning the election.
Similarly, candidate 1 has no incentive to deviate. You should be able to find many, many more. Find all the Nash equilibria of the following game. By a similar reasoning, we can show that player 1 will never place a positive probability on 1. Find playing all the B. Howdeletion does ofyour strictly dominated answer to a strategies? All strategies survive iterated deletion of strictly dominated strategies.
How does your answer to part a change in this case if at all? Therefore when considering mixed strategies, the strategies that survive iterated deletion of strictly dominated strategies are T, M for player 1 and L, C for player 2. Each firm has constant marginal cost c of producing output. What happens to total industry profits as n increases? Show that all firms would want to merge to form a monopoly.
The FTC prohibits monopoly in this industry but is worried about a merger of two firms such that the industry would become a duopoly. It would do better by decreasing output slightly to increase prices.
The remaining firm realizes this and increases its output slightly. This will tempt the merged firm to decrease output even more etc. Two employees work together in a team. This effort causes the worker a disutility of 21 e2i. How much effort should both workers choose? The social planner will choose effort levels to maximize social welfare.
Each player will respond to its own private incentives. This is the pure strategy Nash equilibrium. The Nash equilibrium is clearly suboptimal. The problem is that players do not enjoy the full social benefit of their actions. Therefore, the incentive to work hard is reduced and since the marginal cost of exerting effort increases with ei due to convex effort costs workers will exert less effort than is socially optimal.
Consider the following game-theoretic model of the equilibrium determination of the cleanliness and effort distribution of an apartment shared by two roommates. In the game, the two roommates simultaneously choose the effort, e1 and e2 , to spend on apartment cleaning.
They each get utility from the cleanliness of the apartment which is a function of the sum of the efforts and disutility from the effort they personally expend. Player 1 places a higher valuation on cleanliness. Hint: Your BR function should be defined for each positive effort level and has to be non-negative everywhere.
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