ECON 333/MGEC 333/LAW 435 Game Theory and Strategy Final Examination QUESTIONS AND ANSWERS 2018

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1. (35 points) Two individuals are involved in a synergistic relationship. More effort is better for the relationship, but effort is costly to each individual. Specifically, an effort level is a nonne... gative number, and player 1’s payoff function is e1(1 + e2 − e1), where e1 is player 1’s effort level and e2 is player 2’s effort level. For player 2 the cost of effort is either the same as that of player 1, and hence her payoff function is given by e2(1 + e1 − e2) or effort is very costly for her in which case her payoff function is given by e2(1 + e1 − 2e2). Player 2 knows player 1’s payoff function and if the cost of effort is high for herself or not. Player 1, however, is uncertain about player 2’s cost of effort. He believes that the cost of effort is low with probability p, and high with probability 1 − p, where 0 < p < 1. All of this is common knowledge. Find the Bayesian equilibrium of this game as a function of p. [Show More]

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