Question: . Consider the following stage game between a manager and a worker. Simultaneously, the manager chooses a bonus payment p E [0,oo[ and the worker

. Consider the following stage game between a manager and a

. Consider the following stage game between a manager and a worker. Simultaneously, the manager chooses a bonus payment p E [0,oo[ and the worker chooses an effort level .9 e [0, oo[. The stage game payoffs (for the manager and worker, respectively) are uM(p,e) = 29 'p and uw = p 32. a. Compute the efficient effort level; that is, the level of e that maximizes H)\" + uw. ' b. Find the Nash equilibrium of the stage game. 1c. Suppose that the stage game is to be place twice (a two-period repeated game) and there is no discounting. Find all ofthe subgame perfect equilibria. ' d. Suppose that the stage game is to played infinitely many times in succession (an infinitely repeated game) and assume that players discount the future using the same discount factor 6

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