If the proposal is rejected then the game ends and each player receives a

If the proposal is rejected then the game ends and

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for all players. If the proposal is rejected, then the game ends and each player receives apayoff ofδ23.(a)[20pts]Construct a subgame perfect Nash equilibrium of this game. Briefly discussthe role ofpiin your answer.5. Consider the following “investigation game.” An incumbent is being investigated for cor-ruption.Prior to the game, the incumbent chooses one ofL3 locations to hide the“smoking gun.”This choice is denoted byhL={1,2,...,L}.The choice ofhis notobserved by the other player, the investigator. In the first period, the investigator choosesone of theLlocations to look for the smoking gun. After this choice, denoted byxL, isrevealed, the incumbent observesxand then chooses one of the locations to reveal (truth-fully) to the investigator whether the smoking gun is hidden there or not.This choiceis denoted byrL. The investigator then observes ifr=hor not and, following that,chooses his final investigation location, denoted byyL.The players then receive thefollowing payoffs:UInvestigator=1ify=h0otherwise.UIncumbent=0ify=h1otherwise.(a)[15pts]Construct a perfect Bayesian equilibrium of this game.(b)[5pts]Suppose that the Investigator could pay a costc>0 to reduceLprior to thegame. He or she can choose any number of locations (from 0 toL-1). As a functionofc(and the equilibrium you constructed above), how many locations should theInvestigator remove from the Incumbent’s choice set? 3
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  • Spring '11
  • JohnPaddy
  • Game Theory, investigator, player

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