, must choose whether to audit the effort exerted by the agent. This choice is binaryand denoted bya, witha=1 if the boss audits anda=0 otherwise. Auditing is unpleasant(it costsc>0, but allows the boss to recoup half of the amount of effort that the agentdid not exert (i.e., it gains the boss1-e). The agent incurs a fixed penalty ofP>0 if heis caught exerting less than full effort. The players’ payoffs are as follows:uagent(e,a)=1-eifa=01ifa=1&e=11-e-Pifa=1&e≠1uboss(e,a)=e+1-e2-ca(a)[5pts]What are the players’ strategy spaces?(b)[10pts]Are there any dominated strategies?(c)[10pts]Find all of the Nash equilibria of the game.4
7. Consider a simultaneous first price auction between two players. Each playeri’s type,ti,is privately observed by playeriand is uniformly distributed between 0 and 1. The twoplayers’ types are independently distributed. The players each simultaneously submit abid,bi. Playeri’s payoff, for bothi∈{1,2}andj≡3-i, isui(bi,bj)=ti-biifbi>bj,ti-bi2ifbi=bj,0ifbj>bi.(a)[5pts]What are the dominated strategies in this game?(b)[10pts]Find a perfect Bayesian equilibrium of this game.8. Consider a sequential first price auction between two players.Each playeri’s type,ti,is privately observed by playeriand is uniformly distributed between 0 and 1. The twoplayers’ types are independently distributed. Player 1 submits a bid,b1, which is observedby player 2, who then submits a bid,b2. Playeri’s payoff, for bothi∈{1,2}andj≡3-i,isui(bi,bj)=ti-biifbi>bj,ti-bi2ifbi=bj,0ifbj>bi.