An introduction to multiagent systems - part 1 potx

... mechanism is that it is a dominant-strategy solution to the quasi-linear problem:Theorem 7.2.3 Given a quasi-linear mechanism design problem M, the VCGmechanism for M is a direct dominant-strategy ... Result:The Vickrey-Clarke-Groves MechanismIf we are to design a truthful mechanism that is not dictatorial, we are going to have to relax some of the conditions of the Gibbard-Satterthwaite theorem.The ... conditions cannot beachieved simultaneously.Theorem 7.2.4 (The Myerson-Satterthwaite Impossibility Theorem)No mechanism is simultaneously incentive compatible, efficient, and budget bal-anced.In particular,...

... otherwise.E(u 1 ) =2s 1 0u 1 dv2+ 10 2s 1 u 1 dv2=2s 1 0(v 1 − s 1 )dv2+ 10 2s 1 0dv2=2s 1 0(v 1 − s 1 )dv2= (v 1 − s 1 )v 1 |2s 1 0= 2v 1 s 1 − 2s2 1 Now we have a closed ... player 1 wins when player 2’s valuation is less than twice hisown bid, s 1 , and he loses otherwise. Then player 1 s utility is simply (v 1 − s 1 )when he wins, and 0 otherwise.E(u 1 ) =2s 1 0u 1 dv2+ 10 2s 1 u 1 dv2=2s 1 0(v 1 − ... m + 1- price auction, which play the roles analogous to first- and second-price auctions in the single-unit case. Here too there are issues of tie breaking,which are dealt with similarly to the...