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(b) Show that player 1 playingBand player 2 playingBin the top gameandSin the bottom game is a Bayesian Nash Equilibrium.Solution:9
6*(Tadelis 12.5)A prospector owns a gold mine where he can dig to recover gold.Hisoutput depends on the amount of gold in the mine, denoted byx. Theprospector knows the value ofx, but the rest of the world knows only thatthe amount of gold is uniformly distributed on the interval [0,1]. Beforedeciding to mine, the prospector can try to sell his mine to a large miningcompany, which is much more efficient in its extraction methods.Theprospector can ask the company owner for any pricep≥0, and the ownercan reject (R) or accept (A) the offer. If the owner rejects the offer thenthe prospector is left to mine himself, and his payoff from self-mining isequal to 3x. If the owner accepts the offer then the prospector’s payoff isthe pricep, while the owner’s payoff is given by the net value 4x-p, andthis is common knowledge.(a) Show that for a given pricep≥0 there is a threshold typex(p)∈[0,1]of prospector, such that types belowx(p) will prefer to sell the mine,while types abovex(p) will prefer to self-mine.