In a number of countries, government contracts are awarded by means auctions in which the winner...

  

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In a number of countries, government contracts are awarded by means auctions in which the winner is the bidder whose bid is closest to the average bid. Consider such an auction with three bidders competing to win a single object. Bidder i has a valuation vi for the object, where U₁ > U₂ > V3 > 0. Bidders simultaneously submit bids b; 20. The bidder whose bid is closest to the average of b₁,b₂, and b3 wins the object and pays her own bid (thus if i is the winning bidder, her payoff is vi- b;). In case of a tie, the bidder with the highest valuation wins the object. Losing bidders receive a payoff of 0. (a) Find all (pure strategy) Nash equilibria of this game. (b) Show that in every Nash equilibrium in which the three players do not submit identical bids, at least one player plays a weakly dominated strategy. In a number of countries, government contracts are awarded by means auctions in which the winner is the bidder whose bid is closest to the average bid. Consider such an auction with three bidders competing to win a single object. Bidder i has a valuation vi for the object, where U₁ > U₂ > V3 > 0. Bidders simultaneously submit bids b; 20. The bidder whose bid is closest to the average of b₁,b₂, and b3 wins the object and pays her own bid (thus if i is the winning bidder, her payoff is vi- b;). In case of a tie, the bidder with the highest valuation wins the object. Losing bidders receive a payoff of 0. (a) Find all (pure strategy) Nash equilibria of this game. (b) Show that in every Nash equilibrium in which the three players do not submit identical bids, at least one player plays a weakly dominated strategy.

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a All Nash equilibria of this game are pure strategy Nash equilibria in which all bidders ... View the full answer