Mimic martingales in sequential auctions

Abstract

In the equilibrium of a game, no player has an incentive to unilaterally deviate from equilibrium play. At the same time, players may have no positive incentive to follow equilibrium when every other player follows equilibrium, e.g., as in a mixed-strategy Nash equilibrium. This paper concerns the incentives of players to follow equilibrium in sequential auctions and bargaining games in which winning bids/compensations are disclosed. It shows for theses games that a player obtains his equilibrium payoff for a large class of strategies different from his equilibrium strategy. These deviations from equilibrium, while costless to the player, harm the seller in an auction. These results suggest that it may be di¢ cult for players to learn to play equilibrium and, if reached, for play to remain at equilibrium. For the auction designer, disclosing winning bids may be harmful to the seller.