Mimic martingales in sequential auctions

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 to allocate goods and in auctions to dissolve partnerships, when winning bids are disclosed. It shows for these 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 sequential auctions. These results suggest that it may be difficult 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.