Heuristic and Equilibrium Strategies in Premium Auctions

Premium auctions are conducted in two stages. In the first stage bidders compete in English auction until two bidders remain. The two finalists enter the second stage where they compete in a first-price sealed bid auction (Amsterdam auction) or in another English auction (Antwerp auction). The winner and the runner up obtain the premium that is proportional to the difference between the runner up?s bid and the highest losing bid in the first stage. We compare the equilibrium bidding strategy of the two finalists with the three heuristic strategies when bidders have private values in Amsterdam auction. With the first heuristic strategy, each finalist believes that he will lose in the second stage and that his bid determines the amount of the premium. With the second heuristic strategy, each finalist is optimistic and has second-order belief that the other finalist is pessimistic. With the third heuristic strategy, both finalists are optimistic and have second-order belief that the other finalist is optimistic.The simulation analysis with symmetric bidders shows that the average increase of bid of the runner up relative to the equilibrium bid is the largest with the second heuristic strategy, followed by the third and the first, respectively. The premium with either heuristic strategy is larger than with the equilibrium strategy. The profit of the winner is larger than the equilibrium profit, while seller?s revenue is lower than in equilibrium. The same conclusions hold for strongly asymmetric bidders. The use of heuristic strategies could be considered as a form of tacit collusion between two finalists, and with symmetric bidders who use the first heuristic strategy, the tacit collusion is stable even in a one-shot game.