Bidders’ strategies can be summarized as follows: if a bidder is currently the highest bidder in any auction, he pauses until he is outbid. Otherwise, he always bids on an auction with the lowest standing bid and bids with the minimum increment. The essential idea is that with cross-bidding, bidders bid up prices with each seller as slowly as possible. They try to pick sellers where they can become the highest bidders by bidding the minimum increment. In this way, high valuation buyers are never trapped into bidding a high price by having another high valuation buyer accidentally bid against them. Cross bidding ensures that any mismatch between buyers and sellers can be solved by giving bidders the opportunity to bid on other auctions with low standing bids. As a consequence, all trade occurs at the same price. Most importantly, the outcome of trading is the same as in a double auction.
We are interested to know whether bidders behave as the theory predicts. Economists usually seek clean theoretical results, which lie in the territory of a complete market and rational individuals. In case there is incomplete information, players are required to make probabilistic calculations and forecast future outcomes. Each player is assumed to be fully aware of the strategic value of his own private information and to know the structure of other players’ strategies. Such analysis seeks to characterize the Bayesian Nash equilibrium of the incomplete information game defined by the trading institution and the trading environment. Yet research in psychology and behavioral science is replete with examples in which individuals do not, or perhaps even cannot, perceive circumstance objectively. This raises serious questions about whether markets can achieve efficiency in practice.
There are more and more experiments in economics. Most results seem to support that the efficient outcome of the market can be achieved. One import result gaining support is the Hayek Hypothesis: markets economize on information in the sense that strict privacy together with the public information (about prices) in the market are sufficient to produce efficient competitive equilibrium outcomes.1How and why this is true, there is no general answer. The information flow and the contracting rule in the market may be more important than some traditional structural characteristics in determining the market outcome. However, whether players use strategies in Bayesian Nash equilibrium is dubious. In research by Forsythe et al. (1992), a market worked extremely well, yet traders in the market exhibited substantial amount of judgment bias.