Repeated Contests with Private Information
Abstract: In repeated contests with private information, weak contestants prefer to appear strong while strong contestants prefer to appear weak. In contrast to a single contest, this leads to a partial pooling equilibrium where effort is not strictly monotonic in ability. This allows for a less able contestant to win against a contestant of higher ability even when contestants are ex-ante symmetric. Increasing the stakes of the initial contest will on decrease pooling and on average reduce the competitiveness of future contests. Higher future stakes will increase the incentive to hide information in the first contest, increasing pooling. For a class of effort cost functions and a fixed prize pool, total expected output is improved when the initial contest has lower stakes than the later contest. In particular, a single all-pay auction provides more expected revenue than splitting the stakes over two successive auctions.