Bray Theory Workshop

Abstract

The talk will cover a series of papers. In these papers we study multi-stage all-pay contests (auctions) where heterogeneous contestants are privately informed about a parameter (ability) that affects their cost of effort and are bidding sequentially. We characterize the perfect Bayesian equilibrium of these contests and analyze the effect of the number of contestants and their types on the contestants' expected highest effort. For the two players case we also analyze if giving a head start improves the contestants' performance. In particular, we analyze the difference between a multiplicative head start and an additive head start with respect to the effect on the contestants' performance. We also analyze the case  where the effort  of the first contestant translates into an observable output, but with some noise. The winner is the contestant with the higher output. We study two variations of this model: one in which both contestants do not know the realization of the noise when they exert their effort, and another in which contestant 1 knows the realization of the noise when exerting her effort, while contestant 2 does not. For both variations, we characterize the subgame perfect equilibrium and examine the effect of a random noise on the contestants' equilibrium outputs. In particular we show that contestants' equilibrium behavior in our model is robust to the existence of a small noise. Finally we also analyze sequential bidding in first price auctions and show that with asymmetric bidders it may yield higher expected revenue than simultaneous bidding.

The talk is based on the following papers:

1. Segev E. and A. Sela (2014a), "Multi-Stage Sequential All-Pay Auction", European Economic Review, 70, pp. 371-382. http://www.sciencedirect.com/science/article/pii/S0014292114000932
2. Segev E. and A. Sela (2014b), "Sequential All-Pay Auctions with Head Starts", Social Choice and Welfare, 43 (4), pp. 893-923. http://link.springer.com/article/10.1007/s00355-014-0816-9
3. Segev E. and A. Sela (2014c), "Sequential All-Pay Auctions with Noisy Outputs", The Journal of Mathematical Economics, 50 (1), pp. 251–261. http://www.sciencedirect.com/science/article/pii/S030440681300044X
4. Cohensius G. and  Segev E. (2015) "Sequential Bidding in Asymmetric First Price Auctions", working paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2515790