Sequential all-pay auctions with noisy outputs.

*(English)*Zbl 1284.91192Summary: We study a sequential all-pay auction with two contestants who are privately informed about a parameter (ability) that affects their cost of effort. Contestant 1 (the first mover) exerts an effort in the first period which translates into an observable output, but with some noise, and contestant 2 (the second mover) observes this noisy output. Then, contestant 2 exerts an effort in the second period, and wins the contest if her output is larger than or equal to the observed noisy output of contestant 1; otherwise, contestant 1 wins. 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 (symmetric information), and another in which contestant 1 knows the realization of the noise when exerting her effort, while contestant 2 does not (asymmetric information). 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.

##### MSC:

91B26 | Auctions, bargaining, bidding and selling, and other market models |

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\textit{E. Segev} and \textit{A. Sela}, J. Math. Econ. 50, 251--261 (2014; Zbl 1284.91192)

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