Common-value all-pay auctions with asymmetric information and bid caps

Abstract

We study a class of two-player common-value all-pay auctions (contests) with asymmetric information under the assumption that one of the players has an information advantage over his opponent and both players are budget-constrained. We extend the results for all-pay auctions with complete information, and show that in our class of all-pay auctions with asymmetric information, sufficiently high (but still binding) bid caps do not change the players' expected total effort compared to the benchmark auction without any bid cap. Furthermore, we show that there are bid caps that increase the players' expected total effort compared to the benchmark. Finally, we demonstrate that there are bid caps which may have an unanticipated effect on the players' expected payoffs-one player's information advantage may turn into a disadvantage as far as his equilibrium payoff is concerned.

Invariant Equilibrium in Discontinuous Bayesian Games

“…[24] show that asymmetric bid caps create an existence problem for most tie-breaking rules in all-pay contests with complete information. Two other recent papers, [25,26], include symmetric bidding constraints in all-pay auctions with incomplete information. 7 Projection Theorem: Let X be a Polish space and (S, S, µ) a complete finite measure space.…”

Bid Caps and Disclosure Policies

“…Olszewski and Siegel (2019) consider large contests and exante asymmetric agents. Einy et al (2016) consider one-sided private information and common valuation. Hence, our equilibrium characterization when the designer commits to full concealment contributes to this literature by adding the case of two-sided private information with ex-ante symmetric players and binary types.…”

“…The first strand of the literature investigates the effect on lobbyists' expenditures of a cap in the expenditures itself (e.g., Che and Gale, 1998;Gavious et al, 2002;Sahuguet, 2006;Szech, 2015;Einy et al, 2016;Chen, 2019b;Olszewski and Siegel, 2019). Under linear cost function, in the ex-ante asymmetric setup of Che and Gale (1998), a cap in expenditures may increase total expenditures by constraining the stronger lobbyist and in turn giving hope to the weaker lobbyist (leveling the playing-field), while in the ex-ante symmetric setup of Gavious et al (2002) a cap always decreases total expenditures as the leveling-the-playing-field effect is absent.…”

Disclosure policies in all‐pay auctions with bid caps and stochastic entry: The impact of risk aversion

“…The existing literature investigates the effects of disclosing the actual number of contestants with stochastic entry (e.g., B. Chen et al., 2017; B. Chen, 2020) and bid caps (e.g., B. Chen, 2019a; Che & Gale, 1998, 2006; Einy et al., 2016; Gavious et al., 2002; Olszewski & Siegel, 2019; Szech, 2015) in risk‐neutral contests. In contrast, B. Chen et al.…”

“…Chen, 2020) and bid caps (e.g., B. Chen, 2019a;Che & Gale, 1998, 2006Einy et al, 2016;Gavious et al, 2002;Olszewski & Siegel, 2019;Szech, 2015) in risk-neutral contests. 1 In contrast, B.…”