All-pay auctions with identity-dependent externalities

Bettina Susanne Klose, Purdue University


In the first chapter, we exhibit how the presence of identity-dependent externalities invalidates well established qualitative results concerning the set of equilibria of the first-price all-pay auction with complete information. With identity-dependent externalities identical players may earn different equilibrium payoffs. Moreover, equilibrium payoffs may be greater than, or less than, equilibrium payoffs in a first-price winner-pay auction with identical valuations. These observations show that Siegels (2009) results characterizing the set of equilibrium payoffs in all-pay contests do not extend to environments with identity-dependent externalities. The second chapter investigates the impact of societal structure on behavior in conflicts that can be modeled as all-pay auctions with identity-dependent externalities. The consideration of identity-dependent externalities, which naturally arise in the most common applications of all-pay auctions, enables us to define players individual characteristics in society (in particular radicalism and centrism) not only for arrangements on the line but more generally. We find that even with a high ratio of centrists in comparison to radicals extremism, characterized by higher expenditure by radicals in comparison to centrists, persists. Moreover, for environments with two radical players we show that there exists a symmetric equilibrium in which all moderates bid zero with certainty. This equilibrium is the unique symmetric equilibrium if there is only a single centrist player. Our results contrast with those previously derived for the Tullock lottery contest success function, under which centrists remain active in equilibrium. We thereby highlight the importance of the choice of the contest success function for predictions about extremism and moderation in the political economy literature. In the third chapter we experimentally investigate all-pay and winner-pay auctions with positive and negative identity-dependent externalities. In a symmetric three player environment with complete information we find that, against the theoretical predictions for the chosen environments, the two auction formats are not revenue equivalent in environments with negative identity-dependent externalities. In treatments with positive identity-dependent externalities or without identity-dependent externalities average revenue and bids approximate their theoretical predictions closely when subjects are experienced. In all-pay treatments we observe that even experienced players do not randomize continuously but rather bimodally. Average bids are very close to the risk-neutral Nash equilibrium prediction for the treatment with positive identity-dependent externalities, but significantly higher in both other treatments. We find that the observed bid distributions are well explained when allowing for loss aversion.




Novshek, Purdue University.

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