Non-monotoniticies and the all-pay auction tie-breaking rule
Discontinuous games, such as auctions, may require special tie-breaking rules to guarantee equilibrium existence. The fact that the equilibrium existence for discontinuous games depends on special definition of the payoff at discontinuities was first pointed out for games of complete information by \textit{L. K. Simon} and \textit{W. R. Zame} [Econometrica 58, No. 4, 861--872 (1990; Zbl 0729.90098)], and for games of incomplete information by \textit{M. O. Jackson, L. K. Simon, J. M. Swinkels} and \textit{W. R. Zame} [Econometrica 70, No. 5, 1711--1740 (2002), corrigendum 72, No. 6, 1927--1929 (2004; Zbl 1106.91348)]. Next, \textit{A. Araujo} and \textit{L. I. de Castro} [Games Econ. Behav. 65, No. 1, 25--48 (2009; Zbl 1165.91373)] proved equilibrium existence for single and double asymmetric auctions with interdependent values. The present paper characterizes when a special tie-breaking rules are really needed. The result is established for the set of symmetric auctions with unidimensional types, and partially for a set of multidimensional symmetric auctions with weak monotonicity assumptions. When a special tie-breaking rule is needed, the authors show that the all-pay auction tie-breaking rule is sufficient for the existence of pure strategy equilibrium in a class of auctions. The rule is explicitly defined and does not require communication of private information.
scientific article; zbMATH DE number 5278998
scientific article