We study the symmetric, two-player, complete information all-pay auction in which a tie ensues if neither player outbids the other by more than a given amount. In the event of a tie, each player receives an identical fraction of the winning prize. Thus players engage in competition over two margins: losing versus tying, and tying versus winning. Two pertinent parameters are the margin required for victory, and the value of tying relative to winning. We fully characterize the set of Nash equilibria for the entire parameter space. For much of the parameter space, there is a unique Nash equilibrium which is also symmetric. Equilibria typically involve randomizing over multiple disjoint intervals, so that in essence players randomize between attempting to tie and attempting to win. In equilibrium, expected bids and payoffs are non-monotonic in both the margin required for victory and the relative value of tying.
Building on this theoretical work, we examine the model in a laboratory experiment. We find that revenue is non-monotonic in the margin required for victory and that the standard all-pay auction is not revenue maximizing. We also find that decreasing the value of tying relative to winning may either increase or decrease revenue.
Dan Kovenock is Professor of Economics in the Economic Science Institute at Chapman University. He has also held professorships at the University of Iowa and Purdue University. He previously served as an Editor of the International Journal of Industrial Organization and on the editorial boards of the European Economic Review, Social Choice and Welfare, and the Strategic Management Journal. He is currently a Co-editor of Economic Theory and the Economic Theory Bulletin, and serves on the editorial boards of Games and Economic Behavior and the Journal of Public Economic Theory. He has more than 70 papers in international publications, including outlets such as the American Economic Review, the Review of Economic Studies, Management Science, Naval Research Logistics, Games and Economic Behavior, and Experimental Economics.