Discrete All-Pay Bidding Games

TL;DR

This paper introduces the concept of all-pay bidding games, combining auction theory with combinatorial games, and provides structural results and algorithms for optimal strategies in these games.

Contribution

It presents the first comprehensive analysis of optimal strategies in all-pay bidding games and offers a fast algorithm for computing them.

Findings

Optimal strategies involve probabilistic bidding distributions.

Structural properties of strategies are characterized.

A fast algorithm for strategy computation is developed.

Abstract

In an all-pay auction, only one bidder wins but all bidders must pay the auctioneer. All-pay bidding games arise from attaching a similar bidding structure to traditional combinatorial games to determine which player moves next. In contrast to the established theory of single-pay bidding games, optimal play involves choosing bids from some probability distribution that will guarantee a minimum probability of winning. In this manner, all-pay bidding games wed the underlying concepts of economic and combinatorial games. We present several results on the structures of optimal strategies in these games. We then give a fast algorithm for computing such strategies for a large class of all-pay bidding games. The methods presented provide a framework for further development of the theory of all-pay bidding games.