Immorlica, Nicole Kalai, Adam Tauman Lucier, Brendan Moitra, Ankur Postlewaite, Andrew Tennenholtz, Moshe
Year of Publication:
Discussion Paper, Center for Mathematical Studies in Economics and Management Science 1545
We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two players, whose only goal is to outperform the opponent. Such games are typically exponentially large zero-sum games, but they often have a rich combinatorial structure. We provide general techniques by which such structure can be leveraged to find minmax-optimal and approximate minmax-optimal strategies. We give examples of ranking, hiring, compression, and binary search duels, among others. We give bounds on how often one can beat the classic optimization algorithms in such duels.