  An extensive literature in economics and social science addresses contests,
in which players compete to outperform each other on some measurable criterion,
often referred to as a player's score, or output. Players incur costs that are
an increasing function of score, but receive prizes for obtaining higher score
than their competitors. In this paper we study finite games that are
discretized contests, and the problems of computing exact and approximate Nash
equilibria. Our motivation is the worst-case hardness of Nash equilibrium
computation, and the resulting interest in important classes of games that
admit polynomial-time algorithms. For games that have a tie-breaking rule for
players' scores, we present a polynomial-time algorithm for computing an exact
equilibrium in the 2-player case, and for multiple players, a characterization
of Nash equilibria that shows an interesting parallel between these games and
unrestricted 2-player games in normal form. When ties are allowed, via a
reduction from these games to a subclass of anonymous games, we give
approximation schemes for two special cases: constant-sized set of strategies,
and constant number of players.
