Small-support approximation of other structured Nash equilibria

Investigate whether specific classes of two-player games beyond the maximal-lottery games arising from elections admit approximate Nash equilibria with support sizes independent of the number of pure strategies, and identify the structural conditions that enable such approximations.

Background

The paper shows that maximal lotteries, which are Nash equilibria of a particular two-player zero-sum game induced by an election, can be approximated by mixed strategies with constant support size O(1/[?]^2), avoiding the logarithmic dependence on the number of candidates that is necessary for general approximate Nash equilibria. The authors note that their proof relies strongly on the linear ordering structure of voter preferences and leave unresolved whether analogous advantages occur for other specific equilibrium concepts or game classes.