# The Distribution of Optimal Strategies in Symmetric Zero-sum Games

arXiv: https://arxiv.org/abs/1611.06845 · HTML: https://mlsanity.com/paper/1611.06845/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2016.

## Built on by (most cited first, 1 of 1)

- [Global Policy-Space Response Oracles for Two-Player Zero-Sum Games](https://mlsanity.com/paper/2605.28273/) (2026)

## Abstract (arXiv)

Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is given by the corresponding matrix entry, the column player receives the negative of the row player. A randomized strategy is optimal if it guarantees an expected payoff of at least 0 for a player independently of the strategy of the other player. We determine the probability that an optimal strategy randomizes over a given set of actions when the game is drawn from a distribution that satisfies certain regularity conditions. The regularity conditions are quite general and apply to a wide range of natural distributions.