# Data Structures for Deviation Payoffs

## TL;DR

This paper introduces optimized data structures for symmetric normal-form games that significantly accelerate the computation of symmetric mixed-strategy Nash equilibria, enabling practical analysis of large multi-player games.

## Contribution

The paper presents novel data structures tailored for symmetric games, improving computational efficiency and extending applicability to role-symmetric and action-graph games.

## Key findings

- Dramatic speedup in equilibrium computation
- Efficient representation for large multi-player games
- Extension to role-symmetric and action-graph games

## Abstract

We present new data structures for representing symmetric normal-form games. These data structures are optimized for efficiently computing the expected utility of each unilateral pure-strategy deviation from a symmetric mixed-strategy profile. The cumulative effect of numerous incremental innovations is a dramatic speedup in the computation of symmetric mixed-strategy Nash equilibria, making it practical to represent and solve games with dozens to hundreds of players. These data structures naturally extend to role-symmetric and action-graph games with similar benefits.