# Learning Mixed Strategies in Trajectory Games

arXiv: https://arxiv.org/abs/2205.00291 · HTML: https://mlsanity.com/paper/2205.00291/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2022.

## Built on by (most cited first, 4 of 4)

- [Blending Data-Driven Priors in Dynamic Games](https://mlsanity.com/paper/2402.14174/) (2024)
- [Mixed Strategy Nash Equilibrium for Crowd Navigation](https://mlsanity.com/paper/2403.01537/) (2024)
- [How Bad is Selfish Driving? Bounding the Inefficiency of Equilibria in Urban Driving Games](https://mlsanity.com/paper/2210.13064/) (2022)
- [Online Competitive Information Gathering for Partially Observable Trajectory Games](https://mlsanity.com/paper/2506.01927/) (2025)

## Abstract (arXiv)

In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior. Trajectory games capture these complex effects by design. In competitive settings, this makes them a more faithful interaction model than traditional "predict then plan" approaches. However, current game-theoretic planning methods have important limitations. In this work, we propose two main contributions. First, we introduce an offline training phase which reduces the online computational burden of solving trajectory games. Second, we formulate a lifted game which allows players to optimize multiple candidate trajectories in unison and thereby construct more competitive "mixed" strategies. We validate our approach on a number of experiments using the pursuit-evasion game "tag."