# Contingency Games for Multi-Agent Interaction

arXiv: https://arxiv.org/abs/2304.05483 · HTML: https://mlsanity.com/paper/2304.05483/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2023.

## Built on by (most cited first, 12 of 12)

- [Deception Game: Closing the Safety-Learning Loop in Interactive Robot Autonomy](https://mlsanity.com/paper/2309.01267/) (2023)
- [Blending Data-Driven Priors in Dynamic Games](https://mlsanity.com/paper/2402.14174/) (2024)
- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [Mixed Strategy Nash Equilibrium for Crowd Navigation](https://mlsanity.com/paper/2403.01537/) (2024)
- [Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysis](https://mlsanity.com/paper/2412.15837/) (2024)
- [Integrated Decision Making and Trajectory Planning for Autonomous Driving Under Multimodal Uncertainties: A Bayesian Game Approach](https://mlsanity.com/paper/2409.13993/) (2024)
- [Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions](https://mlsanity.com/paper/2508.19945/) (2025)
- [LinguaGame: A Linguistically Grounded Game-Theoretic Paradigm for Multi-Agent Dialogue Generation](https://mlsanity.com/paper/2601.04516/) (2026)
- [Scalable Multi-modal Model Predictive Control via Duality-based Interaction Predictions](https://mlsanity.com/paper/2402.01116/) (2024)
- [Bayesian Inverse Games with High-Dimensional Multi-Modal Observations](https://mlsanity.com/paper/2601.00696/) (2026)
- [GARL: Game-Theoretic Reinforcement Learning for Multi-Agent Strategic Prioritisation](https://mlsanity.com/paper/2606.05002/) (2026)
- [Multi-Agent Deferred-Decision Trajectory Optimization with Anytime-Valid Target Retention for Moving Candidates](https://mlsanity.com/paper/2610.17003/) (2026)

## Abstract (arXiv)

Contingency planning, wherein an agent generates a set of possible plans conditioned on the outcome of an uncertain event, is an increasingly popular way for robots to act under uncertainty. In this work we take a game-theoretic perspective on contingency planning, tailored to multi-agent scenarios in which a robot's actions impact the decisions of other agents and vice versa. The resulting contingency game allows the robot to efficiently interact with other agents by generating strategic motion plans conditioned on multiple possible intents for other actors in the scene. Contingency games are parameterized via a scalar variable which represents a future time when intent uncertainty will be resolved. By estimating this parameter online, we construct a game-theoretic motion planner that adapts to changing beliefs while anticipating future certainty. We show that existing variants of game-theoretic planning under uncertainty are readily obtained as special cases of contingency games. Through a series of simulated autonomous driving scenarios, we demonstrate that contingency games close the gap between certainty-equivalent games that commit to a single hypothesis and non-contingent multi-hypothesis games that do not account for future uncertainty reduction.