# Stochastic hybrid differential games and match race problems

## TL;DR

This paper introduces a stochastic hybrid differential game framework applied to sailing match races, providing a convergent approximation method for the game's value function and validating it through typical racing scenarios.

## Contribution

It develops a novel stochastic hybrid differential game model for sailing races and offers a convergent numerical scheme for computing the game's value function.

## Key findings

- Validated the approximation scheme on typical racing scenarios
- Demonstrated the model's ability to capture strategic interactions in sailing races
- Provided a computational method for analyzing match race strategies

## Abstract

We discuss the general framework of a stochastic two-player, hybrid differential game, and we apply it to the modelling of a "match race" between two sailing boats, namely a competition in which the goal of both players is to proceed in the windward direction, while trying to slow down the other player. We provide a convergent approximation scheme for the computation of the value function of the game, and we validate the approach on some typical racing scenarios.