# Game theory with integral equations as state dynamics

## TL;DR

This paper develops a game-theoretic framework for systems governed by integral equations, providing necessary and sufficient conditions for optimality in linear-quadratic problems and pursuit-evasion games.

## Contribution

It introduces a novel approach to analyze game problems with integral equation dynamics, including Volterra equations, with new optimality conditions.

## Key findings

- Necessary and sufficient conditions for linear-quadratic problems
- Necessary conditions for pursuit-evasion Volterra games
- Framework applicable to systems with integral dynamics

## Abstract

We formulate and analyze game-theoretic problems for systems governed by integral equations. For Volterra integral equations, we obtain and prove necessary and sufficient conditions for linear-quadratic problems, and for problems that are linear-quadratic in the control. Also, we obtain necessary conditions for one type of pursuit-evasion Volterra games.

---
Source: https://tomesphere.com/paper/1906.10778