Zero-sum continuous-time Markov pure jump game over a fixed duration

TL;DR

This paper studies a two-player zero-sum continuous-time Markov jump game over a finite horizon, establishing the existence of a game value and optimal policies under certain regularity conditions.

Contribution

It proves the existence of a value and optimal policies for the game under regularity conditions, extending the theory of continuous-time Markov games.

Findings

The game has a well-defined value.

Both players possess optimal policies.

The model's regularity conditions ensure solution existence.

Abstract

This paper considers a two-person zero-sum continuous-time Markov pure jump game in Borel state and action spaces over a fixed finite horizon. The main assumption on the model is the existence of a drift function, which bounds the reward rate. Under some regularity conditions, we show that the game has a value, and both of the players have their optimal policies.