We examine the problem of the existence of optimal deterministic stationary strategies in two-players antagonistic (zero-sum) perfect information stochastic games with finitely many states and actions. We show that the existence of such strategies follows from the existence of optimal deterministic stationary strategies for some derived one-player games. Thus we reduce the problem from two-play...

In this lecture we will review several topics that are extensively used in the study of n-player stochastic games. These tools were used in the proof of several results on non zero-sum stochastic games. Most of the results that are presented here appeared in Vieille (1997a,b), and some appeared in Solan (1998, 1999). The first main issue is Markov chains where the transition rule is a Puiseux p...

We provide sufficient conditions in finite-horizon multi-stage games for the value function of each player, associated to extremal Markov perfect equilibria, to display strategic complementarities and for the contemporaneous equilibrium to be increasing in the state variables.

Probabilistic reasoning goes a long way in many popular board games. Abbott and Richey [1] and Ash and Bishop [2] identify the most profitable properties in Monopoly and Tan [3] derives battle strategies for RISK. In RISK, the stochastic progress of a battle between two players over any of the 42 countries can be described using a Markov Chain. Theory for Markov Chains can be applied to address...

Learning in multi-agent settings has recently garnered much interest, the result of which has been the development of somewhat effective multi-agent learning (MAL) algorithms for repeated normal-form games. However, general-purpose MAL algorithms for richer environments, such as generalsum repeated stochastic (Markov) games (RSGs), are less advanced. Indeed, previously created MAL algorithms fo...

Collecting cognitive science data using games has the potential to be a powerful tool for recruiting participants and increasing their motivation. However, designing games that provide useful data is a difficult task that often requires significant trial and error. In this work, we consider how to apply ideas from optimal experiment design to designing games for cognitive science experiments. W...

We consider the problem of approximating the values and the equilibria in two-person zero-sum discounted semi-Markov games with in nite horizon and compact action spaces, when several uncertainties are present about the parameters of the model. Speci cally: on the one hand, we study approximations made on the transition probabilities, the discount factor and the reward functions when the state ...

This paper provides a novel approach to multi-agent coordination in general sum Markov games. Contrary to what is common in multi-agent learning, our approach does not focus on reaching a particular equilibrium between agent policies. Instead, it learns a basis set of special joint agent policies, over which it can randomize to build different solutions. The main idea is to tackle a Markov game...

We study long-term growth-optimal strategies on a simple market with transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal strategies and expected frictional losses of the friction parameter.

The exploitation of symmetries in Markov decision processes has proven to be a powerful concept for state space reduction without compromising solution optimality. In this paper we show how to perform a symmetry reduction for two player zero-sum Markov games with additional symmetry properties. The concept of equivariance symmetry justifies for the first time not only to lift the standard MDP s...