We study tree games developed recently by Matteo Mio as a game interpretation of the probabilistic μ-calculus. With expressive power comes complexity. Mio showed that tree games are able to encode Blackwell games and, consequently, are not determined under deterministic strategies. We show that non-stochastic tree games with objectives recognisable by so-called game automata are determined unde...

The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in NP ∩ coNP which are not known to be in P. However, there are some cases where these games can be easily solved, as for instance when the underlying graph is acyclic. In this work, we try to extend this tractability to several classes ...

In a repeated zero-sum two-person game with incomplete information on both sides, the asymptotic value is defined as v = lim_oo v", where vn is the value of the game with n repetitions. It is shown here that v may be a transcendental number even for games in which all parameters defining the game are rational. This is in contrast to the situation in stochastic games where by the result of Bewle...

Strategies in a stochastic game are δ > 0 perfect if the induced one-stage games have certain δ equilibrium properties. Sufficient conditions are proven for the existence of δ perfect strategies for all δ > 0 implying the existence of equilibria for every > 0. Using this approach we prove the existence of equilibria for every > 0 for a special class of quitting games. The important technique of...

We consider a class of two-player zero-sum stochastic games with finite state and compact control spaces, which we call stochastic shortest path (SSP) games. They are total cost stochastic dynamic games that have a cost-free termination state. Based on their close connection to singleplayer SSP problems, we introduce model conditions that characterize a general subclass of these games that have...

In this chapter, we present a framework for m-person stochastic games with an infinite state space. Our main purpose is to present a correlated equilibrium theorem proved by Nowak and Raghavan [42] for discounted stochastic games with a measurable state space, where the correlation of the different players’ strategies employs only “public signals” [16]. We will also provide a detailed survey of...

Autonomous aerial vehicles play an important role in military applications such as in search, surveillance and reconnaissance. Multi-player stochastic pursuit–evasion (PE) differential game is a natural model for such operations involving intelligent moving targets with uncertainties. In this paper, some fundamental issues of stochastic PE games are addressed. We first model a general stochasti...

We propose a connection between finite zero-sum stochastic games (henceforth games) and multiparameter eigenvalue problems. This connection, which relies on the theory developed by Shapley Snow for matrix games, opens new possibilities in study of games. In particular, we derive from this handful results

This paper introduces Monte Carlo *-Minimax Search (MCMS), a Monte-Carlo search algorithm for finite, turned based, stochastic, two-player, zero-sum games of perfect information. Through a combination of sparse sampling and classical pruning techniques, MCMS allows deep plans to be constructed. Unlike other popular tree search techniques, MCMS is suitable for densely stochastic games, i.e., gam...