Related papers: Solving Simple Stochastic Games with Few Random Ve…

Significant progress has been recently achieved in developing efficient solutions for simple stochastic games (SSGs), focusing on reachability objectives. While reductions from stochastic parity games (SPGs) to SSGs have been presented in…

In common-interest stochastic games all players receive an identical payoff. Players participating in such games must learn to coordinate with each other in order to receive the highest-possible value. A number of reinforcement learning…

We consider some well-known families of two-player, zero-sum, perfect information games that can be viewed as special cases of Shapley's stochastic games. We show that the following tasks are polynomial time equivalent: - Solving simple…

We present a fast numerical algorithm for large scale zero-sum stochastic games with perfect information, which combines policy iteration and algebraic multigrid methods. This algorithm can be applied either to a true finite state space…

Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…

This paper presents new families of algorithms for the repeated play of two-agent (near) zero-sum games and two-agent zero-sum stochastic games. For example, the family includes fictitious play and its variants as members. Commonly, the…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the…

With the success of modern machine learning, it is becoming increasingly important to understand and control how learning algorithms interact. Unfortunately, negative results from game theory show there is little hope of understanding or…

We develop here the Stochastic Perron Method in the framework of two-player zero-sum differential games. We consider the formulation of the game where both players play, symmetrically, feed-back strategies (as in [CR09] or [PZ12]) as…

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its…

Shortest-path games are two-player zero-sum games played on a graph equipped with integer weights. One player, that we call Min, wants to reach a target set of states while minimising the total weight, and the other one has an antagonistic…

We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the…

When a game involves many agents or when communication between agents is not possible, it is useful to resort to distributed learning where each agent acts in complete autonomy without any information on the other agents' situations.…

This paper considers a class of reinforcement-based learning (namely, perturbed learning automata) and provides a stochastic-stability analysis in repeatedly-played, positive-utility, finite strategic-form games. Prior work in this class of…

The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings are uniformly distributed.…

We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…