Related papers: Strategy Improvement, the Simplex Algorithm and Lo…
We consider concurrent games played on graphs. At every round of the game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…
We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted…
Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…
We study a multi-agent decision problem in population games, where agents select from multiple available strategies and continually revise their selections based on the payoffs associated with these strategies. Unlike conventional…
In a mean-payoff parity game, one of the two players aims both to achieve a qualitative parity objective and to minimize a quantitative long-term average of payoffs (aka. mean payoff). The game is zero-sum and hence the aim of the other…
Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…
Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Mean payoff (or long-run average reward) provides a mathematically elegant formalism to express performance related…
Small Progress Measures is one of the most efficient parity game solving algorithms. The original algorithm provides the full solution (winning regions and strategies) in $O(dm \cdot (n/\lceil d / 2 \rceil)^{\lceil d/2 \rceil})$ time, and…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
Graph games provide the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic reactive processes, the traditional model is perfect-information stochastic games, where some transitions of the game graph…
Various social dilemma games that follow different strategy updating rules have been studied on many networks.The reported results span the entire spectrum, from significantly boosting,to marginally affecting,to seriously decreasing the…
Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…
We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…
We consider turn-based stochastic two-player games with a combination of a parity condition that must hold surely, that is in all possible outcomes, and of a parity condition that must hold almost-surely, that is with probability 1. The…
We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of…
The long-run average payoff per transition (mean payoff) is the main tool for specifying the performance and dependability properties of discrete systems. The problem of constructing a controller (strategy) simultaneously optimizing several…
Softmax policy gradient is a popular algorithm for policy optimization in single-agent reinforcement learning, particularly since projection is not needed for each gradient update. However, in multi-agent systems, the lack of central…
We present a generic strategy iteration algorithm (GSIA) to find an optimal strategy of a simple stochastic game (SSG). We prove the correctness of GSIA, and derive a general complexity bound, which implies and improves on the results of…