Related papers: Fast value iteration: A uniform approach to effici…
A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the…
We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such…
Infinitely repeated games can support cooperative outcomes that are not equilibria in the one-shot game. The idea is to make sure that any gains from deviating will be offset by retaliation in future rounds. However, this model of…
This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in discounted repeated games. The process starts with a single hypercube approximation of the set of SPE. Then the initial…
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…
In this paper, we propose a new efficient algorithm to compute the value function for zero-sum stopping games featuring two players with opposing interests. This can be seen as a game version of the ''forward algorithm'' for (one-player)…
We study the process theoretic notion of stuttering equivalence in the setting of parity games. We demonstrate that stuttering equivalent vertices have the same winner in the parity game. This means that solving a parity game can be…
This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods…
We characterize all common notions of behavioral equivalence by one 6-dimensional energy game, where energies bound capabilities of an attacker trying to tell processes apart. The defender-winning initial credits exhaustively determine…
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…
We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying…
When users access shared resources in a selfish manner, the resulting societal cost and perceived users' cost is often higher than what would result from a centrally coordinated optimal allocation. While several contributions in mechanism…
This work investigates the ambient potential identification problem in inverse Mean-Field Games (MFGs), where the goal is to recover the unknown potential from the value function at equilibrium. We propose a simple yet effective iterative…
We consider a multi-organizational system in which each organization contributes processors to the global pool but also jobs to be processed on the common resources. The fairness of the scheduling algorithm is essential for the stability…
Recently Cristian S. Calude, Sanjay Jain, Bakhadyr Khoussainov, Wei Li and Frank Stephan proposed a quasi-polynomial time algorithm for parity games. This paper proposes a short proof of correctness of their algorithm.
The goal of the thesis is to leverage fast graph algorithms and modern algorithmic techniques for problems in model checking and synthesis on graphs, MDPs, and game graphs. The results include symbolic algorithms, a well-known class of…
High performance machine learning models have become highly dependent on the availability of large quantity and quality of training data. To achieve this, various central agencies such as the government have suggested for different data…
Optimal policies in standard MDPs can be obtained using either value iteration or policy iteration. However, in the case of zero-sum Markov games, there is no efficient policy iteration algorithm; e.g., it has been shown that one has to…
The practical scalability of many optimization algorithms for large extensive-form games is often limited by the games' huge payoff matrices. To ameliorate the issue, Zhang and Sandholm (2020) recently proposed a sparsification technique…
In several standard models of dynamic programming (gambling houses, MDPs, POMDPs), we prove the existence of a very robust notion of value for the infinitely repeated problem, namely the pathwise uniform value. This solves two open…