Related papers: Using Strategy Improvement to Stay Alive

Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…

We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode \omega-regular specifications, and the mean-payoff and energy objectives can be used…

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…

Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first…

Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we…

In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the…

A \emph{bidding} game is played on a graph as follows. A token is placed on an initial vertex and both players are allocated budgets. In each turn, the players simultaneously submit bids that do not exceed their available budgets, the…

Strategy improvement is a widely-used and well-studied class of algorithms for solving graph-based infinite games. These algorithms are parameterized by a switching rule, and one of the most natural rules is "all switches" which switches as…

We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In constrast with previous MG, the best strategies are not always targeting the minority but are shifting…

We consider finite-state Markov decision processes with the combined Energy-MeanPayoff objective. The controller tries to avoid running out of energy while simultaneously attaining a strictly positive mean payoff in a second dimension. We…

The proliferation of distributed generation and storage units is leading to the development of local, small-scale distribution grids, known as microgrids (MGs). In this paper, the problem of optimizing the energy trading decisions of MG…

We consider concurrent games played on graphs. At every round of a 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…

Markov games (MGs) provide a mathematical foundation for multi-agent reinforcement learning (MARL), enabling self-interested agents to learn their optimal policies while interacting with others in a shared environment. However, due to the…

We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…

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…

We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…

In a multi-objective game, each individual's payoff is a \emph{vector-valued} function of everyone's actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual's best-response condition, inducing…

The strategy improvement algorithm for mean payoff games and parity games is a local improvement algorithm, just like the simplex algorithm for linear programs. Their similarity has turned out very useful: many lower bounds on running time…

Autonomous marine vehicles play an essential role in many ocean science and engineering applications. Planning time and energy optimal paths for these vehicles to navigate in stochastic dynamic ocean environments is essential to reduce…

Solvency games, introduced by Berger et al., provide an abstract framework for modelling decisions of a risk-averse investor, whose goal is to avoid ever going broke. We study a new variant of this model, where, in addition to stochastic…