Related papers: Least and greatest fixpoints in game semantics
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…
We estimate the maximal length of interactions between strategies in HO/N game semantics, in the spirit of the work by Schwichtenberg and Beckmann for the length of reduction in simply typed lambdacalculus. Because of the operational…
The ``losing positions" of certain combinatorial games constitute linear error detecting and correcting codes. We show that a large class of games that can be cast in the form of *annihilation games*, provides a potentially polynomial…
In this article, we prove the completeness of the following game search algorithms: unbounded best-first minimax with completion and descent with completion, i.e. we show that, with enough time, they find the best game strategy. We then…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
Games are natural models for multi-agent machine learning settings, such as generative adversarial networks (GANs). The desirable outcomes from algorithmic interactions in these games are encoded as game theoretic equilibrium concepts, e.g.…
We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…
Game theory provides the gold standard for analyzing adversarial engagements, offering strong optimality guarantees. However, these guarantees often become brittle when assumptions such as perfect information are violated. Reinforcement…
The known results regarding two-player zero-sum games are naturally generalized in complex space and are presented through a complete compact theory. The payoff function is defined by the real part of the payoff function in the real case,…
We introduce and investigate a range of general notions of a game. Our principal notion is based on a set of agents modifying a relational structure in a discrete evolution sequence. We also introduce and study a variety of ways to model…
We explain a highly efficient algorithm for playing the simplest type of dots and boxes endgame optimally (by which we mean "in such a way so as to maximise the number of boxes that you take"). The algorithm is sufficiently simple that it…
We consider a class of games with continuum of players where equilibria can be obtained by the minimization of a certain functional related to optimal transport as emphasized in [7]. We then use the powerful entropic regularization…
After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an…
Many learning algorithms are known to converge to an equilibrium for specific classes of games if the same learning algorithm is adopted by all agents. However, when the agents are self-interested, a natural question is whether agents have…
Estimating discrete games of complete information is often computationally difficult due to partial identification and the absence of closed-form moment characterizations. This paper proposes computationally tractable approaches to…
We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss…
This paper considers mean field games with optimal stopping time (OSMFGs) where agents make optimal exit decisions, the coupled obstacle and Fokker-Planck equations in such models pose challenges versus classic MFGs. This paper proposes a…
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 $NP \cap coNP$ which are not known to be in $P$. However, there are some…