Related papers: Decomposition of Differential Games
We study zero-sum stochastic games between a singular controller and a stopper when the (state-dependent) diffusion matrix of the underlying controlled diffusion process is degenerate. In particular, we show the existence of a value for the…
This paper proposes a new method for finding closed-loop saddle points in zero-sum linear-quadratic stochastic differential games by decoupling their inherent structure. Specifically, we develop a nested iterative scheme that constructs a…
This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…
We study zero-sum games, a variant of the classical combinatorial Subtraction games (studied for example in the monumental work "Winning Ways", by Berlekamp, Conway and Guy), called Cumulative Subtraction (CS). Two players alternate in…
Subset take-away is a two-player game involving a fixed finite set A. Players alternate choosing a proper, non-empty subset of A, with the condition that one may not name a set containing a set that was named earlier. A player unable to…
This letter employs differential game theory to address the defense problem of a circular target area with perception constraints, involving a single defender and a single attacker. The defender is restricted to moving along the perimeter,…
Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
We provide a formal definition of depth-limited games together with an accessible and rigorous explanation of the underlying concepts, both of which were previously missing in imperfect-information games. The definition works for an…
Answering complex questions often requires multi-step reasoning in order to obtain the final answer. Most research into decompositions of complex questions involves open-domain systems, which have shown success in using these decompositions…
Differential game theory offers an approach for modeling interactions between two or more agents that occur in continuous time. The goal of each agent is to optimize its objective cost functional. In this paper, we present two different…
This paper proposes a game-theoretic approach to address the problem of optimal sensor placement against an adversary in uncertain networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious…
We propose a general framework for modelling and solving deductive games, where one player selects a secret code and the other player strives to discover this code using a minimal number of allowed experiments that reveal some partial…
A Subtraction-Division game is a two player combinatorial game with three parameters: a set S, a set D, and a number n. The game starts at n, and is a race to say the number 1. Each player, on their turn, can either move the total to n-s…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
We generalize gradient descent with momentum for optimization in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and…
Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…
We offer a new approach to the information decomposition problem in information theory: given a 'target' random variable co-distributed with multiple 'source' variables, how can we decompose the mutual information into a sum of non-negative…
We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number…