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In the framework of stochastic zero-sum differential games, we establish a verification theorem, inspired by those existing in stochastic control, to provide sufficient conditions for a pair of feedback controls to form a Nash equilibrium.…
We present a new approach to modeling sequential data: the deep equilibrium model (DEQ). Motivated by an observation that the hidden layers of many existing deep sequence models converge towards some fixed point, we propose the DEQ approach…
Hierarchical Reinforcement Learning promises, among other benefits, to efficiently capture and utilize the temporal structure of a decision-making problem and to enhance continual learning capabilities, but theoretical guarantees lag behind…
Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be…
The next-next-to-leading order QCD corrections to the e+e- annihilation into hadrons are considered. The stability of the predictions with respect to change of the renormalization scheme is discussed in detail for the case of five, four and…
In a graph, a Clique-Stable Set separator (CS-separator) is a family $\mathcal{C}$ of cuts (bipartitions of the vertex set) such that for every clique $K$ and every stable set $S$ with $K \cap S = \emptyset$, there exists a cut $( W,W')$ in…
Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players'…
In this paper, we consider continuous-time quantum walks (CTQWs) on finite graphs determined by the Laplacian matrices. By introducing fully interconnected graph decomposition of given graphs, we show a decomposition method for the…
In this work, we propose a deep learning-based approach for quantum entanglement and discord classification using convolutional autoencoders. We train models to distinguish entangled from separable bipartite states for $d \times d$ systems…
We introduce a guessing game involving a quantum channel, three parties - the sender, the receiver and an eavesdropper, Eve - and a quantum public side channel. We prove that a necessary and sufficient condition for the quantum channel to…
We investigate verification and existence problems for prominent stability concepts in hedonic games with friends, enemies, and optionally with neutrals [8, 16]. We resolve several (long-standing) open questions [4, 16, 20, 23] and show…
Recent video question answering benchmarks indicate that state-of-the-art models struggle to answer compositional questions. However, it remains unclear which types of compositional reasoning cause models to mispredict. Furthermore, it is…
The game Arc-Kayles is played on an undirected graph with two players taking turns deleting an edge and its endpoints from the graph. We study a generalization of this game, Weighted Arc Kayles (WAK for short), played on graphs with…
The use of monotonicity and Tarski's theorem in existence proofs of equilibria is very widespread in economics, while Tarski's theorem is also often used for similar purposes in the context of verification. However, there has been…
It was shown in Flesch and Solan (2022) with a rather involved proof that all two-player stochastic games with finite state and action spaces and shift-invariant payoffs admit an $\epsilon$-equilibrium, for every $\epsilon>0$. Their proof…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
We prove that, under appropriate conditions, an abstract game with quasi-Leontief payoff functions $u_i : \prod_{j=1}^nX_j\to\mathbb{R}$ has a Nash equilibria. When all the payoff functions are globally quasi-Leontief, the existence and the…
With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that…
We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction…
Change-point detection (CPD) aims to locate abrupt transitions in the generative model of a sequence of observations. When Bayesian methods are considered, the standard practice is to infer the posterior distribution of the change-point…