Research
Research
Research
Research
5,868+ open-access research outputs.
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. Howeve…
In this letter, we study a model-based inverse problem for infinite-horizon linear-quadratic differential games with descriptor dynamics. Specifically, we seek to identify the set of all cost function…
Revealing the interaction topology underlying strategic behavior is fundamental to prediction, intervention, and policy design in networked systems. Yet the interaction matrix is often unobservable, a…
The Immersed Boundary Method has long served as a robust computational framework for fluid-structure interactions, yet the rigorous analysis of 1D Peskin filaments anchored to rigid boundaries remains…
We study stochastic differential games with $N$ players, where interactions are determined by sequences of graphs in which the number of neighbours of each node remains bounded as $N$ grows, such as c…
Lutwak's affine quermassintegral theory is a foundational component of modern affine Brunn--Minkowski theory. Developed in the 1980s, it provides affine analogues of the classical quermassintegrals an…
This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games. We reformulate the game as a regenerative problem with deterministic cycles, which allows polic…
This paper studies the Nash equilibrium seeking problem for stochastic games under heavy-tailed noise. The gradient noise is considered to have a finite $\delta$-th moment ($1<\delta\le 2$), which gen…
We show the subgroup of 20 nonzero fourth powers in the finite field of order 81 is a cap set. Similarly, the subgroup of 9 nonzero seventh powers in the field of order 64 is a cap set. These are the …
Our research is closely related to ontological studies in mathematics. It provides crucial insights into the nature of decisions and strategies characterized by Markov moments. In a stopping game, a…
We compute the Atiyah Real $K$-theory of $C_2$-equivariant projective spaces and construct immersions of such spaces into multiples of the regular representation. These computations are made tractable…
We study the control of rumor propagation in large networked populations by using Stackelberg graphon games. We first introduce a principal who wants to incentivize the spread of her preferred news an…
We construct string backgrounds in dimension 2 which connect the Hamilton cigar to the round sphere. Specifically, we construct a 1-parameter family of rotationally symmetric steady gradient Ricci-Yan…
Game-theoretic characterizations of selection principles provide a powerful framework for analyzing covering properties through strategic interactions. For a Tychonoff space $X$ and a non-trivial metr…
In many applications, including Stackelberg games, machine learning, and power systems \cite{Mackay2018Selftuning,Heinrich1952The,Wang2021Bi-Level}, the decisions in a minimax optimization problem can…
This paper investigates a class of linear-quadratic-Gaussian risk-sensitive graphon mean-field games, involving an asymptotically infinite population of heterogeneous agents distributed across an asym…
This paper presents a computational study of P-positions (losing positions for the player to move) in 4 x n Chomp, the combinatorial game played on a 4 x n rectangular grid. An optimized C++ solver wi…
In this work, we establish the small-noise asymptotic behaviour (namely, the functional law of large numbers and the large deviation principle) for multi-scale McKean--Vlasov diffusions with super-lin…
By results of Dantzig (1951) and Adler (2013), computing the optimal solutions of a linear program is equivalent to finding optimal strategies in zero-sum bimatrix games. Dantzig's original result was…
We study linear quadratic dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. Building on recent work on strategica…
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