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The pursuit-evasion game with two persons is considered. Both players are moving in a metric space, have equal maximum speeds and complete information about the location of each other. We study the sufficient conditions for a capture (with…

In this paper, we consider groups of agents in a network that select actions in order to satisfy a set of constraints that vary arbitrarily over time and minimize a time-varying function of which they have only local observations. The…

This article adopts game theory to build a model for explaining the predation behavior of animals.We assume that both the prey and the preydator have two stratigies in this game,the active one and the passive one.By calculating the outcome…

Adversarial online linear optimization (OLO) is essentially about making performance tradeoffs with respect to the unknown difficulty of the adversary. In the setting of one-dimensional fixed-time OLO on a bounded domain, it has been…

This work develops a fully decentralized multi-agent algorithm for policy evaluation. The proposed scheme can be applied to two distinct scenarios. In the first scenario, a collection of agents have distinct datasets gathered following…

The divide and conquer strategy, which breaks a massive data set into a se- ries of manageable data blocks, and then combines the independent results of data blocks to obtain a final decision, has been recognized as a state-of-the-art…

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…

This paper presents a reinforced genetic approach to a defined d-resource system optimization problem. The classical evolution schema was ineffective due to a very strict feasibility function in the studied problem. Hence, the presented…

We propose a general agent population learning system, and on this basis, we propose lineage evolution reinforcement learning algorithm. Lineage evolution reinforcement learning is a kind of derivative algorithm which accords with the…

Humans exhibit remarkable abilities to coordinate in groups. As large language models (LLMs) become more capable, it remains an open question whether they can demonstrate comparable adaptive coordination and whether they use the same…

In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…

Distributed optimization and Nash equilibrium (NE) seeking problems have drawn much attention in the control community recently. This paper studies a class of non-cooperative games, known as N-cluster game, which subsumes both cooperative…

Balancing game difficulty in video games is a key task to create interesting gaming experiences for players. Mismatching the game difficulty and a player's skill or commitment results in frustration or boredom on the player's side, and…

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method…

Stochastic games are a popular framework for studying multi-agent reinforcement learning (MARL). Recent advances in MARL have focused primarily on games with finitely many states. In this work, we study multi-agent learning in stochastic…

This paper introduces a systematic methodological framework to design and analyze distributed algorithms for optimization and games over networks. Starting from a centralized method, we identify an aggregation function involving all the…

We present two improved algorithms for weighted discrete $p$-center problem for tree networks with $n$ vertices. One of our proposed algorithms runs in $O(n \log n + p \log^2 n \log(n/p))$ time. For all values of $p$, our algorithm thus…

We provide a polynomial algorithm to find the value and an optimal strategy for a generalization of the Pig game. Modeled as a competitive Markov decision process, the corresponding Bellman equations can be decoupled leading to systems of…

The LION (evoLved sIgn mOmeNtum) optimizer for deep neural network training was found by Google via program search, with the simple sign update yet showing impressive performance in training large scale networks. Although previous studies…

Recent advances in game AI, such as AlphaZero and Ath\'enan, have achieved superhuman performance across a wide range of board games. While highly powerful, these agents are ill-suited for human-AI interaction, as they consistently…