Related papers: Adversarial Knapsack for Sequential Competitive Re…

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current…

In this paper, we introduce online knapsack problems with a resource buffer. In the problems, we are given a knapsack with capacity $1$, a buffer with capacity $R\ge 1$, and items that arrive one by one. Each arriving item has to be taken…

We study the sequential batch learning problem in linear contextual bandits with finite action sets, where the decision maker is constrained to split incoming individuals into (at most) a fixed number of batches and can only observe…

Sequential allocation is a simple mechanism for sharing multiple indivisible items. We study strategic behavior in sequential allocation. In particular, we consider Nash dynamics, as well as the computation and Pareto optimality of pure…

We introduce Contested Logistics Games, a variant of logistics problems that account for the presence of an adversary that can disrupt the movement of goods in selected areas. We model this as a large two-player zero-sum one-shot game…

In repeated interactions between individuals, we do not expect that exactly the same situation will occur from one time to another. Contrary to what is common in models of repeated games in the literature, most real situations may differ a…

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource.…

We study exploration in stochastic multi-armed bandits when we have access to a divisible resource that can be allocated in varying amounts to arm pulls. We focus in particular on the allocation of distributed computing resources, where we…

We consider a sequential decision-making problem where an agent can take one action at a time and each action has a stochastic temporal extent, i.e., a new action cannot be taken until the previous one is finished. Upon completion, the…

We study the stochastic contextual bandit with knapsacks (CBwK) problem, where each action, taken upon a context, not only leads to a random reward but also costs a random resource consumption in a vector form. The challenge is to maximize…

Stochastic games with discounted payoff, introduced by Shapley, model adversarial interactions in stochastic environments where two players try to optimize a discounted sum of rewards. In this model, long-term weights are geometrically…

We study a contest-theoretic model of adversarial investment in which an attacker and a defender allocate resources to AI-augmented capabilities across multiple attack surfaces. The attacker's investment operates through two channels: it…

We study contextual bandits with ancillary constraints on resources, which are common in real-world applications such as choosing ads or dynamic pricing of items. We design the first algorithm for solving these problems that handles…

We introduce and asses several Divide \& Conquer heuristic strategies aimed to solve large instances of the 0-1 Minimization Knapsack Problem. The method subdivides a large problem in two smaller ones (or recursive iterations of the same…

This paper examines the integration of computational complexity into game theoretic models. The example focused on is the Prisoner's Dilemma, repeated for a finite length of time. We show that a minimal bound on the players' computational…

We propose a novel algorithm for online resource allocation with non-stationary customer arrivals and unknown click-through rates. We assume multiple types of customers arrive in a nonstationary stochastic fashion, with unknown arrival…

A class of nonzero-sum stochastic dynamic games with imperfect information structure is investigated. The game involves an arbitrary number of players, modeled as homogeneous Markov decision processes, aiming to find a sequential Nash…

This paper analyzes the structure of mixed-strategy equilibria for Colonel Blotto games, where the outcome on each battlefield is a polynomial function of the difference between the two players' allocations. This paper severely reduces the…

The Colonel Blotto game, first introduced by Borel in 1921, is a well-studied game theory classic. Two colonels each have a pool of troops that they divide simultaneously among a set of battlefields. The winner of each battlefield is the…

In dynamic noncooperative games, each player makes conjectures about other players' reactions before choosing a strategy. However, resulting equilibria may be multiple and do not always lead to desirable outcomes. These issues are typically…