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Cooperation and competition are fundamental forces shaping both natural and human systems, yet their interplay remains poorly understood. The Prisoner's Dilemma Game (PDG) has long served as a foundational framework in Game Theory for…
We study the fair allocation of indivisible goods with variable groups. In this model, the goal is to partition the agents into groups of given sizes and allocate the goods to the groups in a fair manner. We show that for any number of…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
In Hotelling's model of spatial competition, a unit mass of voters is distributed in the interval $[0,1]$ (with their location corresponding to their political persuasion), and each of $m$ candidates selects as a strategy his distinct…
A \emph{fair competition}, based on the concept of envy-freeness, is a non-eliminating competition where each contestant (team or individual player) may not play against all other contestants, but the total difficulty for each contestant is…
We investigate the effects of competition in a problem of resource extraction from a common source with diffusive dynamics. In the symmetric version with identical extraction rates we prove the existence of a Nash equilibrium where the…
We present a dynamical model of web site growth in order to explore the effects of competition among web sites and to determine how they affect the nature of markets. We show that under general conditions, as the competition between sites…
Explore-and-exploit tradeoffs play a key role in recommendation systems (RSs), aiming at serving users better by learning from previous interactions. Despite their commercial success, the societal effects of explore-and-exploit mechanisms…
We develop a game-theoretic framework for the study of competition between firms who have budgets to "seed" the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of…
In this monograph, we introduce a new model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility. The interactions among these populations are described not in terms of…
We study the framework of a dynamic decision-making scenario with resource constraints. In this framework, an agent, whose target is to maximize the total reward under the initial inventory, selects an action in each round upon observing a…
Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The dynamics of this selection is studied using a simple linear model. It has similarities to…
Natural selection drives species to develop brains, with sizes that increase with the complexity of the tasks to be tackled. Our goal is to investigate the balance between the metabolic costs of larger brains compared to the advantage they…
In a district-based election, we apply a voting rule $r$ to decide the winners in each district, and a candidate who wins in a maximum number of districts is the winner of the election. We present efficient sampling-based algorithms to…
We consider an online resource allocation problem where multiple resources, each with an individual initial capacity, are available to serve random requests arriving sequentially over multiple discrete time periods. At each time period, one…
The rate at which nodes in a network increase their connectivity depends on their fitness to compete for links. For example, in social networks some individuals acquire more social links than others, or on the www some webpages attract…
The capability to widely sample the state and action spaces is a key ingredient toward building effective reinforcement learning algorithms. The variational optimization principles exposed in this paper emphasize the importance of an…
Common-pool resource governance requires users to cooperate and avoid overexploitation, but defection and free-riding often undermine cooperation. We model a human-environmental system that integrates dynamics of resource and users'…
We introduce a game in which two players with opposing objectives seek to repeatedly takeover a common resource. The resource is modeled as a discrete time dynamical system over which a player can gain control after spending a…
In this paper, we study multi-agent systems with decentralized resource allocations. Agents have local demand and resource supply, and are interconnected through a network designed to support sharing of the local resource; and the network…