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Bounded-size rules are dynamic random graph processes which incorporate limited choice along with randomness in the evolution of the system. One starts with the empty graph and at each stage two edges are chosen uniformly at random. One of…

Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's wealth power law distribution. One important factor to be considered is the existence of risk aversion. In…

Wealth inequality remains a critical socioeconomic challenge, driven by systemic dynamics and self-reinforcing mechanisms that amplify the economic imbalances. Simplified models from statistical physics provide valuable insights into the…

We introduce an auto-regressive model which captures the growing nature of realistic markets. In our model agents do not trade with other agents, they interact indirectly only through a market. Change of their wealth depends, linearly on…

In this paper we study the cooperative behavior of agents playing the Prisoner's Dilemma game in random scale-free networks. We show that the survival of cooperation is enhanced with respect to random homogeneous graphs but, on the other…

We introduce a minimal agent-based model to qualitatively conceptualize the allocation of limited wealth among more abundant opportunities. We study the interplay of power, satisfaction and frustration in distribution, concentration, and…

We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous…

We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple…

This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes…

We study a fair division problem in (multi)graphs where $n$ agents (vertices) are pairwise connected by items (edges), and each agent is only interested in its incident items. We consider how to allocate items to incident agents in an…

We study the transition towards effective payoffs in the prisoner's dilemma game on scale-free networks by introducing a normalization parameter guiding the system from accumulated payoffs to payoffs normalized with the connectivity of each…

Cooperation between individuals is emergent in all parts of society, yet mechanistic reasons for this emergence is ill understood in the literature. A specific example of this is insurance. Recent work has, though, shown that assuming the…

Balanced and swap-robust minimal trades, introduced in [1], are important for studying the balance and stability of server access request protocols under data popularity changes. Constructions of such trades have so far relied on paired…

The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according to a random time-varying graph. Specifically, the goal of the network is to minimize the sum of…

We study the problem of fair division of a set of indivisible goods with connectivity constraints. Specifically, we assume that the goods are represented as vertices of a connected graph, and sets of goods allocated to the agents are…

We consider a group of agents on a graph who repeatedly play the prisoner's dilemma game against their neighbors. The players adapt their actions to the past behavior of their opponents by applying the win-stay lose-shift strategy. On a…

Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…

Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various…

We model a closed economic system with interactions that generates the features of empirical wealth distribution across all wealth brackets, namely a Gibbsian trend in the lower and middle wealth range and a Pareto trend in the higher…