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Multi-agent large language model (LLM) and vision-language model (VLM) debate systems employ specialized roles for complex problem-solving, yet model specializations are not leveraged to decide which model should fill which role. We propose…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
We consider two optimization problems in which a planner aims to influence the average transient opinion in the Friedkin-Johnsen dynamics on a network by intervening on the agents' innate opinions. Solving these problems requires full…
To investigate a time-consistent optimal strategy for the continuous time mean-variance model, we develop a new method to establish the Bellman principle. Based on this new method, we obtain a time-consistent dynamic optimal strategy that…
Cooperation underlies many natural and artificial systems. While voluntary participation can sustain cooperation without informational assumptions, real interactions are rarely anonymous, leaving the joint effects of participation and…
Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…
We introduce the incremental voter model (IVM), a discrete-opinion multi-agent system where agents undergo step-wise transitions biased by the opinion of a randomly selected persuader. Our incremental voter model comprises a large…
Online decision-making can be formulated as the popular stochastic multi-armed bandit problem where a learner makes decisions (or takes actions) to maximize cumulative rewards collected from an unknown environment. This paper proposes to…
Tasks that require information about the world imply a trade-off between the time spent on observation and the variance of the response. In particular, fast decisions need to rely on uncertain information. However, standard estimates of…
Reinforcement learning algorithms in multi-agent systems deliver highly resilient and adaptable solutions for common problems in telecommunications,aerospace, and industrial robotics. However, achieving an optimal global goal remains a…
We here discuss a model of continuous opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. We concentrate on the version of the…
In this work we introduce an evolutionary strategy to solve combinatorial optimization tasks, i.e. problems characterized by a discrete search space. In particular, we focus on the Traveling Salesman Problem (TSP), i.e. a famous problem…
We introduce an agent-based model of interaction, drawing on the contingency approach from Luhmann's theory of social systems. The agent interactions are defined by the exchange of distinct messages. Message selection is based on the…
We investigate opinion dynamics in multi-agent networks when a bias toward one of two possible opinions exists; for example, reflecting a status quo vs a superior alternative. Starting with all agents sharing an initial opinion representing…
Here, I study how to obtain an opinion dynamics model for the case where there are $M$ possible discrete choices and there is need to model how strong each agent choice is. The new model is obtained as an extension of the Continuous…
As autonomous agents become more prevalent, understanding their collective behaviour in strategic interactions is crucial. This study investigates the emergent cooperative tendencies of systems of Large Language Model (LLM) agents in a…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
This paper introduces a novel spatial interaction model to explore the decision-making processes of a resource allocator and local agents, with central and local governments serving as empirical representations. The model captures two key…
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…