Competition games between teams vying for common resources under consensus dynamics on networks

摘要

Dynamics on complex networks and associated games have numerous practical applications for a wide range of fields. The analyses addressed in the literature frequently consider game frameworks defined between the individual nodes within a given network. However, many real situations are related to teams of agents which are external to the network but that compete over the state of the network elements. In this paper we carry out an analytical and numerical analysis of games played between two teams that compete to maximize their benefits from the resources of the same population, whose elements form a network. This population could be a group of voters in an election, a set of potential clients within a given market, or a certain species in an ecosystem, whose state favourable to one of the teams (political opinion, volume of purchases or pollination, for example) must be maximized. The dynamics of the state of each node of the network is given by a consensus function, and the steady state depends on the network structure and the external action of each team. We have found an optimal analytical solution for the team's actions that maximize its benefit, when the network of connections with the population is fixed and equal for both teams. Additionally, we find analytically the optimal network of connections from the team agents to the population so that the achievable payoff for said optimal action is maximum over all alternative networks. Finally, we consider the case of a game played on subsets of the general population by each of the two competing teams, ultimately leading to a Nash equilibrium. (C) 2019 Elsevier B.V. All rights reserved.