Reconstructing networks from the algebraic model of networked evolutionary games

Abstract

This paper presents a systematic mathematical analysis of the network reconstruction problem based on the algebraic model of networked evolutionary games, focusing on two data scenarios: (1) players’ payoff and strategy data, and (2) only players’ strategy data. Begin with the first scenario, the players’ payoff functions are transformed into a system of linear equations concerning neighbors using the payoff vector of the fundamental network game. Then the necessary and sufficient conditions for reconstructing the player network from the payoff functions are provided. In the second scenario, by considering the myopic best response and the unconditional imitation updating rules, the conditions under which the fundamental network game ensures that the strategy dynamic equations contain information about all player neighbors are investigated. Moreover, criteria for determining neighbors from these strategy dynamic equations are proposed. Finally, two examples demonstrate the network reconstruction process.