Time-Based Protocol for Continuous Action Iterated Dilemma in Information Lossy Networks

Abstract

This article introduces a novel prescribed time-based method for analyzing the convergence of evolutionary game dynamics in an information lossy network. Traditional game theory limits players to two choices, i.e., either cooperation or defection. However, player behavior in real-world scenarios is often multidimensional and complex; therefore, this work employs a continuous action iterated dilemma that allows players to choose a wider range of strategies. Moreover, traditional convergence analysis often relies on Jacobian matrices, which entail complex derivations. In contrast, the proposed strategy employs a time generator-based protocol that achieves agreement between all the players at a prescribed time, explicitly set by the user through a time parameter within the protocol. A comprehensive Lyapunov analysis affirms the prescribed time convergence even when the network is exposed to information loss during data transfer. Numerical simulations illustrate that the proposed scheme leads to a faster agreement at the preassigned time and with a better resilience performance compared to existing methods.