The Power Allocation Game on Dynamic Networks: Subgame Perfection

TL;DR

This paper reformulates a static power allocation game on signed graphs into an extensive form to analyze subgame perfect Nash equilibria, introducing a novel approach for equilibrium selection in dynamic network games.

Contribution

It introduces the first application of subgame perfect equilibrium analysis based on time-varying graphs in network games, extending equilibrium selection methods.

Findings

Subgame perfect Nash equilibria characterized for the extended game.

First use of subgame perfection in dynamic network games.

Potential applicability to other network game types like congestion games.

Abstract

In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not applicable to games involving both cooperative and noncooperative scenarios (e.g., "games on signed graphs"). With the purpose of equilibrium selection, the power allocation game developed in \cite{allocation}, which is a static, resource allocation game on signed graphs, will be reformulated into an extensive form. Results about the subgame perfect Nash equilibria in the extensive-form game will be given. This appears to be the first time that subgame perfection based on time-varying graphs is used for equilibrium selection in network games. This idea of subgame perfection proposed in the paper may be extrapolated to other network games, which will be illustrated with a simple example of congestion games.