The Power Allocation Game on A Dynamic Network: Equilibrium Selection

This note proposes two equilibrium selection methods and applies them to the power allocation game developed in [1]. The first method has the game take place on a sequence of time-varying graphs, which redefines the PAG in an extensive form game framework, and selects the subgame perfect Nash equilibria. The second method has the power allocation game take place on a different sequence of time-varying graphs and selects the “resilient” Nash equilibria, where the concept of “resilience” is taken from the literature of network security. Certain technical results as well as the link between the two methods will be discussed. Either method is also applicable to equilibrium selection problems involving other network games.