Title: The Power Allocation Game on Dynamic Networks: Subgame Perfection,
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.