Pure-Strategy Equilibria Analysis for Two-Player SISG
As the SISG we describe is game of complete information, pure-strategy equilibria always exist, and the pure-strategy equilibria for both two-player symmetric and asymmetric SISG are analyzed in this section, while that of m-player SISG will also be discussed for both symmetric and asymmetric situation in the next section.
Pure-Strategy Equilibria for Two-Player Symmetric SISG
In two-player symmetric SISG, pure-strategy subgame perfect Nash equilibria (SPNE) will always exist and are symmetric.
Pure-Strategy Equilibria for Two-Player Asymmetric SISG. We then further analyze the pure-strategy equilibria for two-player asymmetric SISG as given in Figure 4.
The following theorem concerning equilibria of two-player asymmetric SISG is put forward for obtaining the individually optimal choice, which is given in the form of the solution of SPNE.
In two-player asymmetric SISG, pure-strategy subgame perfect Nash equilibria (SPNE) will always exist.
The optimal choices for social planner in two-player asymmetric SISG are further explored.
In this section, we show how to extend the theorems concerning pure-strategy equilibria to the situation of m-player SISG. Firstly, in the m-player (m > 2) symmetric SISG, the SPNE is proved to exist with the corresponding analytical solutions being obtained.
Thus, we consider m-player (m > 2) symmetric SISG that all the players excluding Pt act simultaneously, and then according to the strategy chosen by [P.sub.-i], [P.sub.i] decides his own optimal strategy.
In m-player (m > 2) SISG, a pure-strategy subgame perfect Nash equilibrium (SPNE) will always exists.
We then further discuss the socially optimal choices for m-player symmetric SISG. The payoff function of administrator is denoted in (18).