Theorem 1: The proposed game G1 has at least one pure NE, and the optimization solution of OP 1 constitutes a

pure strategy NE of G1.

To be more specific, in the case where the merger turns a

pure strategy equilibrium into a mixed strategy equilibrium, the range of postmerger prices is strictly higher than the premerger prices.

Everett Carl Dolman, who literally wrote the book on

Pure Strategy, begins the series by contemplating the meaning of the word "strategy," setting the pace for the remainder of the book by ruthlessly defining terms and questioning easy answers.

A strategy profile x [member of] X is a

pure strategy Nash equilibrium of a game G if x [[??].sub.i] ([y.sub.i], [x.sub.i]) for all i [member of] I and [y.sub.i] [member of] [X.sub.i].

Dolman,

Pure Strategy: Power and Principle in the Space and Information Age, Frank Cass, New York, 2005, ISBN-13: 978-0714684987.

where i [member of] (1,2,.....,m) = /, is the

pure strategy for player I and) [member of] (1,2,.....,n) = J, is the pure strategies for player II.

The defender's

pure strategy is an assignment of the resources to targets.

In addition, it is noted that although there actually exists [2.sup.m] pure strategies, implementing

pure strategy [mathematical expression not reproducible] has the same result with that of applying [mathematical expression not reproducible].

If [[PI].sub.mc] > [[PI].sub.mn] - [C.sub.m], that is to say, the telecom carrier chooses not to cooperate with the third party payment company and achieves the maximization of profit, in this situation, there does not exist

Pure Strategy Nash Equilibrium, but Mixed Strategy Nash Equilibrium instead.

The local debt market is dominated by banks, and they have a

pure strategy of buy and hold.

Pure strategy advice has fallen out of fashion with clients keen to take action and looking for firms ready to work with them from concept all the way through execution.