The generalized mixed equilibrium problems include, as special cases, some optimization problems, fixed point problems, variational inequality problems, Nash equilibrium problems in noncooperative games, equilibrium problem, Numerous problems in physics, economics and others.
Moreover, it also demonstrates the game equilibrium is unique.
A distributed iterative power algorithm is provided for the problem to obtain the game equilibrium.
In order to study the game equilibrium, let us point out the following remark.
In electricity market research, the major modelling methods include optimization model based, game equilibrium model based and simulation model based.
Using the language of game theory, property rights is the outcome when the players have reached a game equilibrium (Sugden 1989).
Hence, sufficient conditions for existence and uniqueness of the solution are analytically derived, along with a distributed algorithm capable of reaching the game equilibrium.
As for power system energy policy studies, optimization and game equilibrium models are not applicable since the target problem is too complicated and comprises different market participants.
However, Selten [Game Equilibrium Models I. Springer, Berlin 1991, p. 98] argued that such learning rules can be stabilized for some games if there is an anticipation component in the learning process.
Based on the game equilibrium solution, a conclusion is drawn that owner should improve the monitoring efficiency and make powerful punishment to rent-seeking behaviors in order to effectively restrain the rent-seeking behaviors in engineering supervision.
Essential stabilities (which are related to lower semi-continuity) were used to analyze many problems, such as coincidence points [22, 23], fixed points[24], KKM points [25, 26], game equilibrium points [27 31], maximal elements [32], and variational relation problems [33 35], etc.
