Analysis of Competitive and Cooperative Solutions in Dynamic Auction Games

The paper deals with an approach for dynamic games of searching maximum Pareto points which possess special decomposition characteristics, that inherits the properties of the competitive Nash equilibrium. Analysis of properties is implemented for the competitive Nash equilibrium. The set of Pareto points is constructed for cooperative actions of players. In the Pareto set a point of market equilibrium is defined, and the problem is posed to shift the system from the competitive Nash equilibrium to the point of market equilibrium. The shift algorithm is proposed and is based on analytical calculation of the players’ best replies to auction prices. The algorithm is implemented as a system of differential equations, right sides of which describe the mechanism of formation of auction prices and players’ best replies to these prices. Trajectories of the dynamic system describe the shift of players from the Nash equilibrium to Pareto maximum and show stable convergence of the algorithm. The results of the algorithm are demonstrated by the model of the auction game of fast growing economies.