Abstract
In this paper, we discuss continuous game problems for which a normalization constraint (unit simplex constraint) constrains each player's decision-making. These problems can be classified into two types by their constraints. For one type, the simplex constraint applies to the variables for each player independently, such as occurs in a product ability assignment problem. For the other type, the simplex constraint applies to interferences among all the players, such as in a market share competition problem. We assume that the problems have Nash equilibrium solutions, and then we derive gradient system dynamics, which converge to the Nash solutions without violations of the simplex constraints. We discuss the equivalence of the derived dynamics and the replicator dynamics. Lastly, the effectiveness of the derived dynamics is shown by its application to simple example problems.
