Negotiation and Equilibria in User Competition for Resources: A Dynamic Plot Approach

We consider a scenario where two users are competing for substitutable facilities and where the costs to a user for using a facility depend on its usage as well as the usage by the other user. This results in a nonlinear dynamic game the solution of which implies an allocation that satisfies both users. Games with four different types of solution spaces are presented where the equilibria and the process to reach a negotiated compromise solution have different characterizations. Nash equilibria and nondominated points are discussed in this context and an interactive graphical dynamic plot approach is presented for obtaining negotiated solutions in such nonlinear dynamic games.