Counterpoint Theory and the Novel Function Able to Classify All Continuous Solutions to the Nash Bargaining Problem

Abstract

This paper solves the long-standing bargaining problem of how to define the unique equilibrium solution that represents how two firms optimally share a surplus they jointly create in repeated games. A unique equilibrium point is determined, representative of an infinite number of points in R3 that cannot be reached by any two vector combinations. The unique solution is modeled using the continuous bi-continuous function f: J-->R3 of J, an open Mobius band (Vaughan 1977). Applying this unique continuous bi-continuous function, I show how to classify all continuous solutions to Nash’s Bargaining Problem. I introduce the concept of integrated dealmaking without compromise in repeated games called Counterpoint Theory. Applying the theory and function, I solve the long-standing problem of how to model corruption without bribes in repeated games and explain new market creation based on alternative states of the world.