This paper introduces a new formulation for the Coumot game equilibrium analysis that allows arbitrary differentiable cost and utility curves to be implemented, without recourse to conjectures about the behaviour of market participants. The formulation reduces the Coumot equilibrium problem to solving a system of multivariate, nonlinear equations in terms of the cost, utility and price functional and its derivatives. Actual numerical solution of the equation system can then be determined using various nonlinear numerical techniques. As the functionals are only required to be differentiable, the range of cost and utility curves that the new formulation can handle is significantly larger then the often-studied linear and quadratic cost and utility functional.
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