Impossibility of Stable Equilibrium Price

We develop a theory of equilibrium market instability in a general equilibrium duopoly caused merely by strategic trade. An economy is described as a strategic market game, where players have market power as buyers and sellers. First order conditions of individual decisions are the first kind integral equations of Fredholm with probability distributions as unknown variables. The game has multiple mixed strategies Nash equilibria, any of which can be constructed exactly. Hence players do not have a converging belief system. This imposes a restriction to existence of common beliefs of common knowledge, rational expectations equilibrium, information discovery property of market price. We demonstrate multiplicity of Pareto-improving pure strategies, induced prices and allocations, what can be a 'natural instability' of a market