Natural Instability of Equilibrium Prices

We develop a theory of market fluctuations caused by strategic trade with complete information and without outside shocks. The constructed general equilibrium duopoly is a strategic market game with infinite strategies and multiple mixed strategies equilibria. First order conditions (FOC) of the game are the ill-posed problems (Hadamard, 1909), but every equilibrium mixed strategy can be only approximated. This imposes restrictions on convergence of common beliefs of players about actions of each other, existence of rational expectations and a price discovery property of the market, although the market is informationally efficient (Fama, 1970). We suggest a modification of Tikhonov regularization to construct pseudo-solutions. All endogenous variables of the model are exposed to unremovable instabilities, ‘natural instabilities’, specific to parameters of a chosen approximation. Our result is also related to existence of common knowledge, sun-spot equilibrium, and noise trade.