Algorithm of price adjustment for market equilibrium

In this paper, we suggest an algorithm for price adjustment towards a partial market equilibrium. Its convergence properties are crucially based on Convex Analysis. Our price adjustment corresponds to a subgradient scheme for minimizing a special nonsmooth convex function. This function is the total excessive revenue of the market’s participants [16, 18], and its minimizers are equilibrium prices. As the main result, the algorithm of price adjustment is shown to converge to equilibrium prices. Additionally, a market equilibrium clears on average during the price adjustment process. This means that the market clears by historical averages of supply and demand. Moreover, an efficient rate of convergence is obtained. Additionally, we endow our algorithm with decentralized prices by introducing the trade design. The latter suggests that producers settle and update their individual prices, and consumers buy at the lowest purchase price. The proposed price adjustment enjoys a natural behavioral interpretation. First, producers forecast their individual prices to be proportional to their excess demands. For the price update, they subsequently apply an average of these price forecasts over time