Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Spontaneous Pricing Order in the Noncooperative Game of Monopolistic Manufacturer and Many Retailers

Version 1 : Received: 29 June 2021 / Approved: 30 June 2021 / Online: 30 June 2021 (10:27:43 CEST)

How to cite: Si, T. The Spontaneous Pricing Order in the Noncooperative Game of Monopolistic Manufacturer and Many Retailers. Preprints 2021, 2021060728 (doi: 10.20944/preprints202106.0728.v1). Si, T. The Spontaneous Pricing Order in the Noncooperative Game of Monopolistic Manufacturer and Many Retailers. Preprints 2021, 2021060728 (doi: 10.20944/preprints202106.0728.v1).

Abstract

We consider the collective pricing orders in a minimum supply chain that is composed of a monopolistic manufacturer and many retailers that belong to the same chain store firm. The retailers have the freedom to raise or lower the local price. The chain store firm sets up the commercial rules for local retail stores to maximize its total payoff. The monopolistic manufacturer firm controls the total quantity supplied for the market to achieve maximum benefits. We applied the two dimensional Ising model in statistical physics to map the collective distribution of microscopic strategy of local retailers into the macroscopic total payoff of the chain store firm. The local stores choose to raise the price or lower the price based their own mind when the supply in market surpasses the demand. When the supply in market is far less than the demand, the stores synchronously raise prices, even though a local store only have the incomplete information of their nearest neighboring supermarket. We find the critical equation for the balance point between the action of supplier and the action of chain store management based on game theory and statistical physics. The critical equation can identify the Nash equilibrium point of the non-cooperative game between the manufacturer and the chain-store seller, and reveal different levels of collective operations. This statistical physics method also holds for more complicate supply chains and economic systems.

Subject Areas

Spontaneous order; Price formation; Non-cooperative game theory; Statistical physics; Supply chain; two dimensional Ising model

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