差价合约市场力抑制效应的Bertrand博弈模型分析

A Bertrand Model based on Contracts for Difference for Inhibiting Market Power

本文通过拓展经典的Bertrand对称双寡头博弈模型,运用勒拿指数测度电力市场绝对电量差价合约对发电商市场力的抑制效应。在发电商二次幂函数成本函数假定下,得到了双寡头对称发电商Bertrand博弈纳什均衡的解析表达式,并且发现发电商绝对量差价合约电量的增加会导致发电商均衡状态勒拿指数的可能取值范围会下降,因而具有抑制其市场力的效应。本文获得的拓展Bertrand博弈模型还将经典Bertrand博弈模型加以推广,得到二次幂函数成本函数条件下存在正均衡利润Bertrand的充分必要条件,为研究差价合约的其他相关问题提供了工具。

In this paper, the market power inhibiting effects of contracts for differences are studied. Due to oligopolistic characters owned by the electricity market, it is of great importance to focus on methods that could help restricting the market power of generators. The contract for differences is considered an effective way to control market power according to former researches, but the model we propose has the following characters that make our research special and creative. First of all, it is based on Bertrand model, which is properly applied in the electricity market, without adding any exogenous factors suggesting the relationship between the bidding price and the electricity quantity. It provides conditions that guarantee positive profit of generators. Secondly, Lerner index is introduced to the model for assessing market power. The main parts of this paper include the Nash equilibrium of generators in an identical duopoly electricity market （which is gained by analyzing the best responses of each generator）, the superior limit of both equilibrium price and Lerner index, the conditions to guarantee positive profit and illustration of identical duopoly electricity market by data simulation. Finally, the conclusion that the absolute electric quantity contract for difference has inhibiting effect on market power in an identical duopoly electricity market is drawn through the movement of the superior limit of Lerner index. This research provides a tool for other researches that consider using Bertrand model for analyzing contractual problems in electricity market, which is not often used in former researches due to the zero profit of classical Bertrand model, though it actually matches the electricity market.