Analysis of Two Game Theory Models: Cournot Model and Stackelberg Model

Abstract

Game theory has long been an important branch of economics, and many of its models have been able to find specific examples in real life. It solves practical problems by considering the predicted and actual behavior of individuals in the game and studying their optimization strategies. This article focuses on two classical models in game theory, the Cournot model and the Stackelberg model, and compares the two models from the perspective of the fundamental model and two special cases, respectively. Firstly, the paper introduces two basic models, enumerates real cases, and deduces the function relation of the optimal production quantity of each enterprise. Then, considering that production quantity and profit may be related to cost, number of enterprises and other factors, the paper changes the relationship between the number of enterprises and cost to explore the impact on the two models. To make the results more intuitive, the authors plug in two sets of data to calculate the profits in each case. The results show that when the number of firms increases, the profits obtained by both Firm1 and Firm2 in Cournot's model decrease. In Stackelberg, Firm 2 made half as much profit as Cournot, and Firm 1 remained the same. With different costs, firms with smaller production costs produce larger quantities and profits. In conclusion, this study compares the two models from the basic case and two additional cases, analyzes which model should be chosen respectively in which cases, and provides effective strategies for real life firms.