ANALYSIS ON THE AGENT-BASED BERTRAND DUOPOLY GAME MODEL

Аннотация

The duopoly market research has a long history. Due to such reasons as material supply, product pa-tent right and concession of the government, development of many economic industries is similar to the process of duopoly. In game theory, the Bertrand model which considers price to be a strategic variable is closer to reality and provides the market with more references, especially for retail market and electricity market, as the competitive world develops.
Firstly, we analyze the classical Bertrand model and the Nash equilibrium in the model.
Secondly, multi-agent technology is applied and the Bertrand duopoly game bidding process is con-ducted; meanwhile, in order to help agents find the optimal solutions, genetic algorithm based on multi-agent Bertrand model is chosen as the main algorithm for the research; and we finish with software im-plementation of the algorithm and with example analysis. In the end, oligopoly market bidding is also modelled in MATLAB simulation, which provides us with more accuracies and flexibilities.
It is evidently shown in the model that when none of the two companies are able to meet all the de-mands in the market, the bigger the price gap, the more oscillated it is in the process; thus, the pure stra-tegic Nash equilibrium doesn’t exist. However, when one of the two can offer the demands independent-ly, Nash equilibrium appears and is shown as the calculated results in Bertrand-Edgeworth model where the equilibrium reaches the cost price. Further, the reason for no pure strategic Nash Equilibrium is also discussed