Complexity Analysis For A Duopoly Dynamic Game With Bounded Rationality In Electric Power Market

The information of the previous oligopoly market research is assumed perfectinformation, and the market participants are considered perfectly rational, but suchassumptions are away from the social reality, to be bound by the reality of theeconomic situation, the nominal maximization may not be the best. Society is full of avariety of uncertainties, and kinds of decisions are made by independent individuals,but because of personal information is limited and incomplete cognitive ability tomake decisions that what we make may be not completely rational. With the gradualexpansion of technological progress and expanded market size, China’s power marketis facing a shortage of resources, power shortage, electricity pricing system andunreasonable situation. In order to solve these grave situations, appropriate policy isurgent for Chinese government. In order to analyze how the market can be able toachieve maximize profits, we simplify the model and adjust appropriate factors toexplore the complexity of the duopoly dynamic game with bounded rationality inelectric power market.In the paper, bounded rationality and delayed bounded rationality are applied tothe electric power market, through appropriate assumptions and numericalsimulations to study the stability of the system, such as system complexity and chaosin order to be able to provide the best theoretical basis for power producers inconsider of making policy.To simplify the model analysis, we assume that the price function is linear, thecost function is taken as a quadratic function, and there is a linear form over the netcosts. Through the numerical simulation, we study the Nash equilibrium conditions and complex dynamics, and further stability region, bifurcation diagram, the largestLyapunov exponent diagram, strange attractor, fractal dimension, and the yield on theinitial value sensitive dependence. In reality, the delay bounded rationality means thatmanufacturers should consider not only the opponent’s current situation, but alsotaking into account the production strategy of the past period in order to make hisown next tactics. The weighted average method makes this electricity manufacturersdo decisions more appropriate to maximize profits. Through the numericalsimulations by the use of matlab, we analyze the electric producers’ dynamics withbounded rationality and delay bounded rationality and compare the situation of thesetwo hypothetical theories.Strange attractor is highly sensitive dependence on the initial conditions, thefinal track will be separated from each other when the presence of small changes inthe initial value, and to be local instability. If the initial value changes0.001unit, theelectric producers’ output will be dramatic fluctuations that is chaos. The stabilitydomain of assuming the delayed bounded rationality is easier to achieve than boundedrationality assumptions. In other words, the delay bounded rationality enlarge thestability domain of power market, making it easier for manufacturers to achievepower Nash equilibrium.The study based on bounded rationality and delayed bounded rationality is ofsignificance for further academic research. By studying this paper we hope to providea theoretical basis for the policy makers, so that management can develop optimaldecisions. Before making decisions, oligarchic manufacturers in the electric marketwill try their best to get more complete information and rational analysis of theopponent’s production decisions and decisions of their opponent’s reactions. Theymay develop the most suitable strategy and through all the information to adjust theirown strategies in a timely manner to maintain dominance and reap excessive profitsin the market. Finally, oligarchic manufacturers in the electric market should be noted that even subtle changes in their own production, as it might result in minor changesof the system and finally completely deviate from the optimal economic conditionsand ultimate chaotic state of disorder. Through the analysis of the power market, wehope that we can prevent chaos, so that the system can be controlled within the range;by analyzing the results and we hope to take full advantage of the chaotic phenomena.