基于Moran过程的制造商生产策略演化动态

考虑生产同质产品的Ⅳ个制造商生产策略的演化性态,每个制造商可选择利润最大化或者收入最大化两种生产策略.基于Moran过程的固定点概率,计算出在有限个制造商中,利润最大化生产策略和收入最大化生产策略成功入侵的概率,计算只有一个个体选择利润最大化或收入最大化生产策略时,单个制造商分别选择两种策略之一所得的期望收益,认为选择行为支持收益较大的策略入侵.在选择行为支持策略入侵与取代的意义下,分别得到利润最大化生产策略和收入最大化生产策略占优的条件.研究发现,制造商生产策略的选择取决于制造商的总体数量和其生产成本因子.若生产成本因子很小,则收入最大化策略是更合适的生存策略;若生产成本因子较小,在制造商数量少时,收入最大化生产策略占优;若生产成本因子较大,则制造商数量多时,利润最大化策略占优,制造商数量少时,收入最大化策略是占优策略.进一步通过数值例子发现,若制造商数量一定,在生产成本因子比较小时,收入最大化生产策略是占优策略,当生产成本因子比较大时,利润最大化生产策略是占优策略;若生产成本因子很大,则利润最大化策略是更合适的生存策略.

Evolutionary dynamics of manufacturers' production strategies based on Moran process

Consider the evolutionary dynamics of N manufacturers' production strategies with homogeneous goods, each manufacturer chooses profit maximization or revenue maximization to produce his products. Based on Moran process, we obtain the fixation probability of profit maximization and revenue maximization. Meanwhile, we calculate the difference of expect payoff between manufacturers used different strategies when just one manufacturer chooses the profit maximization or revenue maximization production strategy, and consider selection favored the strategy with larger payoff than another invading the other strategy. Then we get the dominant strategy in the sense that selection favored one strategy invading and replacing the other. By analyzing, we obtain the dominant strategy depends on the population size and the production cost of manufacturers. The revenue maximization is dominant strategy as the production cost factor is very little, and production cost factor is relatively small, the revenue maximization is a dominant strategy if there are less manufacturers, and when the production cost factor is relatively high, then the profit maximization is dominant strategy if there are a lot of manufacturers, the revenue maximization is a dominant strategy if there are relatively few manufacturers. Furthermore, by using numerical examples, we obtain the conclusions that the number of manufacturers is certain, the revenue maximization is the dominant strategy if the production cost factor is relatively small, and the profit maximization is the dominant strategy if the production cost factor is relatively large, and the profit maximization is a dominant strategy as production cost factor is very large.