A Stackelberg Game: Exploration and Development of Entrepreneurial Resources

In this paper, a mathematical model of entrepreneurial resource development was established. Entrepreneurs are mainly faced with competition from other companies in the same industry and mature large-sized developing enterprises. These players not only possess more initial resources, but also are more capable at occupying resources. Then the equilibrium solution to zero-sum differential games of entrepreneurial resources was investigated, and the optimal strategy and its relationship with the economic environment were analyzed. The cons and pros of the equilibrium solutions under different scenarios were compared by considering small-sized enterprises and mature developing large-sized enterprises as the leader or the follower of Stackelberg games. Introduction Entrepreneurship is a long-standing social phenomenon, and its success results in the continuous change of social economy and promotes the development of social economy. As for local economy, economic growth should be targeted at private economy, and private economy must encourage entrepreneurship. Along with deepening into entrepreneurship knowledge, problems of entrepreneurship risks and finite resource utilization have gradually emerged. Whether entrepreneurs can grasp and use the integrated resources largely decides if they can triumphantly create opportunities and establish new enterprises or expand new business. One method of resource utilization by entrepreneurs is to exploit and integrate the existing resources. This method is low-risk, but the entrepreneurs have to face resource competition from other entrepreneurs and must conquer the large resource occupation, large productivity and strong marketing ability of large-sized enterprises. Another method is to explore new resources. This method is featured by large investment, high yield and large risks, but avoids competition from other entrepreneurs. Moreover, if it succeeds, the entrepreneurs also have to decide whether to run alone or cooperate with other large-size enterprises. The Britain management expert Elton Penrose pointed out in 1959 the importance of corporate resources to corporate growth and how to utilize corporate resources in the growing strategies. Wernerfel agreed with this view and stated from the perspective of resources rather than products that corporate growth strategy was a balance between “to use the existing resources” and “to develop new resources” [1]. Currently, some active management experts (e.g. Zhang Yuli, Cai Li) stated that entrepreneurs should pay more attention to the use of limited resources into entrepreneurship; though they cannot compete with mature large-size companies for resources, they possess unique creativity and other strategic resources [2,3]. Entrepreneurship researchers have made profound theoretical achievements in resource management and clarified the principles of entrepreneurial resource integration. However, this qualitative method is generalized and does not obey the change of the dynamic market environment, and thus is unable to respond to emergent resource variation. The commonly-used case-study result analysis is non-specific and dependent on the unique properties and personality of entrepreneurs, and thus could not guide so many future entrepreneurs. To depict the dynamic market environment and quantitatively study the variation of entrepreneurial resources, we established a mathematical model of resource distribution, and used the differential game theory to investigate entrepreneurial resource management. We presented the equilibrium strategy between entrepreneurs and mature large-sized enterprises, and thereby precisely and efficiently assessed the resource decision-making, providing some guidance suggestions. Modeling We think that a differential game has two state functions ) ( ), ( t y t x , where ) (t x and ) (t y are the resource conditions of a small-sized enterprise under entrepreneurship and a mature large-sized developing enterprise, respectively. The mature large-sized developing enterprise and the small-sized enterprise under entrepreneurship were the players 1 and 2 of a differential game. In other words, the control function ) ( 1 ) ( 0 ), ( < < t u t u of player 1 means its resource occupying ability; then ) ( 1 t u − is its ability of resource development. ) (t v is the control function of player 2 and means its ability to occupy resources. The dynamic system equation is: