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We take a differential game approach to study the optimal choices of managerial firms concerning efforts in product a process innovation. We find the Nash equilibria under the open-loop and closed-loop information structure, and we compare the steady state allocations with the corresponding equilibria of markets populated by standard profit-maximising firms. We find that the managerial incentive leads firm to underinvest in product differentiation and to overinvest in process innovation, as compared to standard profit-maximising firms.

Since joining Bennett College in 2008, Dr. Oh has directed 17 undergraduate students’ research projects in applied mathematics. The National Science Foundation (NSF) awarded Dr. Oh grants from the Historically Black Colleges and Universities – Undergraduate Program (HBCU-UP). The grants allowed her to mentor eight mathematics majors/minors in summer research for four years (2009–2012). Based on the four years of successful undergraduate research (UGR) experiences, she, together with Dr. Jan Rychtar from the University of North Carolina at Greensboro (UNCG), received funding for two summers National Research Experience for Undergraduates (NREUP), an activity of Mathematical Association of America (MAA), funded by the NSF in 2013 and 2014. During the six years of funded UGR, Bennett students made 33 presentations at regional, state, and national conferences; two teams won the outstanding student presentation award and first place for presentation. Three papers were published; two of them by Dr. Oh and one of them with a UGR coauthor. Three projects resulted in manuscripts. As a result of the UGR experiences in 2015, Dr. Oh received three more grants: the MAA NREUP, the NSF’s Center for Undergraduate Research in Mathematics (CURM), and the NSF’s Preparation for Industrial Careers in Mathematical Sciences (PIC Math) program awarded grants. A grant was also submitted to HBC-UP-Targeted Infusion Projects: Computational Mathematics at Bennett College.

Overall, the six years of UGR at Bennett College attained the three goals of: (1) enhancing the quality of undergraduate STEM education and research for a deeper appreciation in those disciplines; (2) supporting increased graduation rates in STEM undergraduate education of females; and (3) broadening participation in the nation’s STEM workforce as well as enrollments in graduate schools.

The objective of this chapter is to discuss how different techniques in Regional Science and Peace Science and the emerging techniques in Management Science can be used in analysing Disaster Management and Global pandemic with special reference to developing countries. It is necessary for me to first discuss the subjects of Disaster Management, Regional Science, Peace Science and Management Science. The objective of this chapter is to emphasise that the studies of Disaster Management should be more integrated with socioeconomic and geographical factors. The greatest disaster facing the world is the possibility of war, particularly nuclear war, and the preparation of the means of destruction through military spending.

In today's world, all firms’ corporate social responsibility (CSR) actions are coming under increasing public scrutiny. This is especially true for large companies whose decisions can and do have impact on society. Public service advertisements (PSAs), a mass-media approach, are advertisements which inform audiences of a firm's CSR actions and enhance its public image. In this chapter, we focus on a supply chain system consisting of two firms and their coordination strategy for public service advertising. To describe the synergistic effect between a PSA and a normal commercial advertisement, a modified Nerlove–Arrow model is employed in this chapter. Using differential game theory, we calculate and compare the optimal advertising levels for each stage of the supply chain system under two different decision scenarios, i.e., (i) the two firms make decisions independently and (ii) the two firms make decisions as an integral system. A coordination mechanism on the public service advertising between the two firms has also been proposed for the supply chain system and has been proved effective.

This chapter develops a growth model of a country under a Hobbesian environment with international conflicts in which national defense is the only way to prevent external predation. The long run growth path is determined by the equilibrium of a dynamic game with three players: the external predator, the government, and the family. The equilibrium growth path has three phases: submissive equilibrium, tolerant equilibrium, and full-protected equilibrium. Different defense strategies result in different growth prospects, and sustainable growth will endogenously induce adjustment of defense strategies.