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A Game Theoretic Approach to the Selection, Mentorship, and Investment Decisions of Start-Up Accelerators

Start-up accelerators have attracted increasing attention from start-ups in recent years. However, little is known about how they interact with start-ups and investors, how they prioritize a wide variety of their services, and how macro-level factors affect their performance. We use a game-theoretic approach to study mutual effects between an accelerator, a venture capitalist (VC), and start-ups. In the model, the accelerator selects start-ups and invests in them. During its program, it provides intensive mentorship for the selected start-ups and screens them to determine whether or not they are successful. Finally, it introduces successful start-ups to the VC to obtain financing for their ideas. Our results indicate that 1) the most vital role of an accelerator is its screening services. 2) Given limited resources of accelerators, prioritizing their services is the key to their efficacy. Screening, mentorship, and seed investment services possess the first, second, and third priorities, respectively. 3) Although accelerators are anywhere beneficial, macro-level heterogeneity of entrepreneurial ecosystems is associated to their efficacy. Their efficacy is higher (lower) in less (more) developed regions. 4) Institutional reforms targeting mentoring or entrepreneurial communities are unexpectedly detrimental to the efficacy of accelerators, while they may enhance start-ups’ equilibrium willingness to participate.