Investment and operational decisions for start-up companies: a game theory and Markov decision process approach

Thomas W Archibald,Edgar Possani

doi:10.1007/s10479-019-03426-5

Abstract

This paper analyses the contract between an entrepreneur and an investor, using a non-zero sum game in which the entrepreneur is interested in company survival and the investor in maximizing expected net present value. Theoretical results are given and the model’s usefulness is exemplified using simulations. We have observed that both the entrepreneur and the investor are better off under a contract which involves repayments and a share of the start-up company. We also have observed that the entrepreneur will choose riskier actions as the repayments become harder to meet up to a level where the company is no longer able to survive.

Highlights

A start-up company is created when an entrepreneur with an idea for a new product or service is supported by investors who can provide sufficient capital to allow the new venture to become established
This paper analyses the contract between an entrepreneur and an investor, using a non-zero sum game in which the entrepreneur is interested in company survival and the investor in maximizing expected net present value
Investors are seeking a good return on their investment in the company, while some entrepreneurs might be more interested in establishing the company as a viable business to provide sufficient income and a stimulating working environment in the future

Summary

Introduction

A start-up company is created when an entrepreneur with an idea for a new product or service is supported by investors who can provide sufficient capital to allow the new venture to become established. Most models of start-up finance contracts assume that the success or failure of the venture is revealed at a fixed point in time (for example Vergara et al 2016; Fairchild 2011b; Elitzur and Gavious 2003a; Zhong et al 2018) This does not reflect the way in which an entrepreneur may draw on capital reserves to endure a run of poor outcomes or accumulate resources before pursuing a high growth strategy. Elitzur and Gavious (2003b) assume that for as long as the company remains successful, the venture capitalist invests in the stage, pays the entrepreneur an agreed amount in each period and accumulates any surplus value We argue that this implies a high level of investor control which is not the scenario we wish to investigate.

Basic setup

Entrepreneur’s objective

Investor’s objective

Findings

Conclusion