Explanation of increasing wealth gap from microeconomics prospective

This explanation of increasing wealth gap from microeconomics prospective comes from the work of Marina Halac, Ilan Kremer and Eyal Winter, 'Raising Capital from Heterogeneous Investors'. Suppose a company requires a certain amount of money to start its project (assume as long as the money is sufficient, the project will succeed) and there are two investors available, one is a wealthier investor and the other is a less wealthy investor, but either can pay the project alone. Under such circumstance, the company has to get the money from both investors. To convince the two investors, a company has to ensure one investor's dominant strategy is to invest his or her money, then when having one investor secured, the other investor will follow as he or she knows the project will succeed. Here comes a question which investor the company should pay more in order to guarantee his or her investment. The answer is the wealthier investor, because once the wealthier investor invests, the probability of succeed increases more significantly, so the risk premium paid to the wealthier is actually proportionally lower and the less wealthy investor only gets an ordinary interest rate, since his or her investment is risk-free; overall, the company will pay less comparing with proposing to the less wealthy investor first

This answer is also true when it comes to a larger number of investors problem. The company always proposes to the wealthy investors first, so the wealthy investors get better deals than the less wealthy investors. Under such circumstance, the wealthy investors become wealthier after investment, and the less wealthy investors do not change as they are offered the risk-free interest rate. After several periods of investment, the wealth gap between the wealthier investors and the less wealthy investors will increase over time. This can at least partially explain the increasing wealth gap in the real world.

I find the result is rather brutal that their work could potentially imply investment, this kind of economic activities, naturally make the richer rich, if companies behave rationally.