A Utility Function Derived from a Survival Game

摘要

A simple problem is solved of economic survival, closely related to the classical problem of the gambler's ruin. It is shown that the solution to this problem can be interpreted as a utility function in the sense of Von Neumann and Morgenstern. This means that the solution to the dynamic problem automatically gives one the solution to a class of static problems of decision making under uncertainty. The starting point of the paper is a firm engaged in a risky business. The policy which will maximize the expected discounted value of the dividends which the firm can pay before it goes bankrupt. It is then shown that the solution of the dividend problem gives a utility function which governs the firm's decisions under uncertainty. From this it appears that a number of decisions which seem irrational when studied in isolation become perfectly rational when seen in their proper dynamic setting.