SOLVENCY GAMES NOAM BERGER, NEVIN KAPUR, LEONARD J. SCHULMAN, AND VIJAY V. VAZIRANI Summary: SOLVENCY GAMES NOAM BERGER, NEVIN KAPUR, LEONARD J. SCHULMAN, AND VIJAY V. VAZIRANI Abstract. We study the decision theory of a maximally risk-averse investor -- one whose objec- tive, in the face of stochastic uncertainties, is to minimize the probability of ever going broke. With a view to developing the mathematical basics of such a theory, we start with a very simple model and obtain the following results: a characterization of best play by investors; an explanation of why poor and rich players may have different best strategies; an explanation of why expectation- maximization is not necessarily the best strategy even for rich players. For computation of optimal play, we show how to apply the Value Iteration method, and prove a bound on its convergence rate. 1. Introduction A key concern in computer science and operations research is decision-making under uncertainty. We define a very simple game that helps us study the issue of solvency, or indefinite survival, in the presence of stochastic uncertainties. In Section 1.1 below we provide some motivating reasons for studying this issue. We start by defining the model. A state of the game is an integer, which we call the wealth of the player. An action (representing, say, an investment choice) is a finitely supported probability distribution on the integers; this distribution specifies the probabilities with which various payoffs are received, if this action is chosen. Let w be the wealth of the player at time t. Let A be a set of actions. Suppose that after choosing a particular action from A, the random variable sampled from that action is a. Then at time t + 1 the wealth of the player is w + a. The game terminates Collections: Computer Technologies and Information Sciences