Narrow Results

One of the missions of the cognitive process of animals, including humans, is to make reasonable judgments and decisions in the presence of uncertainty. The balance between exploration and exploitation investigated in the reinforcement-learning paradigm is one of the key factors in this process. Recently, following the pioneering work in behavioral economics, growing attention has been directed to human behaviors exhibiting deviations from the simple maximization of external reward. Here we study the dynamics of betting behavior in a simple game, where the probability of reward and the magnitude of reward are designed to give a "zero" expected net reward ("flat reward condition"). No matter how the subject behaves, there is on average no change in one's resources, and therefore every possible sequence of action has the same value. Even in such a situation, the subjects are found to behave not in a random manner, but in ways showing characteristic tendencies, reflecting the dynamics of brain's reward system. Our results suggest that brain's reward system is characterized by a rich and complex dynamics only loosely coupled with external reward structure.

The impossibility of speculative trade result (Milgrom and Stokey, 1982) provokes the questions why traders care about their private information, if they cannot profit from it and how the aggregate information can then be reflected in REE prices. This paper answers these questions by analyzing a speculative market as a game, which has the advantage of making the equilibrium strategies explicit. We introduce the new equilibrium selection concept of best reply resistance, which singles out those equilibria that remain an equilibrium even if opponent(s) deviate to a best reply. In the unique best reply resistant equilibrium of the two-player game trade at the REE price occurs each time both traders receive contradicting private information.

The central problem for gamblers is to find positive expectation bets. But the gambler also needs to know how to manage his money, i.e., how much to bet. In the stock market (more inclusively, the securities markets) the problem is similar but more complex. The gambler, who is now an “investor”, looks for “excess risk adjusted return”. In both these settings, we explore the use of the Kelly criterion, which is to maximize the expected value of the logarithm of wealth (“maximize expected logarithmic utility”). The criterion is known to economists and financial theorists by names such as the “geometric mean maximizing portfolio strategy”, maximizing logarithmic utility, the growth-optimal strategy, the capital growth criterion, etc. The author initiated the practical application of the Kelly criterion by using it for card counting in blackjack. We will present some useful formulas and methods to answer various natural questions about it that arise in blackjack and other gambling games. Then we illustrate its recent use in a successful casino sports betting system. Finally, we discuss its application to the securities markets where it has helped the author to make a thirty year total of 80 billion dollars worth of “bets”.