Allocating resources across time in a cumulative allocation game

Abstract

We investigate an alternative to decision under risk where players begin with an endowment of wealth, and their goal is to increase this wealth as rapidly as possible by repeatedly investing part of it. In such a Cumulative Allocation Game (CAG), expected wealth can grow exponentially but - if wealth ever goes to zero - the game is over and the participant wins nothing (ruin). CAGs can be used to model a wide range of biological and economic activity from casino gambling to animal foraging to stock market investment (Kelly Criterion). However, there is little previous research concerning human performance in CAGs and how it relates to human performance in similar decision-under-risk tasks. In two experiments we asked participants to complete four CAGs designed to allow us to test a series of hypotheses about human performance and compare it to normative play maximizing their log rate of growth. In the main experimental conditions, participants performance was initially close to normative but their proportion bet decreased by almost a factor of two over the course of the experiment. This reduction in proportion-bet decreased their expected rate of growth by roughly 25% - a substantial deviation from optimal. Why would participants systematically abandon a normative strategy? We conjecture that a possible reason is loss aversion, well documented in decision under risk. We conjecture that while loss aversion in decision under risk is sub-optimal, there is an intrinsic asymmetry between losses and gains in CAGs that could explain the loss aversion we observe.