Repeated Gambles, Learning, and Risk Aversion

We analyze a decision problem with repeated gambles and find that under some seemingly reasonable risk-averse utility functions, recommended behavior for the initial decision can be highly risk-taking and counterintuitive. Further analysis reveals that the derived utility function for the return on the first gamble is discontinuous because gains or losses carry with them positive or negative signals regarding future prospects. A variant of the basic model without a discontinuity in derived utility has essentially the same implications. The issues raised in this paper present no conceptual difficulties for the standard expected utility theory; in principle, we can model the grand world and understand fully all implications of grand-world utility functions. In practice, however, this ideal may not always be attainable and as a result we may be faced with serious modeling and assessment problems.