Skill reputation, prospect theory, and regret theory

When a risky decision involves both skill and chance, success or failure provides information about the decision maker’s skill. Using standard models from the principal—agent literature, we show that a concern for skill reputation can help explain the central prediction of prospect theory that people tend to overweight small probabilities and underweight large probabilities. When the odds of success are low, failure is common but of little damage to the person’s reputation since even skilled people are likely to fail. Conversely, when the odds of success are high, failure is rare but far more embarrassing because a person who fails is probably unskilled. Decision makers who are risk averse with respect to their reputations therefore have smaller risk premia for gambles with a low probability of success than for gambles with a high probability of success. If, as in regret theory, the outcome of a gamble is observable even when it is not taken then failure to take a gamble that wins is as embarrassing as taking a gamble that loses. We show that the attraction to low probability gambles is thereby strengthened. These results on probability weighting all depend on the assumption that the average odds of the gamble are known to the observer. If not, then the decision maker is afraid to take low probability gambles and the results are reversed. We find that a rational concern to avoid looking like a “loser” can also induce other behaviors predicted by prospect theory, including “loss aversion” and “framing”. JEL Classification Categories: D81