Many people believe in the "Law of Small Numbers," exaggerating the degree to which a small sample resembles the population from which it is drawn. To model this, I assume that a person exaggerates the likelihood that a short sequence of i.i.d. signals resembles the long-run rate at which those signals are generated. Such a person believes in the "gambler's fallacy", thinking early draws of one signal increase the odds of next drawing other signals. When uncertain about the rate, the person over-infers from short sequences of signals, and is prone to think the rate is more extreme than it is. When the person makes inferences about the frequency at which rates are generated by different sources -- such as the distribution of talent among financial analysts -- based on few observations from each source, he tends to exaggerate how much variance there is in the rates. Hence, the model predicts that people may pay for financial advice from "experts" whose expertise is entirely illusory. Other economic applications are discussed.

Arrow (1971) shows that an expected-utility maximizer with a differentiable utility function will always want to take a sufficiently small stake in any positive-expected-value bet. That is, expected-utility maximizers are arbitrarily close to risk neutral when stakes are arbitrarily small. While most economists understand this formal limit result, fewer appreciate that the approximate risk-neutrality prediction holds not just for very small stakes, but for quite sizable and economically important stakes. Diminishing marginal utility of wealth is not a plausible explanation of people's aversion to risk on the scale of $10, $100, $1000 or even more. After illustrating and providing intuition for these claims, I shall argue that economists often reach misleading conclusions by invoking expected-utility theory to explain substantial risk aversion in contexts where the theory actually predicts virtual risk neutrality.

Within the expected-utility framework, the only explanation for risk aversion is that the utility function for wealth is concave: A person has lower marginal utility for additional wealth when she is wealthy than when she is poor. This paper provides a theorem showing that expected-utility theory is an utterly implausible explanation for appreciable risk aversion over modest stakes: Within expected-utility theory, for any concave utility function, even very little risk aversion over modest stakes implies an absurd degree of risk aversion over large stakes. Illustrative calibrations are provided.

Experiments with the ultimatum game -- where one party can make a take-it-or-leave-it offer to a second party on how to split a pie -- illustrate that conventional game theory has been wrong in its predictions regarding the simplest of bargaining settings: Even when one party has enormous bargaining power, she may be able to extract all the surplus from trade, because the second party will reject grossly unequal proposals. But ultimatum games may lead us to misconstrue some general lessons: Given plausible assumptions about what preferences underlie ultimatum-game behavior, alternative bargaining structures that also give a Proposer enormous bargaining power may lead to very different outcomes. For virtually any outcome in which the Proposer gets more than half the pie, there exists a bargaining structure yielding that outcome. Notably, many bargaining structures can lead to inefficiency even under complete information. Moreover, inefficiency is partly caused by asymmetric bargaining power, so that "fairer environments" can lead to more efficient outcomes. Results characterize how other features of simple bargaining structures affect the efficiency and distribution of bargaining outcomes, and generate testable hypotheses for simple non-ultimatum bargaining games.

This essay provides a perspective on the trend towards integrating psychology into economics. Some topics are discussed, and arguments are provided for why movement towards greater psychological realism in economics will improve mainstream economics.