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This study first replicates, then perturbs, the centipede game as implemented by McKelvey and Palfrey (1992). It is thus both a replication study and an original research study. We use controlled laboratory experiments, with computer interfaces for each treatment, anonymous round-robin matching among the subjects across rounds, multiple (10) rounds within each treatment, and incremental changes between adjacent treatments allowing for an assessment of effects at the margin of different game configurations. We find unraveling to the subgame perfect equilibrium somewhat faster than did McKelvey and Palfrey (1992), when using their exact design. Perturbations to that design show that setting non-taker payoffs to zero induces earlier unraveling, as does the use of higher stakes (as in Murphy, Rapoport, and Parco (2006), and Rapoport, Stein, Parco, and Nicholas (2003), respectively). Other, subsequent perturbations show: that there is at most a subtle effect associated with using a 10-second timer with a default move, relative to untimed active moves; and that clock format versus tree format has a minimal effect in common information, unchanging payoff-parameterization environments. We verify the robustness of some key past findings in real-time games. We also explore in a common information environment, the effect of design features previously used in independent private values settings; here we find new evidence that features which might modulate information acquisition and/or processing in an independent private values setting may not restrict behavior in a common information setting.

Much of the literature on theories of decision making under risk has emphasized differences between theories. One enduring theme has been the attempt to develop a distinction between “normative” and “descriptive” theories of choice. Bernoulli (1738) introduced log utility because expected value theory was alleged to have descriptively incorrect predictions for behavior in St. Petersburg games. Much later, Kahneman and Tversky (1979) introduced prospect theory because of the alleged descriptive failure of expected utility (EU) theory (von Neumann & Morgenstern, 1947).

Attitudes to risk play a central role in economics. Policy makers should know them in order to judge the certainty equivalent of the effects of policy on individuals. What might look like a policy improvement when judged by the average impact could easily entail a welfare loss for risk averse individuals if the variance of expected impacts is wide compared to the alternatives.

We review the experimental evidence on risk aversion in controlled laboratory settings. We review the strengths and weaknesses of alternative elicitation procedures, the strengths and weaknesses of alternative estimation procedures, and finally the effect of controlling for risk attitudes on inferences in experiments.

Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

Measuring risk aversion is sensitive to assumptions about the wealth in subjects’ utility functions. Data from the same subjects in low- and high-stake lottery decisions allow estimating the wealth in a pre-specified one-parameter utility function simultaneously with risk aversion. This paper first shows how wealth estimates can be identified assuming constant relative risk aversion (CRRA). Using the data from a recent experiment by Holt and Laury (2002a), it is shown that most subjects’ behavior is consistent with CRRA at some wealth level. However, for realistic wealth levels most subjects’ behavior implies a decreasing relative risk aversion. An alternative explanation is that subjects do not fully integrate their wealth with income from the experiment. Within-subject data do not allow discriminating between the two hypotheses. Using between-subject data, maximum-likelihood estimates of a hybrid utility function indicate that aggregate behavior can be described by expected utility from income rather than expected utility from final wealth and partial relative risk aversion is increasing in the scale of payoffs.