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Motivated by Roemer s Kantian equilibrium (John Roemer, 2010, 2015, In Press) we performed some experiments on cooperation in extremely simple treatments (Bosch-Domènech and Silvestre, 2017, and Appendix below). Here we comment on some lessons that we have learned from them, and offer some thoughts on Roemer s theory of cooperation based on social situations that can be easily compared to those in our experiments.

We report on a simple experiment that addresses three factors in the frequency of cooperation: (i) framing, (ii) the number of players and (iii) the perceived risk of cooperating. We work with a (two-player) Prisoner s Dilemma and with a three-player, two-strategy Public Good Game. These themes have been separately studied by a large number of experimental papers, using diverse methodologies. Our experiment targets them in a common, clear-cut framework. We find three strong effects (a) Framing; (b) The number of players (there is less cooperation in the three-person games that in the two-person ones); (c) The neutralization of risk (about 50% of participants cooperate when risk is neutralized). Both (a) and (c) go in the expected direction but, in all three cases, the strength of the effect is surprising.

The Cognitive Reflection Test (CRT) is a test introduced by S. Frederick (2005) Cognitive reflection and decision making, J Econ Perspect 19(4): 25-42. The task is designed to measure the tendency to override an intuitive response that is incorrect and to engage in further reflection that leads to the correct response. The consistent sex differences in CRT performance may suggest a role for gonadal hormones, particularly testosterone. A now widely studied putative marker for fetal testosterone is the second-to-fourth digit ratio (2D:4D). This paper tests to what extent 2D:4D, as a proxy for prenatal exposure to testosterone, can predict CRT scores in a sample of 623 students. After controlling for sex, we observe that a lower 2D:4D (reflecting a higher exposure to testosterone) is significantly associated with a higher number of correct answers. The result holds for both hands 2D:4Ds. In addition, the effect appears to be sharper for females than for males. We also control for patience and math proficiency, which are significantly related to performance in the CRT. But the effect of 2D:4D on performance in CRT is not reduced with these controls, implying that these variables are not mediating the relationship between digit ratio and CRT.

The Cognitive Reflection Test (CRT) is a test introduced by S. Frederick (2005) Cognitive reflection and decision making, J Econ Perspect 19(4): 25-42. The task is designed to measure the tendency to override an intuitive response that is incorrect and to engage in further reflection that leads to the correct response. The consistent sex differences in CRT performance may suggest a role for gonadal hormones, particularly testosterone. A now widely studied putative marker for fetal testosterone is the second-to-fourth digit ratio (2D:4D). This paper tests to what extent 2D:4D, as a proxy for prenatal exposure to testosterone, can predict CRT scores in a sample of 623 students. After controlling for sex, we observe that a lower 2D:4D (reflecting a higher exposure to testosterone) is significantly associated with a higher number of correct answers. The result holds for both hands 2D:4Ds. In addition, the effect appears to be sharper for females than for males. We also control for patience and math proficiency, which are significantly related to performance in the CRT. But the effect of 2D:4D on performance in CRT is not reduced with these controls, implying that these variables are not mediating the relationship between digit ratio and CRT.

Various experimental procedures aimed at measuring individual risk aversion involve a list of pairs of alternative prospects. We first study the widely used method by Holt and Laury (2002), for which we find that the removal of some items from the lists yields a systematic decrease in risk aversion and scrambles the ranking of individuals by risk aversion. This bias, that we call embedding bias, is quite distinct from other confounds that have been previously observed in the use of the Holt and Laury method. It may be related to empirical phenomena and theoretical developments where better prospects increase risk aversion. Nevertheless, we also find that the more recent elicitation method due to Abdellaoui et al. (2011), also based on lists but using only one and the same probability in the list, does not display any statistically significant bias when the corresponding items of the list are removed. Our results suggest that methods other than the popular Holt and Laury one may be preferable for the measurement of risk aversion.

Considering a pure coordination game with a large number of equivalent equilibria, we argue, first, that a focal point that is itself not a Nash equilibrium and is Pareto dominated by all Nash equilibria, may attract the players' choices. Second, we argue that such a non-equilibrium focal point may act as an equilibrium selection device that the players use to coordinate on a closely related small subset of Nash equilibria. We present theoretical as well as experimental support for these two new roles of focal points as coordination devices.

We experimentally question the assertion of Prospect Theory that people display risk attraction in choices involving high-probability losses. Indeed, our experimental participants tend to avoid fair risks for large (up to 90), high-probability (80%) losses. Our research hinges on a novel experimental method designed to alleviate the house-money bias that pervades experiments with real (not hypothetical) loses. Our results vindicate Daniel Bernoulli s view that risk aversion is the dominant attitude, But, contrary to the Bernoulli-inspired canonical expected utility theory, we do find frequent risk attraction for small amounts of money at stake. In any event, we attempt neither to test expected utility versus nonexpected utility theories, nor to contribute to the important literature that estimates value and weighting functions. The question that we ask is more basic, namely: do people display risk aversion when facing large losses, or large gains? And, at the risk of oversimplifying, our answer is yes.

We test whether risk attitudes change when losses instead of gains are involved. The study of gain-loss asymmetries has been largely confined to reflected choices, where all the money amounts of a positive prospect are multiplied by minus one. We define the decomposition reflection = translation + probability switch, and experimentally find both a translation effect (risk attraction becomes more frequent when gains are translated into losses) and a probability switch effect (risk attraction becomes more frequent when the probability of the best outcome decreases). Surprisingly, the switch effect is somewhat stronger than the translation effect, negating a conventional reflection effect when one starts with choices between gains with a low probability of the best outcome. We conclude by arguing that, while both the translation effect and the switch effect contradict the expected utility hypothesis, the translation effect implies a deeper violation of standard preference theory.

"Beauty-contest" is a game in which participants have to choose, typically, a number in [0,100], the winner being the person whose number is closest to a proportion of the average of all chosen numbers. We describe and analyze Beauty-contest experiments run in newspapers in UK, Spain, and Germany and find stable patterns of behavior across them, despite the uncontrollability of these experiments. These results are then compared with lab experiments involving undergraduates and game theorists as subjects, in what must be one of the largest empirical corroborations of interactive behavior ever tried. We claim that all observed behavior, across a wide variety of treatments and subject pools, can be interpreted as iterative reasoning. Level-1 reasoning, Level-2 reasoning and Level-3 reasoning are commonly observed in all the samples, while the equilibrium choice (Level-Maximum reasoning) is only prominently chosen by newspaper readers and theorists. The results show the empirical power of experiments run with large subject-pools, and open the door for more experimental work performed on the rich platform offered by newspapers and magazines.

Our work attempts to investigate the influence of credit tightness or expansion on activity and prices in a multimarket set-up. We report on some doubleauction, two-market experiments where subjects had to satisfy an inequality involving the use of credit. The experiments display two regimes. characterized by high and low credit availability. The critical vakre of credit at the common boundary of the two regimes has a compelling interpretation as the maximal credit use at the Arrow-Debreu equilibrium of the abstract economy naturally associated to our experimental environment. Our main results are that changes in the availability of credit: (a): have minor and unsystematic effects on real and nominal variables in the high-credit regime; (b): have substantial effects, both real and nominal, in the low-credit regime.

Does risk attitude (aversion or attraction) vary with the level of the income at risk? About half of our subjects chose to insure all levels, whereas another half chose instead not to insure low levels, but to insure high levels.

This paper introduces a mixture model based on the beta distribution, without preestablishedmeans and variances, to analyze a large set of Beauty-Contest data obtainedfrom diverse groups of experiments (Bosch-Domenech et al. 2002). This model gives a bettert of the experimental data, and more precision to the hypothesis that a large proportionof individuals follow a common pattern of reasoning, described as iterated best reply (degenerate),than mixture models based on the normal distribution. The analysis shows thatthe means of the distributions across the groups of experiments are pretty stable, while theproportions of choices at dierent levels of reasoning vary across groups.

Smith et al. (1988) reported large bubbles and crashes in experimental asset markets, a result that has been replicated by a large literature. Here we test whether the occurrence of bubbles depends on the experimental subjects' cognitive sophistication. In a two-part experiment, we first run a battery of tests to assess the subjects' cognitive sophistication and classify them into low or high levels of cognitive sophistication. We then invite them separately to two asset market experiments populated only by subjects with either low or high cognitive sophistication. We observe classic bubble- crash patterns in the sessions populated by subjects with low levels of cognitive sophistication. Yet, no bubbles or crashes are observed with our sophisticated subjects. This result lends strong support to the view that the usual bubbles and crashes in experimental asset markets are caused by subjects' confusion and, therefore, raises some doubts about the external validity of this type of experiments.

In Selten (1967) Strategy Method, the second mover in the game submits a complete strategy. This basic idea has been exported to nonstrategic experiments, where a participant reports a complete list of contingent decisions, one for each situation or state in a given sequence, out of which one and only one state, randomly selected, will be implemented. In general, the method raises the following concern. If S0 and S1 are two different sequences of states, and state s is in both S0 and S1, would the participant make the same decision in state s when confronted with S0 as when confronted with S1? If not, the experimental results are suspect of suffering from an embedding bias. We check for embedding biases in elicitation methods of Charles Holt and Susan Laury (Laury and Holt, 2000, and Holt and Laury, 2002), and of the present authors (Bosch-Domènech and Silvestre, 1999, 2002, 2006a, b) by appropriately chosen replications of the original experiments. We find no evidence of embedding bias in our work. But in Holt and Laury s method participants tend to switch earlier to the riskier option when later pairs of lotteries are eliminated from the sequence, suggesting the presence of some embedding bias.