Learning and Insight

I consider next whether there is any connection between subjects’ apparent propensity to learn in these various games. As discussed in Section 2.2, there is some evidence that behaviour changes throughout both AG and the jury voting games. The regressions in Tables 2.6 and 2.7 provide further support for this, with the coefficient on the round number (weakly) significant in each. In keeping with the previous discussion, the signs

Figure 2.6: Distributions of Net Expected Payoffs by Jury Voting Strategies (a) By HGU Classification

(b) By ICG Classification

Notes: Informative subjects are those who play ˆσ(r) = 1, ˆσ(b) = 0, mixers play ˆσ(r) = 1, ˆσ(b) ∈ (0, 1), pure red subjects play ˆσ(r) = 1, ˆσ(b) = 1, and red errors subjects play ˆσ(r) < 1.

on the coefficients suggest that while overbids become less common over time, the overall expected payoff also decreases. Again, this is because while subjects become less likely to make overbids, those that they do make become worse on average, with the rate of large overbids (bids of at least 90 points) increasing at the expense of smaller

overbids.

I thus measure each subject’s long-term behavioural changes in AG by measuring the increase in each of their mean expected payoffs and overbid rates from the first seven rounds (that is, the first half of the rounds) to the last seven rounds. By averaging behaviour over several rounds, I hope to account somewhat for the high short-term variability of bids discussed above.

To measure each subject’s learning in the jury voting games I take a similar ap-proach, taking the difference of the observed ˆσ(b) between the first and last seven rounds of each of HGU and ICG. To reflect the fact that learning in each of these games appears to carry over to the other, as discussed in Chapter 1, I also compare the first seven rounds of the first of these two treatments that a subject plays to the last seven rounds of the second. Although such measures could be misleading in HGU, in which any ˆσ(b) can be a best response to reasonable beliefs about others’ behaviour, red votes with blue signals remain the best available indicator of sophisticated behaviour.⁸ Table 2.8 shows linear regressions of these changes in AG behaviour - mean expected payoff in Column (a) and overbid rate in Column (b) - on the above changes in jury voting behaviour. Within-treatment changes in ˆσ(b) do not appear to impact learning in AG, but the change in ˆσ(b) across the two treatments together does. In particular, more learning across HGU and ICG combined - as measured by a higher increase in ˆ

σ(b) from the first seven rounds of the first of these treatments to the last seven rounds of the second - results in a greater decrease (or lower increase) in the rate of overbids from the first seven rounds of AG to the last seven.

It is also worth noting that the overbid rate increases more for subjects that play AG before the jury voting games. Said another way, the overbid rate increases less (or decreases more) amongst those who have already played the jury voting games. It is not

8Moreover, Chapter 1 presents evidence that in HGU informative voting, in which only σ(b) = 0 is rational, is generally a result of naivety rather than sophistication and appropriate beliefs.

clear, however, whether this effect is due to experience playing the jury voting games in particular, which would suggest a link between the games, or if it is simply due to playing at the end of an experimental session rather than the beginning. Equivalent regressions presented in Chapter 1 show that behaviour in the jury voting games is unaffected by whether or not subjects have first played AG.

Table 2.8: Regressions of AG learning on changes in jury voting behaviour.

Variable ∆E[Payoff] ∆ Overbid Rate

Notes: In all regressions standard errors are clustered by subject and p-values are presented below the estimates.

The question arises, then, as to whether any changes in jury voting behaviour carry over to AG, as they presumably would if they were driven by insights relevant to both games. In particular, if that which is learned in the jury voting games is applicable to AG then we would expect those who learn more in the former to then perform better in the latter when playing it afterwards. Table 2.9 thus restricts to those who play the jury voting games before AG and regresses the two measures of overall AG performance - that is, the levels rather than the changes over time - upon the previous measures of learning in the jury voting games. There is no evidence that learning in the jury voting games carries over, however, as none of the coefficients are significant.

Table 2.9: Regressions of AG behaviour on jury voting behaviour.

Notes: In all regressions standard errors are

clustered by subject and p-values are presented below the estimates.

2.4 Conclusions

It is often assumed that sophistication in jury voting games and resilience to the Win-ner’s Curse are related, due to both relying on the ability to condition on, and extract information from, hypothetical events. The experiment presented here shows little ev-idence for this, however. While those who deviate from informative voting in jury voting games in irrational ways tend to do worse in AG - overbidding more and achiev-ing lower expected payoffs - there is no difference for those who deviate in ways that suggest hypothetical thinking, whether measured directly by raw strategy values or by categorization of subjects.

There is some evidence that those whose behaviour changes more in the jury voting games also improve more in AG, but it is not clear whether this is due to developing insights into hypothetical thinking, or to simply due to a more ready response to gains and losses. Regardless, those who learn more in the jury voting games do not appear to then play better in AG, suggesting that this learning does not translate between games.

Thus while the games are clearly bound in theory by the potential for inference

from hypothetical events, there remains no evidence of a relationship in practice.

Chapter 3

Stochastic Choice in Games: an