Results: Order Behavior

Low profit and small groups

We first analyze the results from the small group (M = 4), low profit condition (w = 9) which entails four treatments (τ = 3 vs. τ = 9 plus a within-subject newsvendor control treatment each). The descriptive statistics are given in Figure 6.2.3 with the results from significance tests being provided separatedly in Table 6.2.²⁸

We observe average order quantities in both newsvendor treatments to be significantly above the theoretical prediction for the standard newsvendor, q_nv^∗ .

27The symmetric equilibrium order quantities q_i^∗(Q^∗₋₁) were calculated numerically (see Appendix A.2.3).

28Throughout this section we use non-parametric tests (Siegel 1956): Wilcoxon for one-sample and related-one-sample tests, Mann-Whitney-U for independent-one-sample tests. The tests for the secondary market treatments are based on group averages. As in previous chapters, we let “ˆ” denote empirically observed quantities.

(a) Average order quantities (b) Average profits

(c) Order quantities over time

Figure 6.1: Order quantities and profits for w = 9 and M = 4

Moreover, we observe that average orders in the presence of the secondary mar-ket are significantly above the theoretical predictions (but below µ) for both τ = 3 and τ = 9. These findings are in line with the mean anchoring behav-ior consistently observed in newsvendor experiments. We now check whether subjects in the secondary market treatments converge towards the equilibrium prediction. Fitting a simple trend line (Figure 6.1(c)) reveals this is indeed the case for the low transfer price treatment (standardized β = −0.548, p < 0.001) but subjects in the high transfer price treatments failed to adjust their ini-tially high orders towards the equilibrium prediction q^∗_sm = 141 (standardized β = −0.078, p = 0.632). A direct comparison of order behavior under the two different transfer prices shows significantly higher average order quantities un-der τ = 9, in line with what theory predicts. This suggests some sensitivity of order quantities with respect to the transfer price τ . However, this finding is somewhat convoluted by the fact that average order quantities are already sig-nificantly higher under τ = 9 even without the option to trade in the secondary market.

Even though subjects on average do not significantly change their behavior after the introduction of the secondary market, they increases average profits ¯π significantly (383 vs. 310 for τ = 3, 383 vs. 318 for τ = 9). It is worthwhile to note that the increased performance has to be attributed solely to the option to trade excess inventories, and not by the potential of the secondary market

τ = 3 τ = 9

to change initial stocking decisions. To appreciate this finding, we compute the hypothetical average profits (for the demand realizations d implemented in the experiment) had all subjects consistently ordered the optimal newsvendor quantity q^∗_nv= 125, i.e. ¯π(q^∗_nv, d). Interestingly, this benchmark is 373 for both τ = 3 and τ = 9, which corresponds to approximately 97% of average profits captured by the participants in the secondary market treatments.

Medium profit and small groups

We now turn to the medium-profit case with w = 6 (Figure 6.2 and Table 6.3).

We find little evidence for anchoring behavior which was to be expected since the medium-profit condition effectively controls for this bias. For the low transfer price condition, the secondary market affects average orders as theory predicts.

We find average period-by-period orders to move slowly downward over time (standardized β = −0.244), but this trend is not significant (p = 0.129), which is reassuring since initial orders are already reasonably close to the equilibrium prediction q_sm^∗ = 141. For the high transfer price condition, average orders fall short of the equilibrium prediction, but a simple linear trend line reveals that subjects, initially anchoring around the mean, slowly converge towards q^∗_sm = 157 (standardized β = 0.293, p = 0.067). Overall, subjects seem to respond qualitatively correct to the incentives set by the transfer price. This is supported by a direct comparison between the order quantities under τ = 3 and τ = 9, showing that subjects order significantly more under the latter. Lastly, we check how order behavior translates into profits. The option to trade excess inventories in the secondary market increases average profits significantly (803 vs. 729 for τ = 3, 812 vs. 735 for τ = 9). Interestingly, average realized profits seem to be higher under τ = 9, where average orders deviate from the theoretical prediction, than under τ = 3 (812 vs. 803), but the difference is not significant (p = 0.142).

Medium profit and large groups

In order to investigate the impact of group size on ordering and trading behavior, our last subset of treatments was carried out in the medium-profit condition with a larger group size of M = 10. As to the ordering behavior, discussed in this section, we observe qualitatively similar effects as in the small group condition (Figure 6.3). First, the order quantities from the newsvendor control treatment are not significantly different from q_nv^∗ = µ (Figure 6.3). For the low transfer price τ = 3, our data shows ordering behavior that is consistent with the theoretical prediction. As predicted, subjects order significantly less

(a) Average order quantities (b) Average profits

(c) Order quantities over time

Figure 6.2: Order quantities and profits for w = 6 and M = 4

than in the absence of the excess inventory market (p = 0.068) and, on average, not significantly different from the equilibrium prediction q_sm^∗ = 141. While anchoring in initial rounds, a simple linear regression shows that orders move downward over time (standardized β = −0.823, p < 0.001), and appear to remain relatively stable over the last 10 periods. With a high transfer price τ = 9, average order quantities are slightly and insignificantly higher in the presence of the secondary market, relative to newsvendor orders without the option to trade. Nevertheless, they fall short of the equilibrium prediction q_sm^∗ = 159 (p = 0.043), although exhibiting a significant upward trend (standardized β = 0.299, p = 0.061). A direct comparison between the two treatments shows that average orders increase in the transfer price τ (p = 0.021). Lastly, we check how order behavior translates into profits. The option to trade excess inventories in the secondary market increases average profits significantly (821 vs. 745 for τ = 3, 837 vs. 745 for τ = 9). Average realized profits are significantly lower (p = 0.083) under τ = 3 than under τ = 9 (812 vs 803). Although average orders in the latter case deviate from the theoretical prediction, it is interesting to note that these deviations entail higher system efficiency. Average profits from the orders with τ = 9 are not statistically significantly different from the hypothetical benchmark of a central planner which, given the implemented demand realizations, would have reaped an average profit of 856 (p = 0.118).

Comparing the treatments with M = 4 and M = 10, we can analyze the

τ = 3 τ = 9

impact of market size on the efficiency of the secondary market as well as on initial order quantities (Table 6.4). Under the low transfer price, the average order quantity ˆq^{M =4}_sm , 141, is not statistically significantly different from the average order quantity ˆq^{M =10}_sm = 142 (p = 0.564). Under the high transfer price, the average order quantity ˆq_sm^{M =4}= 152, is not statistically significantly different from the average order quantity ˆq^{M =10}_sm = 153 (p = 0.462). This is consistent with the theoretical equilibria which predict only a minor impact of the number of players on initial order quantities. However, since finding demand (supply) for a leftover (shortage) unit is more likely when the secondary market is large, we hypothesize that average profits increase as we move from M = 4 to M = 10.

Theoretically, players in large groups should on average earn 836 (836) when τ = 3 (9) while players in small groups have to settle for 821 (821). This is replicated in our data. For τ = 3 (9), participants in larger groups earn on average 821 (837), which is significantly higher than the average profit in small groups, which is 803 (812).

We now analyze bidding behavior in the secondary market in more detail. We capture buyers’ (sellers’) aggregate bidding behavior in excess supply markets (where O > U ) by bO =P

bi/U (sO =P

si/O). Equivalently, for excess de-mand markets (where U > O), we define bU =P

bi/U (sU =P si/O).

Low profit and small groups

Figure 6.4 summarizes the aggregate secondary market bidding behavior for the treatments with w = 9 and M = 4. Comparing first buyers’ bidding quantities with their actual shortage position shows a consistent bid inflation (significant