Optimal design of the online auction channel: Analytical, empirical, and computational insights

Decision Sciences, Fall 2002 by Bapna, Ravi, Goes, Paulo, Gupta, Alok, Karuga, Gilbert

Each one of these are compared to the following two scenarios obtained from using the simulation tool:

* The maximum revenue R^sub S^(k^sub SO^) obtained by using the simulation tool to computationally evaluate each feasible bid increment and identify the optimal one (k^sub SO^). This comparison is intended to measure the accuracy of our analytical approach in deriving the optimal revenue.

* The optimal revenue generated by the simulation tool using the corresponding optimal bid increment, RS(k^sub TO^) or RS(k^sub TU^). This comparison test is intended to measure the impact of using the optimal bid increment derived by each theoretical model.

Recalling that the auctioneers' primary interest is in maximizing revenue, we wish to test the accuracy of the analytical model using our simulation tool under two different levels of information intensity (empirical and uniform). Our focus is on the examination of the equivalence of the revenue structures. We do this in a two-stage process beginning first by exploring simple percentage deviations between the theoretical and simulated revenues, followed by a rigorous trace drive simulation validation procedure suggested by Kleijnen et al. (1996, 1998).

Exploratory Data Analysis

Based on the data acquired from real-world auctions as discussed in the previous section, we ran 31 replications for each auction at each of the three revenue cases: Rs(k^sub SO^), RS(k^sub TO^), and RS(k^sub TU^). We used the average of the 31 runs for each of the 65 auctions under each revenue case to compare to the theoretical cases R(k^sub TO^) and R(k^sub TU^). The results for the 65 auctions are presented in Table 5 in terms of the mean percentage deviation from the corresponding simulated case.

The first row indicates that when using real valuations in the theoretical model, we achieve an average deviation of 0.48%lo from the simulation results using the best possible bid increment. This leads us to form an initial belief that given the empirically derived probability p, the theoretically optimal revenue is structurally similar to the simulated maximum revenue.

The theoretically determined optimal bid increment is often different from the bid increment at which the simulated revenue is maximized. Therefore, another issue worth exploring is whether the simulated revenue at the theoretically optimal bid increment is significantly lower than the estimated theoretical revenue. In row two of Table 5 we observe that while applying the theoretically derived bid increment in the simulation, the deviation is 0.47%. This result further adds a measure of robustness to our initial belief that the analytically determined bid increment is the one that maximizes the auctioneers' revenue. Both rows 1 and 2 of Table 5 were examined under the high information intensity case when the auctioneer had empirical distributions of consumer's valuations.

However, in many instances an auctioneer may have a more limited set ot information regarding the consumer valuations. For example, an auctioneer may only have estimates of lower and upper bounds on expected prices that consumers might be willing to pay. Based on our findings of the previous section, the revenue comparisons in rows 3 and 4 of Table 5 are conducted using a uniform distribution for the consumer valuations. It is clear that with lower information intensity, as compared to the empirical knowledge case, the accuracy of the theoretical model is not as high as the mean percentage deviation increases to 5.85%, but is still within a very reasonable range.