### Table 3: Price Discrimination in

2004

"... In PAGE 33: ... We report the evidence on price-discrimination for our sample briefly here. Table3 presents some very limited data for our sample of 30 econometric software packages. Of the 30, 5 are distributed freely and a further 8 are distributed as services, possibly bundled with consulting (such sales are essentially all commercial); this is the added value business model discussed earlier.... ..."

### Table 3. Test of Direct Price Discrimination, By Market Structure of Insurance Sector

2007

"... In PAGE 16: ... However, there is no obvious reason why firms with high profits would increase benefits the most in sites served by a small number of carriers. Table3 illustrates that the positive coefficient estimates in Table 2 are driven entirely by markets with 8 or fewer carriers. In general, the magnitudes decline as the number of carriers increases.... In PAGE 17: ... To the extent the costs of SI plans are an appropriate counterfactual for FI plans, these findings suggest the main results underestimate the extent of price discriminaton. 12 I obtain this estimate using the average of the relevant coefficients in the specification with plan fixed effects (column 3, Table3... ..."

### Table 6. Test of Direct Price Discrimination, By Market Structure of Insur Sector and Ownership Type of Insurer

2007

"... In PAGE 22: ...ccount for 99.5 perent of enrollees in the LEHID-FI sample. Disaggregated to the plan-year level, there are 49,915 plan-year observations with ownership status, 59 percent of which are for-profit. Table6 presents the results from estimating specification (2) of the price discrimination test separately for for-profit and nonprofit plans. I present only the two most stringent specifications: columns (1) and (3) include plan fixed effects; columns (2) and (4) add market-year effects as well.... ..."

### Table 2 Progol and HR results for 818 algebraic discrimination problems

"... In PAGE 34: ... In order to determine the extra-logical settings for Progol, we experimented until it could solve the problem of discriminating between two groups of size 6, one of which is Abelian and one of which is not (note that this is not one of the 818 discrimination problems in the main experiments). The settings determined in this manner were as follows: :- set(nodes,2000)? :- set(inflate,800)? :- set(c,2)? :- set(h,100000)? :- set(r,100000)? The results from these experiments are given in Table2 . For an initial application, the results are very promising: Progol solved 558 of the 818 discrimination problems (68%) compared to HR which achieved 96%.... ..."

### Table 2 Progol and HR results for 818 algebraic discrimination problems

"... In PAGE 34: ... In order to determine the extra-logical settings for Progol, we experimented until it could solve the problem of discriminating between two groups of size 6, one of which is Abelian and one of which is not (note that this is not one of the 818 discrimination problems in the main experiments). The settings determined in this manner were as follows: :- set(nodes,2000)? :- set(inflate,800)? :- set(c,2)? :- set(h,100000)? :- set(r,100000)? The results from these experiments are given in Table2 . For an initial application, the results are very promising: Progol solved 558 of the 818 discrimination problems (68%) compared to HR which achieved 96%.... ..."

### Table 4 Number of solved pricing problems.

2004

"... In PAGE 25: ...ave been solved to proven optimality. The run-time is 160.68s on average, which is the fastest of our four B amp;P variants. In Table4 , the total number of pricing problems solved in each class and their sums are given for the B amp;P approaches. Furthermore, the bar charts shown in Fig.... In PAGE 29: ...Table4 we can observe that when using FFBC only (BPNoR) the number of solved pricing problems is lower than the one of BP where CPLEX(restricted 3-stage 2DKP) is used. Pricing using a more sophisticated heuristic, in this case exactly solving restricted 3-stage 2DKP, can therefore improve the overall results, see also Table 3.... In PAGE 29: ... These pricing problems can be denoted as easy ones. Looking at absolute numbers shows that CPLEX(restricted 3-stage 2DKP) successfully solved 21 500 pricing problems, which approximately corresponds to the increase of solved pricing problems when comparing BPNoR to BP in Table4 . The bar charts showing the relative success rates of the pric- ing algorithms indicate that the absolute number of easy pricing problems roughly remained the same.... ..."

Cited by 3

### Table 4 Number of solved pricing problems.

2004

"... In PAGE 28: ...nstances have been solved to proven optimality. The run-time is 160.68s on average, which is the fastest of our four B amp;P variants. In Table4 , the total number of pricing problems solved in each class as well as their sums are given for the B amp;P approaches. Furthermore, the bar charts shown in Fig.... In PAGE 28: ...lass. The origin of the charts were shifted to 0.5 because for almost all the variants, the greedy FFBC algorithm solved more than half of the pricing problems. In Table4 , we can observe that, when using FFBC only (BPNoR), the number of solved pricing problems is lower than the one of BP where CPLEX(restricted 3-stage 2DKP) is used. Pricing using a more sophisticated heuristic, in this case exactly solving restricted 3-stage 2DKP, can therefore improve the overall results, see also Table 3.... In PAGE 30: ... These pricing problems can be denoted as easy ones. Looking at absolute numbers shows that CPLEX(restricted 3-stage 2DKP) successfully solved 21 500 pricing problems, which approximately corresponds to the increase of solved pricing problems when BPNoR is compared to BP in Table4 . The bar charts showing the relative success rates of the pric- ing algorithms indicate that the absolute number of easy pricing problems roughly remained the same.... ..."

Cited by 3

### Table 1: CPU time for solving the pricing problem

"... In PAGE 22: ...8 0.9 1 Retailer W/H Figure 1: Warehouse-Retailer Locations Table1 presents the relation between the average CPU time needed (over 20 different instances) and the number of retailers in the problem. Figure 2 is plotted using the data in Table 1.... In PAGE 22: ...9 1 Retailer W/H Figure 1: Warehouse-Retailer Locations Table 1 presents the relation between the average CPU time needed (over 20 different instances) and the number of retailers in the problem. Figure 2 is plotted using the data in Table1 . Indeed for large retailers set, the submodular function minimization problem can be solved almost instantaneously, using only several seconds (CPU time) to solve a problem involving up to 200 retailers.... ..."

### Table 2: Performance of AC-Discrimination Nets

"... In PAGE 15: ...36 0.94 Table 1: Timings for some Non-AC Problems Using Standard Net and AC-Net In Table2 , timings for several AC-problems are presented, and in particular for the AC-benchmark problems described earlier. We compare the performance of our AC-discrimination nets (under columns labelled by ACN in the table) with two normalization strategies, Na-I and Na-II6.... ..."