### Table 3: Variably dimensioned linear complementarity problems.

"... In PAGE 13: ...60 3.E-16 Table3 : continuation.... In PAGE 14: ...Table3 seem to con rm that using (6) and a box-constrained optimization solver is a reliable approach for solving many LCP apos;s, even when the problem is not monotone. (The matrix M of problem VD2 is positive semide nite, so the problem is monotone, but this is not the case of Problem VD1.... ..."

### Table 1: Comparison of Linearized Complementarity Equations

1995

Cited by 52

### Table 1: Comparison of Linearized Complementarity Equations

1995

Cited by 52

### Table 2: Results for linear complementarity problems

"... In PAGE 12: ... If in the rst iteration the stepsize of one is accepted we use the nomonotone strategy of Algorithm B, otherwise we use algorithm A for the rst ve iterations and then switch to Algorithm B. In all the algorithms the following constants were used: quot; = 1; = 10?4; = 10?8; p = 2:1; = 0:9: We tried the algorithm on several test problems taken from the literature, we considered nonlinear (Table 1) but also linear problems ( Table2 ); the test set includes problems that are not P0 and problems that are not R-regular or b-regular at the solution. Some details on these problems, the starting points, and adequate references are reported in the appendix.... ..."

### Table 7: Monotonicity of linear terms

1994

"... In PAGE 12: ...3 Computing monotonicity of X in r We now give an inductive de nition of the monotonicity of X in r which is used as the basis of an algorithm for checking the monotonicity. We use mutually recursive de nitions ( Table7 and 8) to compute when r is mono- tone, and when r is anti-monotone. The de nitions state which variables occurring in r that must be determined before r is monotone (Mr), and which variables in r which must be determined before r is anti-monotone (Ar).... In PAGE 12: ... Let t be a linear term. The sets St (shrinking) and Gt (growing) are two sets of variables de ned by Table7 . The intuition being that if all variables in St (Gt) are determined (constants), then t takes on decreasing (increasing) values.... ..."

Cited by 24

### Table 7: Monotonicity of linear terms

"... In PAGE 13: ...3 Computing monotonicity of X in r We now give an inductive de nition of the monotonicity of X in r which is used as the basis of an algorithm for checking the monotonicity. We use mutually recursive de nitions ( Table7 and 8) to compute when r is mono- tone, and when r is anti-monotone. The de nitions state which variables occurring in r that must be determined before r is monotone (Mr), and which variables in r which must be determined before r is anti-monotone (Ar).... In PAGE 14: ... Let t be a linear term. The sets St (shrinking) and Gt (growing) are two sets of variables de ned by Table7 . The intuition being that if all variables in St (Gt) are determined (constants), then t takes on decreasing (increasing) values.... ..."

### Table 2: Monotonicity of linear terms

"... In PAGE 15: ...et t be a linear term, e.g. a sum composed of linear products, and (x) be a function such that (n) = ;, where n is a number, and (v) = fvg, where v is a variable. In Table2 two sets of variables, St and Gt, are de ned such that if all variables in St (Gt) are determined in , then t t 0 (t t 0) for any 0 such that v 0.... ..."

### Table 1: Results for nonlinear complementarity problems

"... In PAGE 12: ... If in the rst iteration the stepsize of one is accepted we use the nomonotone strategy of Algorithm B, otherwise we use algorithm A for the rst ve iterations and then switch to Algorithm B. In all the algorithms the following constants were used: quot; = 1; = 10?4; = 10?8; p = 2:1; = 0:9: We tried the algorithm on several test problems taken from the literature, we considered nonlinear ( Table1 ) but also linear problems (Table 2); the test set includes problems that are not P0 and problems that are not R-regular or b-regular at the solution. Some details on these problems, the starting points, and adequate references are reported in the appendix.... In PAGE 15: ... This problem has two solutions: x1 = (0:5p6; 0; 0; 0:5) and x2 = (1; 0; 3; 0); x1 fails to be R-regular and is degenerate. In the results of Table1 convergence always occurred to x1 except in the case indicated by an asterisk. The linearized complementarity problem at 0 has no solution.... ..."

### Table 8. Complementarities (I): Unconditional Correlations

"... In PAGE 23: ....4. Complementarities and Substitutabilities As section 2 has argued, there are reasons to believe that there exist interactions between the different elements of the system. Table8 presents the unconditional correlations between each pair of decision variables. These unconditional correlations are all positive with the exception of those between the realized quasi-rents and the rest of the variables, suggesting that a change in any contractual variable is related with a change in the same direction of any of the others.... In PAGE 23: ... These unconditional correlations are all positive with the exception of those between the realized quasi-rents and the rest of the variables, suggesting that a change in any contractual variable is related with a change in the same direction of any of the others. While Table8 is consistent with the existence of complementarities between contractual decision variables, it cannot help to reject the hypothesis that each contractual choice is unrelated to any other choice. Comovements in all the contractual variables may simply respond to movements in the same underlying variable.... In PAGE 23: ... As we have seen during the previous sections, it is indeed the case that all of these variables respond to similar considerations. [Note: Table8... In PAGE 24: ... Since the estimation of the monetary incentive equations relies on non-linear MLE methods, we use the generalized residuals proposed by Bourieroux, Monfort, Renault and Trognon (1987). [Note: Table 9 here, with conditional correlations] Controlling for common sources of variation reduces the covariation from the one that could be observed in Table8 . This suggests that part of the covariation that could be observed was the consequence of a common response of the different contractual elements to the same problem, namely the risk of moral hazard.... ..."

### Table 9. Complementarities (II): Conditional Correlations

"... In PAGE 24: ... It will appear that different practices are complementary when, in fact, they are simply moving together as a result of the impact of a third variable unknown to us. Table9 presents the conditional correlations between the different measures of discretion. They have been calculated as the correlations between the residuals of the contract regressions, the monetary incentive Tobits, and the profitability panel.... In PAGE 24: ... Since the estimation of the monetary incentive equations relies on non-linear MLE methods, we use the generalized residuals proposed by Bourieroux, Monfort, Renault and Trognon (1987). [Note: Table9 here, with conditional correlations] Controlling for common sources of variation reduces the covariation from the one that could be observed in Table 8. This suggests that part of the covariation that could be observed was the consequence of a common response of the different contractual elements to the same problem, namely the risk of moral hazard.... In PAGE 25: ...particular, Table9 points to complementarities between completion and termination rights, and between monitoring and incentive intensity. The evidence on the positive conditional correlation between completion and termination rights may suggest that manufacturer discretion in termination, a dimension of enforcement, is present when the manufacturer also has more scope for decision making.... In PAGE 25: ... The result is consistent, however, with the alternative hypothesis we advanced, which recognizes the need for the right to establish obligations to covary with the right to enforce those obligations. Also, the second column of Table9 suggests that it is indeed the case that more monitoring intensity covaries with more incentive intensity, as measured by either any of the monetary discounts or by termination rights. Only in one case is this correlation significant at the 95% level, 17 but four of the correlations would be significant at the 85% level.... In PAGE 25: ...5% level. This is consistent with what the theory would lead us to predict. As moral hazard increases, incentive provision needs to be stronger, and this implies that monitoring intensity must increase. 18 The last four rows of Table9 present the evidence on the use of sales and service discounts. The only coefficients that are significantly different from zero relate the level and the range of discounts, which is of limited economic interest and suggests simply that both are measures of incentive intensity.... ..."