1. It follows that these constraints would continue to be satisfied at such w if B were slightly lower. Figure A1 illustrates. Two-Step Collusive Schemes: The Uniform-Distribution Example. Suppose costs are uniformly distributed over dfc �o, o ' � and firms revert forever to the static Nash equilibrium following any off-schedule deviation. Calculations reveal that Z ' �*Sc R Q Ew ' �*E2 w c B 9 ' S*., / ) Ew ' d� w n Ew o*�2c l Q Ew ' w *d2E2 w o and l Ew ' d� w o *2 . As Figure A.2 illustrates, as w moves from f to �, l Q climbs (monotonically, in this case) from f to Q , and l falls from Q to f. The uniform distribution function is log concave, so / ) Ew takes a convex shape. This function is minimized at the cost level of Q , and it assumes its maximum value (corresponding to rigid pricing at o ' �) at either endpoint;Next;Ew exceeds that of l Ew , when both are evaluated at w ' w if the small-density condition is satisfied. Clearly, dB 9
2. Figure 3—figure supplement 5. dilp8 is needed for EW in adults and additional dilp8 increases the frequency.
3. Proof of Proposition 19: Consider a candidate solution which specifies strictly increasing pricing on interval Ew !Q c w o Consider introducing a tiny step on the interval Ew 0c w o (for example, by introducing an additional potential step into the firms' objective between w !Q and w ; since the firms can choose the number of intervals, an additional step is always feasible and thus was in the original choice set) If there is some gain to future cooperation, then for 0 small enough, introducing a tiny step does not introduce a new off-schedule incentive constraint;Efc � satisfies both off-schedule incentive compatibility constraints when B ' B 9