Competition Policy - Spring 2005 Collusion II Antonio Cabrales - PowerPoint PPT Presentation

Prepared with SEVI SLIDES Competition Policy - Spring 2005 Collusion II Antonio Cabrales & Massimo Motta April 22, 2005 ➪ ➪ ➲

➟ ➠ ➪ Summary Symmetry helps collusion ➟ ➠ • • Multimarket contacts ➟ ➠ • Cartels and renegotiation ➟ ➠ • Optimal penal codes ➟ ➠ • Leniency programmes (simp. Motta-Polo) ➟ ➠ ➪ ➲ ➪ ➟ ➠

➣➟ ➠ ➪ Symmetry helps collusion (1/2) (resp. 2 ) has share s A (resp. s A • Market A : Firm 1 1 = λ 2 = 1 − λ ). • λ > 1 2 : firm 1 “large”; firm 2 is “small”. • Firms are otherwise identical. • Usual infinitely repeated Bertrand game. • ICs for firm i = 1 , 2 : s A i ( p m − c ) Q ( p m ) − ( p m − c ) Q ( p m ) ≥ 0 , 1 − δ ➪ ➪ ➟➠ ➣ ➥ ➲ 1 28

➢ ➟ ➠ ➪ Symmetry helps collusion (2/2) λ • Therefore: IC A 1 : 1 − δ − 1 ≥ 0 , or: δ ≥ 1 − λ. 2 : 1 − λ • IC A 1 − δ − 1 ≥ 0 , or: δ ≥ λ (binding IC of small firm). • Higher incentive to deviate for a small firm: higher additional share by decreasing prices. • The higher asymmetry the more stringent the IC of the smallest firm. ➪ ➪ ➟➠ ➥ ➢ ➲ 2 28

➣➟ ➠ ➪ Multimarket contacts (1/3) (resp. 1 ) with share s B (resp. s B • Market B : Firm 2 2 = λ 1 = 1 − λ ): reversed market positions. • ICs in market j = A, B considered in isolation : s j i ( p m − c ) Q ( p m ) − ( p m − c ) Q ( p m ) ≥ 0 , 1 − δ λ • IC B 2 : 1 − δ − 1 ≥ 0 , or: δ ≥ 1 − λ . 1 : 1 − λ • IC B 1 − δ − 1 ≥ 0 , or: δ ≥ λ . • By considering markets in isolation (or assuming that firms 1 and 2 in the two markets are different) collusion arises if δ ≥ λ > 1 / 2 . ➟ ➠ ➪ ➪ ➟➠ ➣ ➥ ➲ 3 28

➢ ➣➟ ➠ ➪ Multimarket contacts (2/3) • If firm sells in two markets, IC considers both of them: s A + s B i ( p m − c ) Q ( p m ) i ( p m − c ) Q ( p m ) − 2 ( p m − c ) Q ( p m ) ≥ 0 , (1) 1 − δ 1 − δ or: (1 − λ ) ( p m − c ) Q ( p m ) + λ ( p m − c ) Q ( p m ) − 2 ( p m − c ) Q ( p m ) ≥ 0 . (2) 1 − δ 1 − δ • Each IC simplifies to: δ ≥ 1 2 . • Multimarket contacts help collusion, as critical discount factor is lower: 1 2 < λ . ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 4 28

➢ ➟ ➠ ➪ Multimarket contacts (3/3) • Firms pool their ICs and use slackness of IC in one market to enforce more collusion in the other. • In this example, multi-market contacts restore symmetry in markets which are asymmetric. ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➲ 5 28

➣➟ ➠ ➪ Cartels and renegotiation (1/6) • Consider explicit agreements (not tacit collusion). • McCutcheon (1997): renegotiation might break down a cartel. • Same model as before, but firms can meet after initial agreement. • After a deviation, incentive to agree not to punish each other. • = ⇒ since firms anticipate the punishment will be renegotiated, nothing prevents them from cheating! • Collusion arises only if firms can commit not to meet again (or further meetings are very costly). • This conclusion holds under strategies other than grim ones. ➟ ➠ ➪ ➪ ➟➠ ➣ ➥ ➲ 6 28

➢ ➣➟ ➠ ➪ Cartels and renegotiation (2/6) • Asymmetric (finite) punishment (to reduce willingness to renegotiate): • for T periods after a deviation, the deviant firm gets 0; non-deviant gets at least π ( p m ) / 2 . After, firms revert to p m . chosen to satisfy IC along collusive path: • T 2(1 − δ ) ≥ π ( p m )+ δ T +1 π ( p m ) π ( p m ) 2(1 − δ ) , (3) • or: δ (2 − δ T ) ≥ 1 . • But deviant must accept punishment. ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 7 28

➢ ➣➟ ➠ ➪ Cartels and renegotiation (3/6) • IC along punishment path (if deviating, punishment restarted): δ T π ( p m ) 2(1 − δ ) ≥ π ( p m ) + δ T +1 π ( p m ) (4) 2(1 − δ ) . 2 • False, since it amounts to δ T ≥ 1 . • Under Nash reversal or other strategies, no collusion at equilibrium if (costless) renegotiation allowed. ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 8 28

➢ ➣➟ ➠ ➪ Cartels and renegotiation (4/6) Costly renegotiation: Can small fines promote collusion? • Every meeting: prob. θ of being found out. • Expected cost of a meeting: θF ( F = fine). • Benefit of initial meeting: π ( p m ) / (2(1 − δ )) . • It takes place if: θF < π ( p m ) / (2(1 − δ )) . ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 9 28

➢ ➣➟ ➠ ➪ Cartels and renegotiation (5/6) • Benefit of a meeting after a deviation (asymmetric punishments): � � T − 1 δ t π ( p m ) = π ( p m ) 1 − δ T � . 2 2 1 − δ t =0 • It takes place if: θF < π ( p m )(1 − δ T ) / (2(1 − δ )) . 1. θF ≥ π ( p m ) / (2(1 − δ )) . Each meeting very costly: no collusion. 2. π ( p m ) / (2(1 − δ )) > θF ≥ π ( p m )(1 − δ T ) / (2(1 − δ )) . Initial meeting yes, renegotiation no: collusion (punishment is not renegotiated). 3. π ( p m )(1 − δ T ) / (2(1 − δ )) > θF . Expected cost of meetings small: renegotiation breaks collusion. ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 10 28

➢ ➟ ➠ ➪ Cartels and renegotiation (6/6) Discussion • Importance of bargaining and negotiation in cartels. • No role in tacit collusion. • But such further meetings might help (eg., after a shocks occur, meet- ings might avoid costly punishment phases). • Genesove and Mullin (AER, 2000): • renegotiation crucial to face new unforeseeable circumstances; • infrequent punishments, despite actual deviations... • ... but cartel continues: due to such meetings? ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➲ 11 28

➣➟ ➠ ➪ Optimal penal codes (1/9) Abreu: Nash forever not optimal punishment, if V p i > 0. Stick and carrot strategies, so that V p i = 0 : max sustainability of collusion. An example of optimal punishments Infinitely repeated Cournot game. n identical firms. Demand is p = max { 0 , 1 − Q } . ➟ ➠ ➪ ➪ ➟➠ ➣ ➥ ➲ 12 28

➢ ➣➟ ➠ ➪ Optimal penal codes (2/9) Nash reversal trigger strategies IC for collusion: π m / (1 − δ ) ≥ π d + δπ cn / (1 − δ ) , (1 + n ) 2 1 + 6 n + n 2 ≡ δ cn . → δ ≥ Under Nash reversal, V p = δπ cn / (1 − δ ) > 0 . ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 13 28

➢ ➣➟ ➠ ➪ Optimal penal codes (3/9) Optimal punishment strategies Symmetric punishment strategies might reduce V p . and earns π p < 0 Each firm sets same q p for the period after deviation, then reversal to collusion: V p ( q p ) = π p ( q p ) + δπ m / (1 − δ ) . so that V p = 0 , punishment is optimal. If q p Credibility of punishment if: V p ( q p ) ≥ π dp ( q p ) + δV p ( q p ) , or � � δπ m δπ m π p ( q p ) + (1 − δ ) ≥ π dp ( q p ) + δ π p ( q p ) + . (1 − δ ) (If deviation, punishment would be restarted.) ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 14 28

➢ ➣➟ ➠ ➪ Optimal penal codes (4/9) Therefore, conditions for collusion are: π d − π m π m − π p ( q p ) ≡ δ c ( q p ) (ICcollusion) δ ≥ π dp ( q p ) − π p ( q p ) ≡ δ p ( q p ) δ ≥ (ICpunishment). π m − π p ( q p ) Harsher punishment: ICcollusion relaxed: dδ c ( q p ) < 0 , dq p dδ p ( q p ) ...but IC punishment tightened: > 0 . dq p ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 15 28

➢ ➣➟ ➠ ➪ Optimal penal codes (5/9) Linear demand Cournot example: for q p ∈ ( 1 − c n + 1 , 1 (1 − nq p − c ) q p , π p ( q p ) = n ) for q p ≥ 1 π p ( q p ) − cq p , = n. (for q ≥ 1 /n , p = 0 ). for q p ∈ ( 1 − c n + 1 , 1 − c (1 − ( n − 1) q p − c ) 2 / 4, π dp ( q p ) = n − 1) for q p ≥ 1 − c π dp ( q p ) = 0, n − 1 . (Note that 0 = V p ≥ π dp + δV p which implies π dp = 0 .) ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 16 28

➢ ➣➟ ➠ ➪ Optimal penal codes (6/9) (1 − c ) 2 ( n − 1) 2 for 1 − c n + 1 < q p < 1 δ c ( q p ) = 4 n (1 − c − 2 nq p ) 2 , n (1 − c ) 2 ( n − 1) 2 for q p ≥ 1 δ c ( q p ) = 4 n (1 − 2 c + c 2 + 4 ncq p ), n, and: n (1 − c − q p − nq p ) 2 for 1 − c n + 1 < q p < 1 − c δ p ( q p ) = , (1 − c − 2 nq p ) 2 n − 1 4 nq p ( − 1 + c + nq p ) for 1 − c n − 1 ≤ q p < 1 δ p ( q p ) = , (1 − c + 2 nq p ) 2 n 4 ncq p for q p ≥ 1 δ p ( q p ) = 1 − 2 c + c 2 + 4 ncq p , n. q p , determines lowest δ . Figure: intersection between ICC and ICP, � ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 17 28

➢ ➣➟ ➠ ➪ Optimal penal codes (7/9) , , 1 1 0.5 0.5 0.2 0.2 Figure 1b Figure 1a Incentive constraints along collusive and punishment paths. Figure drawn for c = 1 / 2 and: (a) n = 4; (b) n = 8. ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 18 28

➢ ➣➟ ➠ ➪ Optimal penal codes (8/9) √ q p q p = (3 n − 1)(1 − c ) 1 < 1 − c Figure 1a: � ≡ � (for n < 3 + 2 2 ≃ 5 . 8 ) n − 1 2 n ( n +1) q p = (1+ √ n ) 2 (1 − c ) √ q p 2 > 1 − c Figure 1b � n − 1 (for n > 3 + 2 2 ) 4 n √ n ≡ � Therefore: δ = ( n + 1) 2 √ , for n < 3 + 2 2 16 n ( n − 1) 2 √ ( n + 1) 2 , for n ≥ 3 + 2 2 . ➟ ➠ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 19 28