Signaling , Fines and Bonuses

Hamid Aghadadashlia and Patrick Legrosb

aUniversit´elibre de Bruxelles (ECARES)

bUniversit´elibre de Bruxelles (ECARES), Northeastern University, and CEPR

CRESSE, 30 June 2017

Aghadadashli and Legros Signaling Collusion April 8, 2017 1 / 22 Introduction Introduction

• Usually, managers are uninformed about each other’s willingness to collude. • Communication plays a central role for collusion... → as it can facilitate coordination between the managers; → (managers can also transmit “hard” information while communicating.) • However, managers can also signal their types through market actions. • Compared to tacit collusion, communication... → allows the managers to coordinate earlier (prevent free riding by non-collusive managers), → but also is likely to be detected and fined.

Aghadadashli and Legros Signaling Collusion April 8, 2017 2 / 22 Introduction

We show...

• Collusive under can be replicated in communication game for a large set of fines. • Consumers can be better off in communication game if the managers can also coordinate through market signaling. • Corporate responsibility: owners may use bonuses to induce managers to communicate.

Aghadadashli and Legros Signaling Collusion April 8, 2017 3 / 22 Introduction Literature

• Antitrust fines and communication: → McCutcheon (1997) and Andersson and Wengstr¨om(2008) - high fines can deter renegotiation and facilitate collusion; → Mouraviev (2013), Genesove and Mullin (2001), and Spector (2015) - communication helps monitoring - high fines deter communication; → All these works show the monotonic effect of fines. • Collusion through market signaling: → Harrington and Zhao (2012) → Lefez (2017).

Aghadadashli and Legros Signaling Collusion April 8, 2017 4 / 22 Model Model with Unitary Firms

• We consider two firms and each firm’s owner is also the manager. • There can be two types of managers: ... δ - who value future profit flows (with a discount rate δ) and may be open to collusion; ... 0 - who does not value future profit flows and is not willing to collude. • A manager is type δ with a probability of α...... α is independent and identical for both managers. • Manager i ∈ {1, 2}’s utility is equal to the firm i’s profit and given by π(si, sj).

Aghadadashli and Legros Signaling Collusion April 8, 2017 5 / 22 Model Unitary Firms - cont.

• To avoid trivialities, we assume:

πM ≥ (1 − δ)πD + δπc.

• When the condition holds, then under perfect information managers...

→ immediately coordinate on collusive (monopoly) strategies (sM , sM ), when both have type δ,

→ otherwise they play competitive strategies (sc, sc) in all periods.

Aghadadashli and Legros Signaling Collusion April 8, 2017 6 / 22 Market Signaling Market Signaling

• Without explicit communication, managers can still collude by signaling their types in the market.

• We consider symmetric focal equilibria which maximizes the expected payoff of the collusive types.

• And we assume the managers have pessimistic beliefs about the type of the other manager.

Aghadadashli and Legros Signaling Collusion April 8, 2017 7 / 22 Market Signaling Market Signaling - Strategies I

• At time 1, type δ manager signals its type by playing sδ...... any other s′ ≠ sδ is perceived as an action by type 0. • Type 0 plays his to sδ:

s0(α, sδ) = arg max απ(s, sδ) + (1 − α)π(s, s0), s • We focus on equilibria that maximize the collusive types’ expected profit:

arg max απ(sδ, sδ)) + (1 − α)π(sδ, s0(α, sδ)) sδ tacit δ δ tacit 0 δ δ s.t. ICδ: Πδ (s , s ) ≥ Πδ (s (α, s ), s )

Aghadadashli and Legros Signaling Collusion April 8, 2017 8 / 22 Market Signaling Market Signaling - Strategies II

At time t ≥ 2, • if the history is collusive → type δ managers play sM ;

→ while type 0 plays sD.

• and any deviation leads to trigger of reversal to sc.

Aghadadashli and Legros Signaling Collusion April 8, 2017 9 / 22 Market Signaling Market Signaling - Results

Lemma There can be information transmitted through market signaling if, and only if, the IC condition for δ type holds: δ δ α ‹π(sδ, sδ) + πM  + (1 − α)‹π(sδ, s0(α, sδ)) + πc ≥ 1 − δ 1 − δ δ δ α ‹π(s0(α, sδ), sδ) + πc + (1 − α)‹π(s0(α, sδ), s0(α, sδ)) + πc. 1 − δ 1 − δ

Aghadadashli and Legros Signaling Collusion April 8, 2017 10 / 22 Communication Explicit Communication

• Managers can communicate explicitly their willingness to collude. • Explicit communication...... reduces information cost: δ types can coordinate on sM in the first period. ... but it can be detected and fined by antitrust authority.

Aghadadashli and Legros Signaling Collusion April 8, 2017 11 / 22 Communication Explicit Communication - IC Condition

• Type δ communicates with the other manager if

πM πc πc α + (1 − α) − F ≥ 1 − δ 1 − δ 1 − δ

• It is not incentive compatible for type 0 to communicate if

πc ≥ απD + (1 − α)πc − F (1)

Aghadadashli and Legros Signaling Collusion April 8, 2017 12 / 22 Communication Explicit Communication - Results

• The types can separate via communication in period 1 by using the if, and only if,

πM − πc α ‰πD − πcŽ ≤ F ≤ α  1 − δ

• The LHS is the IC condition for type 0, while the RHS is from the IC condition for type δ. Proposition There exists an interval [F , F ] such that whenever F belongs to this interval, there exists an equilibrium strategy of the game with imperfect information and costly communication that leads to the same outcomes as the games of perfect information.

Aghadadashli and Legros Signaling Collusion April 8, 2017 13 / 22 Value of Communication Value of Communication

• Communication has both costs and benefits for the collusive types δ... + collusion allows types δ to coordinate on the monopoly strategy in the first period instead of sδ, πM > π(sδ, sδ);

− expected fine that will be imposed by antitrust authorities F ;

? difference in profit with respect to market signaling when a collusive type “meets” a myopic player:

π(sδ, s0(α, sδ)) − π(sc, sc).

Aghadadashli and Legros Signaling Collusion April 8, 2017 14 / 22 Value of Communication Value of Communication

• There are some interval of fines the collusive types prefer the communication equilibrium over market signaling equilibrium.

• However, the expected profits of the firms may be lower with communication.

• Consumer surplus may be in fact greater when collusive types communicate than when they use market signaling.

Aghadadashli and Legros Signaling Collusion April 8, 2017 15 / 22 Cournot Example

Cournot Example: linear demand p1 = 1 − s1 − γs2

Figure: Difference in consumer surplus: Communication vs Market Signaling

Aghadadashli and Legros Signaling Collusion April 8, 2017 16 / 22 Managerial Firms Model with Managerial Firms

• At time 0, each owner offers a long-term contract to its manager which specifies bonuses proportional to the profit, i.e., b ⋅ π.

• The managers can choose the market actions and also effort levels ei e2 at cost 2 . • Given market actions (si, sj), effort level ei and bonus bi...

... firm’s profit is eiπ(si, sj);

... owner’s profit is (1 − bi)eiπ(si, sj); ( ) − e2 ... manager’s utility is bieiπ si, sj 2 . • If the antitrust authority detects collusion, it fines managers f and owners F , separately.

Aghadadashli and Legros Signaling Collusion April 8, 2017 17 / 22 Managerial Firms 1. Confirm Previous Results

• In the market signaling game, owners cannot influence the managers’ incentives to collude and set bonuses at the “efficient” level b = 1~2, to exert optimal effort. • Under communication the incentive of the managers to collude depends on the bonus and fine levels. • The welfare results from the unitary firm model are robust in managerial firms case.

Aghadadashli and Legros Signaling Collusion April 8, 2017 18 / 22 Managerial Firms 2. Corporate Responsibility — Using Bonuses to Induce Communication Bonuses

1.0

0.8 b

0.6 1/2

0.4 b

0.2

f 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 Figure: Bonus levels in Cournot example (solid: separation, dotted: pooling-communication, dashed: pooling no-communication).

Aghadadashli and Legros Signaling Collusion April 8, 2017 19 / 22 Managerial Firms 3. Corporate Responsibility — The Role of Allocation of Fines

50% ] Π [ 40% of % 30%

20%

10% Fines on owners as a

0%

0% 2% 4% 6% 8% 10% fines on managers as a % of [U] Figure: Owner-optimal induced communication strategy of the manager given

f, FAghadadashli. and Legros Signaling Collusion April 8, 2017 20 / 22 Managerial Firms Conclusion

• Preventing communication may lead managers to collude through market actions.

• When collusion is possible both with and without communication communication can be pro-competitive.

• The allocation of fines between owners and managers affects the willingness of owners to prevent communication.

Aghadadashli and Legros Signaling Collusion April 8, 2017 21 / 22 Managerial Firms

Thank you for your attention!

Aghadadashli and Legros Signaling Collusion April 8, 2017 22 / 22