An Experiment on Strategic Capacity Reduction

1. An Experiment onStrategic Capacity Reduction Mikhael Shor Vanderbilt University May 2008

2. Motivation • Health insurers • restrict the number of drugs on their formulary • Pharmaceutical benefit managers • restrict the number of drug stores in their retail networks • Private airports • artificially limit the availability of gates or runways • Grocery stores • limit available shelf space for competing products

3. Shelf-Space Models & Slotting Allowances • Theoretical concerns have mostly focused on supplier market power, not buyer market power • Competitor foreclosure through slotting allowances • Yet, slotting allowances usually buyer-initiated (Arquit 1991) • Slotting allowances can be pro-competitive • Align retailer-manufacturer incentives (Klein and Wright 2007) • Decrease consumer search costs (Sullivan, 1997) • Traditional equilibrium bargaining models show little incentive to limit capacity But may rest on behaviorally untenable assumptions

4. Thought Experiment • You are the director of a commercial-free music video channel • Perhaps jazz, pop, polka, or classic rock? • Cable companies pay you a fixed fee to carry your content • You make a take-it-or-leave-it price request to each cable company

5. Thought Experiment • Market • There are a total of 20 (homogeneous) suppliers • Cable Companies • Each music channel adds $10M to profit • Cable companies have varying capacities (k) • Cable companies select the k lowest offers • Market 1: k = 30 (unlimited capacity) • Market 2: k = 12 (constrained capacity) How much do you ask for in each market?

6. Research Question • How does a firm’s capacity impact the allocation of bargaining power between it and its suppliers? • What happens to a firm’s revenue if it commits to insufficient capacity to deal with all suppliers? • Outline: • Experiment • Theory for our thought experiment • Results • Subject behavior

7. Experiment • Identical to thought experiment • A market consists of N =20 suppliers (subjects) • Each market has a capacity level k {4,6,…,18,20} • Each supplier contributes $10 to monopolist profits • Subjects make simultaneous proposals. A proposal of p implies, if accepted, the subject receives p and the monopolist receives $10-p. • The lowest k proposals are accepted and paid; remaining subjects are paid $0.

8. Theoretical Predictions • If k≥ N • Suppliers should request the whole $10 (or a bit less) • Buyer is left with zero profits • If k < N • Unique equilibrium: each requests $0 • Buyer captures entire surplus ( 10k million) Equilibrium in weakly dominated strategies Only strategy that guarantees zero profit

9. Equilibrium Requests Monopolist captures entire surplus whenever k<N

10. Equilibrium Revenue There is incentive to exclude at most one supplier

11. Market Games • Nine proposers for a single prize Roth, Vesna, Okuno-Fujiwara, and Zamir, 1991 Prasnikar and Roth, 1992 • Two to four proposers for a single prize Dufwenberg and Gneezy, 2000 Dufwenberg, Gneezy, and Rustichini, 2005 • Three sequential proposals for a single prize Abbink, et al, 2001 • In all of these, only one bargain may be consummated How does altering the number of accepted offers change subjects’ bids?

12. Experiment • Subjects: 60 MBA students • Each subject bid in three different capacity conditions • 180 bids total, 20 at each capacity level

13. Results: Price Requests Bids increase with available capacity and do not correspond to theoretical predictions

14. Results: Accepted Price Requests Winning bids increase with available capacity and do not correspond to theoretical predictions

15. Results: Buyer’s Profit • Experiment: Firm has incentive to decrease capacity by 30% 55% profit increase 19% profit increase 606% profit increase

16. Robustness • Subject Pool • Executives at two manufacturing firms yield similar results • Executive Subject Price Requests

17. Robustness • Subject Pool • Executives at two manufacturing firms yield similar results • Learning • Introducing multiple rounds does not lead to equilibrium convergence • Repeated Experiment Price Requests (k=12)

18. Explaining Subject Behavior • An executive subject: “ This game is simplistic but still similar to what we face every day. In our business, we compete against other suppliers in what is, essentially, a commodity business. Our only differentiation is price. ” • Equilibrium fails to describe behavior • Bounded rationality (QRE) fails, too

19. Explaining Subject Behavior • An executive subject: “ The idea is to treat everyone fairly, while still securing a sufficient profit for ourselves. ” • Consider behavior in the classic ultimatum game: Equity norm (even split) + Strategic considerations • In the present context, some modifications

20. Surveys • What is an equitable payment to a supplier (considering that some suppliers will earn nothing)? What is a fair profit for one of k accepted suppliers? 100 respondents, 20 for each k{4,8,12,16,20} • Strategic considerations: what is a reasonable profit share for the cable company to maintain position? What percentage of profits need an accepted supplier share with the buyer to secure his position? 50 respondents, 10 for each k{4,8,12,16,20}

21. Results: Both Surveys • Start with a “fair profit,” adjust for strategic concerns • Fairness norms tempered with strategic concerns accurately describe subject behavior Survey Experiment

22. Conclusions Experiments • In a competitive ultimatum / market game setting, subjects react to capacity constraints Implications for firms • Reducing capacity is inefficient, but profitable • Efficiency loss of at least 30% Behavior • Weakly dominated strategies are not rational • Strategic concerns tempered by fairness predict data