An Experiment onStrategic Capacity Reduction

Mikhael ShorVanderbilt University

May 2008

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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

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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

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Thought Experiment

You are the director of a commercial-free music video channelPerhaps 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

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Thought Experiment

MarketThere are a total of 20 (homogeneous) suppliers

Cable CompaniesEach music channel adds $10M to profitCable 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?

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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

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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.

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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 strategiesOnly strategy that guarantees zero profit

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Equilibrium Requests

Monopolist captures entire surplus whenever k<N

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Capacity

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Equilibrium Revenue

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enue

Capacity

There is incentive to exclude at most one supplier

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Market Games

Nine proposers for a single prizeRoth, Vesna, Okuno-Fujiwara, and Zamir, 1991Prasnikar and Roth, 1992

Two to four proposers for a single prizeDufwenberg and Gneezy, 2000Dufwenberg, Gneezy, and Rustichini, 2005

Three sequential proposals for a single prizeAbbink, et al, 2001

In all of these, only one bargain may be consummated

How does altering the number of accepted offers change subjects’ bids?

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Experiment

Subjects: 60 MBA students

Each subject bid in three different capacity conditions

180 bids total, 20 at each capacity level

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Results: Price Requests

Bids increase with available capacity and do not correspond to theoretical predictions

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Price RequestsMean

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Winning bids increase with available capacity and do not correspond to theoretical predictions

Results: Accepted Price Requests

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Accepted RequestsRejected RequestsMean Accepted

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55% profit increase19% profit increase

Results: Buyer’s Profit

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2 4 6 8 10 12 14 16 18 20Capacity

Prof

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Experiment:

Firm has incentive to decrease capacity by 30%

606% profit increase

Subject Pool Executives at two manufacturing firms yield similar results

Executive Subject Price Requests

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Relative Capacity (k/N)

ExecutivesMBAs

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Robustness

Repeated Experiment Price Requests (k=12)

Subject Pool Executives at two manufacturing firms yield similar results

Learning Introducing multiple rounds does not lead to equilibrium

convergence

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Robustness

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0 5 10 15 20Round

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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

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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

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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}

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Results: Both Surveys

Start with a “fair profit,” adjust for strategic concerns Fairness norms tempered with strategic concerns

accurately describe subject behavior

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Survey

Experiment

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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