vanderbilt university1 competitive revenue management: evaluating mergers among cruise lines luke...
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Competitive Revenue Management: Evaluating
Mergers Among Cruise Lines
Luke Froeb & Steven TschantzVanderbilt University
April 5, 2003IIOC, Boston
"Structural Empirical Models for Merger Analysis"
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Talk outline Revenue mgt. and cruise line merger Revenue mgt. for economists Nash equilibrium when firms “revenue
manage” Preliminary conclusions based on few
numerical examples Usual ownership effect raises price Information-sharing effect can raise or lower price
Model extensions Policy conclusions
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RelatedWork
"Mergers Among Parking Lots," J. Econometrics.
Constraints on merging lots attenuate price effects by more than constraints on non-merging lots amplify them
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Carnival-Princess & Revenue Mgt. Revenue management: problem of matching
uncertain demand to available capacity. Hotels, airlines, cruise lines
British Competition Commission, U.S. FTC, EC all cleared cruise line merger filling-the-ship concern unaffected by mergerno
price change No quantity effect, but higher prices to less-
elastic customers Analysis of usual market power concerns Were theories correct? What was
Magnitude?
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Revenue Mgt. for Economists Set price before demand realized. Fixed capacity (big fixed costs, low marginal
cost) Q=min[demand(p), K]
demand[p] is log normally distributed with mean of q[p]; σ/µ=40%
q[p] is a logit function of price. If C(Q) is linear,
With uncertainty, firms price higher or lower than deterministic price depending on which side of deterministic profit peak is steeper.
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Typical Profit Curvewith a Rounded Peak
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Non-binding capacity constraint:Steeper on left side
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Binding capacity constraint:Steeper on right side
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Expected profit curve:price increases w/uncertainty
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Expected profit curve: price decreases w/uncertainty
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It takes a lot of uncertainty to make a noticeable difference
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Poisson arrival process on top of logit choice model Poisson arrival
process with mean µ
On top of n-choice logit demand model
Implies n independent arrival processes with means (siµ)
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Role of information Gamma(α, β) prior on
unknown mean arrivals
Conjugate to Poisson Each firmi observes
fraction βi (common knowledge), and gets a private signal αi successes.
Firm’s posterior information characterized by Gamma(α+αi, β+βi) on unknown µ
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Nash Equilibrium Optimal price maximizes expected
profit as a function of own signal, pi(αi)
Expectation over all possible signals and all possible quantities
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Individual profit, deterministic and expected
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Individual profit, deterministic and expected
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Optimal pricing as a function of signal
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Post merger optimal pricing functions, i.e. ownership effect
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Joint profit function, determinate
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Joint profit function, expected
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Merger numerical example
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Merger numerical example(cont.)
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Extension:Dynamic pricing strategy
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Dynamic pricing (cont.)
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Conclusions based on numerical examples Two merger effects
Ownership effect raises price Information-sharing effect raises or lowers price
But always increases quantity
Both effects small and disappear as uncertainty decreases
Confirm basic intuition from parking lot paper, i.e. firms price to fill the ships, and this profit calculus is unaffected by merger.
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Open Questions Conjectures
Can we find an ownership effect that reduces price? Since dynamic pricing reduces uncertainty, it would
also reduce merger effect. Small price discrimination effect.
Models to be built Price discrimination between two customer types Dynamic price adjustment Modeling rejections (currently, overbooked passengers
go home disappointed) Instead allow them to switch to unconstrained carriers, if
any Conjecture that this is likely to be very small.
How to estimate or calibrate model to real data