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Competitive Revenue Management: Evaluating Mergers Among Cruise Lines. Luke Froeb & Steven Tschantz Vanderbilt University April 5, 2003 IIOC, Boston "Structural Empirical Models for Merger Analysis". Talk outline. Revenue mgt. and cruise line merger Revenue mgt. for economists
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Competitive Revenue Management: Evaluating Mergers Among Cruise Lines Luke Froeb & Steven Tschantz Vanderbilt University April 5, 2003 IIOC, Boston "Structural Empirical Models for Merger Analysis"
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
RelatedWork • "Mergers Among Parking Lots," J. Econometrics. • Constraints on merging lots attenuate price effects by more than constraints on non-merging lots amplify them
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?
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.
It takes a lot of uncertainty to make a noticeable difference
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)
Role of information • Gamma(α, β) prior on unknown mean arrivals • Conjugate to Poisson • Each firmi observes fractionβi (common knowledge), and gets a private signalαi successes. • Firm’s posterior information characterized by Gamma(α+αi, β+βi) on unknown µ
Nash Equilibrium • Optimal price maximizes expected profit as a function of own signal, pi(αi) • Expectation over all possible signals and all possible quantities
Post merger optimal pricing functions, i.e. ownership effect
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.
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