Competitive Revenue Management: Evaluating Mergers Among Cruise Lines

1. 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"

2. 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

3. RelatedWork • "Mergers Among Parking Lots," J. Econometrics. • Constraints on merging lots attenuate price effects by more than constraints on non-merging lots amplify them

4. 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 mergerno price change • No quantity effect, but higher prices to less-elastic customers • Analysis of usual market power concerns • Were theories correct? What was Magnitude?

5. 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.

6. Typical Profit Curvewith a Rounded Peak

7. Non-binding capacity constraint:Steeper on left side

8. Binding capacity constraint:Steeper on right side

9. Expected profit curve:price increases w/uncertainty

10. Expected profit curve:price decreases w/uncertainty

11. It takes a lot of uncertainty to make a noticeable difference

12. 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)

13. 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

14. Nash Equilibrium • Optimal price maximizes expected profit as a function of own signal, pi(αi) • Expectation over all possible signals and all possible quantities

15. Individual profit, deterministic and expected

16. Individual profit, deterministic and expected

17. Optimal pricing as a function of signal

18. Post merger optimal pricing functions, i.e. ownership effect

19. Joint profit function, determinate

20. Joint profit function, expected

21. Merger numerical example

22. Merger numerical example(cont.)

23. Extension:Dynamic pricing strategy

24. Dynamic pricing (cont.)

25. 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.

26. 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