Vanderbilt University1 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"

Vanderbilt University2 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

Vanderbilt University3 Related Work "Mergers Among Parking Lots," J. Econometrics. Constraints on merging lots attenuate price effects by more than constraints on non-merging lots amplify them

Vanderbilt University4 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?

Vanderbilt University5 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.

Vanderbilt University6 Typical Profit Curve with a Rounded Peak

Vanderbilt University7 Non-binding capacity constraint: Steeper on left side

Vanderbilt University8 Binding capacity constraint: Steeper on right side

Vanderbilt University9 Expected profit curve: price increases w/uncertainty

Vanderbilt University10 Expected profit curve: price decreases w/uncertainty

Vanderbilt University11 It takes a lot of uncertainty to make a noticeable difference

Vanderbilt University12 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 (s i µ)

Vanderbilt University13 Role of information Gamma(α, β) prior on unknown mean arrivals Conjugate to Poisson Each firm i observes fraction β i (common knowledge), and gets a private signal α i successes. Firm’s posterior information characterized by Gamma(α+α i, β+β i ) on unknown µ

Vanderbilt University14 Nash Equilibrium Optimal price maximizes expected profit as a function of own signal, p i (α i ) Expectation over all possible signals and all possible quantities

Vanderbilt University15 Individual profit, deterministic and expected

Vanderbilt University16 Individual profit, deterministic and expected

Vanderbilt University17 Optimal pricing as a function of signal

Vanderbilt University18 Post merger optimal pricing functions, i.e. ownership effect

Vanderbilt University19 Joint profit function, determinate

Vanderbilt University20 Joint profit function, expected

Vanderbilt University21 Merger numerical example

Vanderbilt University22 Merger numerical example (cont.)

Vanderbilt University23 Extension: Dynamic pricing strategy

Vanderbilt University24 Dynamic pricing (cont.)

Vanderbilt University25 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.

Vanderbilt University26 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