market forces meet behavioral biases · 2006-05-14 · market forces meet behavioral biases cost...

IntroductionStatic model

Dynamics and learningImplications and conclusions

Market Forces meet Behavioral BiasesCost Mis-allocation and Irrational Pricing

Nabil I. Al-Najjar Sandeep Baliga David Besanko

Kellogg School of ManagementNorthwestern University

May 13, 2006

Al-Najjar, Baliga & Besanko Market Forces meet Behavioral Biases



evidenceoverview of the paperLiterature

Evidence of Sunk Cost Bias in Pricing

The evidence that firms take sunk and fixed cost into account inpricing decisions is overwhelming.

In a survey of Fortune 100 companies, Govindan andAnthony (1995) found that most firms price their productsbased on average cost, computed according to a “fullcosting” methodologyMaher, Stickney and Weil (2004) assert that, when itcomes to pricing practices:“[o]verwhelmingly, companies around the globe use fullcosts rather than variable costs.”They cite surveys of U.S. industries “showing that full-costpricing dominated pricing practices (69.5 percent), whileonly 12.1 percent of the respondents used a variable-costbased approach.”





Another Example

A management book (Shank and Govindarajan) state (p. 29,emphasis in original):

“Looking at incremental business on an incremental cost basiswill, at best, incrementally enhance overall performance. Itcannot be done on a big enough scale to make a big impact. Ifthe scale is that large, then an incremental look is notappropriate!”

Shank and Govindarajan make it clear that they believe thatmanagers should incorporate sunk costs into pricing decisions:“Business history reveals as many sins by taking anincremental view as by taking the full cost view.”





..yet another example

Edgar Bronfman, former owner of Universal Studios, proposescharging higher prices for movies that cost more to make.

"He ... observed that consumers paid the same amounts to seea movie that costs $2 million to make as they do for films thatcost $200 million to produce. ‘This is a pricing model thatmakes no sense, and I believe the entire industry should andmust revisit it.’ "

The Wall Street Journal, April 1, 1998.





But does the sunk cost bias matter in pricing?

Offerman and Potters (2003)’s experiments

Price competition treatmentSymmetric Bertrand games with product differentiation, lineardemand, and constant marginal cost

Baseline treatment: No fixed or sunk costprices converge to the Bertrand equilibrium

Sunk cost treatment: Subjects pay a sunk entry feeprices are significantly higheraverage markup over marginal cost increased by 30%





The sunk cost bias does not always persist

Monopoly treatmentThere was no final difference between the sunk cost andbaseline treatments for a monopolist..prices went to “rational” monopoly prices despite thepresence of sunk cost!





Methodology

We introduce psychologically plausible biases in a model ofprice competition

The presence of irrelevant costs (e.g., sunk cost) triggers apredisposition among firms to use full-cost pricing.Myopic, boundedly rational players; little understanding oftheir environments.When subjected to competitive pressures, firms adjusttheir prices and, less frequently, their “costingmethodologies” by reinforcing the practices that yielded thebest past results.Firms adjust prices and costing practices based on naivelearning rules





Findings

The sunk cost bias not only survives in certain marketstructures—but not others.

Where it survives, it is in fact self-reinforcing: firms achievebetter outcomes, and firms’ distorted perceptions is notcontradicted by evidence.





Outline of the talk1 Introduction


2 Static modelModel overviewStatic price competitionLinear example

3 Dynamics and learningadaptive learning; Theorem 1reinforcement learning; Theorem 2

4 Implications and conclusionsLinear special case; experimental TestsNo distortion resultsliterature revisitedConcluding remarksAl-Najjar, Baliga & Besanko Market Forces meet Behavioral Biases




Economics literature

The basic idea is old: Commitment alters outcomes in oligopoly

Delegation literatureEvolution of preferences





Delegation

Fershtman-Judd (1987) and others..

Key assumptions:players are fully rational, fully anticipating the strategicconsequences of their commitmentscommitments are observable

Details..





Evolution of preferences

Guth-Yaari (1991)JET special issue (2001)Dekel-Ely-Yilankaya (1989)Heifetz-Shannon-Spiegel (2003)

Key assumptions: players are fully rational and commitmentsare observable.

Details..





Accounting literature

Cost accounting as a compilation of “best practices”No rigid prescriptive recommendations on how to imbedcostRecommendation: be flexible; do what seems to work best

Empirical regularities

simplicityPrevalence of cost-plus-pricingCosting methodologies change slowly relative to prices





Accounting practices

Our model of costing procedure

Determine amount of sunk cost allocated as relevant costTextbooks recommends flexibility and have no rigidprescriptions.

Compute per-unit distortion to relevant costs and priceaccordingly

Firms forecast budgets of costs and sales based on recentexperience. E.g. unit cost based on recent output.

Reconcile actual and budgeted profitsVariances are the difference between actual and budgetedperformance. Hence, a firm can determine the impact of itscosting approach on economic profits.




Model overviewStatic price competitionLinear example





Static game

N firms engaged in differentiated product Bertrandcompetition

constant marginal cost cnRental cost of sunk capital Fn ≥ 0.

Firm n’s demand is qn = Dn(p), where p = (p1, . . . , pN).Dn is differentiable (and a bunch of other things..) andlog-supermodular,

∂2 log Dn(pn, p−n)

∂pn∂pm≥ 0.

Firm n’s objective measure of success is economic profit

πen(p) ≡ (pn − cn)Dn(p)− Fn





Cost Distortions and Accounting Profits

Firm n’s perception of economic profits is distorted:

It inflates its true marginal cost by a constant distortioncomponent, sn.sn is the part of sunk cost (mis-) allocated as variable cost.

The firm’s accounting profit (gross of unallocated sunkcost)

πn(p, sn) ≡ (pn − cn − sn)Dn(p).

This is the measure of performance relevant to themanager’s decision making





Coherence and Self-justification

Firms display a minimum degree of coherence:

Fn = 0 =⇒ sn = 0

Firms do not “make-up” fixed and sunk costs where there arenoneA more elaborate and detailed version of this assumption is inthe paper.

Justifications:

Psychological: Eyster, Arkes-AytonAccounting practices: Faithful representation; GAAPLong-run consistency





The Game with Cost Distortions

Given a vector of distortions s, we have a game Γ(s)

This is the same as the original game, except that thepayoff function of player n is πn(p, sn)

Vector of reaction functions

r(s) : PN → PN





A Simple Example to build Intuition(... and why it is misleading)

Two firms, n, m, each with marginal cost of 10.Demand for firm n is

Dn = 124− 2pn + 1.6pm.

Imagine that we are initially in a situation where no firmdistorts, then Nash equilibrium is pn = pm = 60.Now suppose the manager of firm 1 “mutates” so hedistorts with s = 10.





Why the Story in the Example is Incoherent

1 How would firms reach NE if cost distortions are,presumably, unobservable by opponents.

2 There is fundamental inconsistency in assuming that firmswho are confused about cost can figure out equilibrium byintrospection.

3 What if there is multiple equilibria in the pricing game.

ISSUES DEALT WITH IN THEOREM 1

4 Precisely what sort of mechanism gives rise to thedistortion ‘mutations’

ISSUES DEALT WITH IN THEOREM 2




adaptive learning; Theorem 1reinforcement learning; Theorem 2

Adaptive Learning: Motivation

We use (a slight modification of) the Milgrom-Roberts (1990)model of adaptive learning:

Boundedly rational players who only know their own payofffunctions and the prices of their rivals.

Player act adaptively...





Adaptive Learning: Details 1

Fix an integer γ ≥ 1

Start with an old equilibrium p, and suppose that schanges.Consider a sequence of price vectors

p = p0, p1, p2, . . .

At time t , look at the (γ-)recent past:

inf{pt−γ , . . . , pt−1} and sup{pt−γ , . . . , pt−1}





Adaptive Learning: Details 2

{pt} is an adaptive pricing adjustment for Γ(s) starting at p if atevery time t every player n plays a best response to a beliefwith support in the cube:

[inf{pt−γ , . . . , pt−1} , sup{pt−γ , . . . , pt−1}]

Milgrom-Roberts (90): Any adaptive sequence converges to theset of serially undominated strategy profiles.

This class includes as special cases:Fictitious play (with bounded memory)

Sequential best response dynamic

Cournot Dynamic





Theorem 1: Statement

Fix any:

Firm nVector of distortions by other firms s−n ≥ 0Any equilibrium p of Γ(s−n, sn = 0)

Then, there exists sn > 0 such that for any adaptive pricingadjustment {pt} for Γ(s−n, sn) starting at p there is a time Tsuch that:

πen(pt) > πe

n(p) for every t ≥ T





What can go wrong ..

Suppose the game has multiple equilibria

Start with (sn = 0, s−n) and an equilibrium p ofΓ(s−n, sn = 0)sn ↑ s′n > 0pt adjust to a new equilibrium p′ of Γ(s−n, s′n)

If p′ < p, then firm n is worse off under the cost distortion;While if p′ > p, then firm n is better off under the costdistortion;

The conclusion of the analysis hinges on equilibriumselection rather than the fundamentals of the game





Learning gives the right Comparative Statics

Suppose that p ≤ r(p, s). Then for any adaptive pricingadjustment {pt} for Γ(s) starting at p,

limt→∞

pt = inf{z ≥ p; z is a NE of Γ(s)}

This is basically Echenique (2003)

Theorem 1 requires more: it is not enough that prices increase,but payoffs must increase.





Adaptive Adjustments of Cost Distortions: Motivation

Each firm chooses from a finite grid of possible cost distortions

{0,∆, 2∆, . . . , K∆}

where ∆ > 0 is a small positive number

Costing methodologies change much more slowly thanprices

Firms reinforce the practices that seem to generate thehighest payoff





How are Payoffs Determined?

Given the prevailing equilibrium price from the last periodpτ−1,And given firms’s choice of distortions in the current periodsτ

Prices adjust, {pt}, generating a new equilibriumpτ = limt→∞ pt

Payoffs in round τ are those calculated at pτ





Problems

This is a well defined dynamic game. But there are problems:

Problem 1: Firms do not know the costing practices of theiropponents

Problem 2: It is not reasonable to assume that firms know theirpayoffs!





Learning models

We know of three learning models that can deal with gameswhere players do not observe others’ actions or know theirpayoff function:

Hart-Mas-Colell (Econometrica 2001)Friedman-Mezzeti (JET 2001)Milgrom and Roberts (GEB 91)

All of these models require experimentation.





Experimentation: Details

We consider a model of random, infrequent, experimentation (aal Milgrom-Roberts, 1991)

Firms experiment with new distortions at randomProbability of experimentation εnτ

In an experimentation period, the firm chooses uniformlyfrom

{0,∆, 2∆, . . . , K∆}

Firms experiment independently from each other and overtime.Experimentations are rare: εnτ → 0.





Theorem 2

TheoremAll firms eventually suffer from the sunk cost bias and choose apositive distortion is all non-experimental periods, almost surely.

Intuition:When firms use adaptive pricing adjustments, choosingzero distortion is a“dominate” action (Theorem 1).Hence, the expected payoff from a small positive distortionto relevant costs is greater than the expected payoff to zerodistortion.Expected payoffs are eventually reflected in realizedaverage payoffs.




Linear special case; experimental TestsNo distortion resultsliterature revisitedConcluding remarks

Symmetric Linear Model

Firms face symmetric linear demand with equal marginal costs.In this case, the distortion game is itself:

supermodularDominance solvableHas a unique correlated equilibrium, which is in purestrategies.

The dynamic of Theorem 2 converges almost surely to theequilibrium level of distortions.The magnitude of the limiting level of distortion is the same asthe one derived from solving a two-stage game.





Experimental Test

Offerman and Potter’s (2003) tested a two-firm symmetricmodel:

Each firm has marginal cost of 10.Demand for firm n is

Dn = 124− 2pn + 1.6pm.

Symmetric Nash equilibrium prices is 60.

Our model predicts a price of 78.18In two treatments, Offerman and Potters obtain prices of 75.65and 72.73





No Distortion Results

Our explanation of the sunk bias implies that no such biasshould be observed in:

Homogenous good Bertrand competitionMonopolyIn Offerman-Potter’s experiment, subject in a monopoly positiondo not display the sunk cost bias.

Perfect competitionWe only have indirect evidence. A leading managerialaccounting textbook (Maher, Stickney and Weil) notes:“Cost-based pricing is far less prevalent in Japaneseprocess-type industries (for example, chemicals, oil, and steel).”





Evolution of Preferences Literature (EPL)

Small point: Ours is a model based on learning rather thanevolutionResults in EPL have no bite when preferences are notobservableEPL usually does not

model the stage gamedeal with multiple equilibria and comparative statics issues

We look at the consequences of a specific, psychologicallyplausible preference distortionThe logic of the EPL literature is independent of whetherthere is sunk cost





Delegation Literature (DL)

As in the EPL

The logic of the DL literature is independent of whetherthere is sunk costDL usually does not deal with multiple equilibria andcomparative statics issues

Our model predicts sunk cost effects in experiments,where delegation is not an issueSophisticated backward induction vs. naive adaptivelearningThere is no evidence of a “vast right-wing conspiracyagainst” consumers ... but there is lots of evidence of acollective, self-reinforcing confusion about cost





Concluding remarks

Methodological points:Evidence whether firms play equilibrim in high-stakedecisions, like pricing, is, at best, scant;The standard argument is that rational behavior andequilibrium are plausible theoretical predictions becausesystematic deviations from rationality will be eliminated bythe forces of competition, learning, and evoltion

What we do in this paper:We examine whether psychological biases disappear onceconfronted with competitive forces in the context of costallocations and pricing decisions;We show that whether or not biases disappear depends onmarket structure, thus generating testable predictions onthe way biases vary across environments





THE END !!


market forces meet behavioral biases · 2006-05-14 · market forces meet behavioral biases cost...

Documents