Reputation Leaders and Quality Laggards: The Incentive Structure in Markets with Both Private and Collective Reputations

Reputation Leaders, Quality Laggards:Incentive Structure in Markets withBoth Private and CollectiveReputations

Marco Costanigro, Craig A. Bond and Jill J. McCluskey1

(Original submitted May 2011, revision received September 2011, acceptedNovember 2011.)

Abstract

A theoretical model is developed to illustrate the economic incentives to invest inquality in markets with a dual reputation structure: private (firm reputation)and collective (regional reputation). Numerical dynamic programming tech-niques are then used to simulate firms’ strategic behaviour, and competitive out-comes are compared to the optimal investment of a regional planner. Marketand product characteristics inducing asymmetric and ⁄or sub-optimal investmentstrategies, potentially destabilising for the region, are investigated.

Keywords: Collective reputation; dynamic games; firm reputation; geographicalindications; information and product quality.

JEL classifications: L14, L15, Q14.

1. Introduction

In markets where consumers are uncertain about product quality until after con-sumption (experience goods and services (Nelson, 1970)), reputations play animportant role. Product, firm, regional names (such as geographical indications), orother similar signals are often (imperfectly) associated by consumers with qualityoutcomes. Realising that names and reputations can be private or collective in nat-ure, an extensive theoretical and empirical literature has been developed on product,brand, regional and franchise reputations (e.g. Klein and Leffler, 1981; Shapiro,1982; Kreps and Wilson, 1982; Jarrell and Peltzman, 1985; Gale and Rosenthal,

1Marco Costanigro and Craig Bond are with the Department of Agricultural and ResourceEconomics, Colorado State University, USA. E-mail: [email protected] for

correspondence. Jill McCluskey is Professor, School of Economic Sciences, Washington StateUniversity, USA. The authors wish to thank without implicating Ron Mittelhammer and JonYoder for helpful comments on the early stages of this research, and also the reviewers andeditors for their help with the final version.

Journal of Agricultural Economicsdoi: 10.1111/j.1477-9552.2011.00331.x

� 2012 The Agricultural Economics Society. Published by Blackwell Publishing,

9600 Garsington Road, Oxford OX4 2DQ, UK, and 350 Main Street, Malden, MA 02148, USA.

1994; Barber and Darrough, 1996; Tadelis, 1999, 2003 for private reputations; Blairand Kaserman, 1994; Tirole, 1996; Winfree and McCluskey, 2005 for collective rep-utations).Even though most of the literature focuses on either private or collective reputa-

tions, in many instances they are coexistent. In addition to private brand reputa-tion, products such as Japanese cars, Italian shoes, and Swiss watches (or banks)also share a collective reputation. Agricultural products pairing brand names andcertified indications of origin (e.g. Roquefort cheese, Scotch whiskeys, prosciutto diParma) are common. In the wine industry, each winery has its own brand name(s),yet the region of production is so important that retailers often display their wineofferings by country and region of origin to facilitate consumer choice.Few studies have examined the dual impact of private and collective reputation

indicators on firms’ investment in quality. Landon and Smith (1998) studied themarket for Bordeaux wines to show that models including proxies for firm reputa-tion (past quality scores in specialised magazines) and collective reputations (region-specific intercept shifters) are more predictive than private-only or collective-onlymodels. In a related paper, Costanigro et al. (2010) highlighted how names and rep-utations nest within each other to identify producers with increasing specificity.They found that reputation premia for good names tend to migrate from collectiveto specific (private) names as product prices increase, mainly because the greater‘cost of being wrong’ (buying poor quality at high prices) justifies the extra searchcost necessary to switch from using few aggregate names to more numerous andmore specific firm labels. In a recent article, Menapace and Moschini (2010)extended Shapiro’s (1983) study on private reputations to analyze the case in whichcollective reputations associated with geographical indications (GIs) are used inaddition to private names associated with trademarks. Their principal result is thatwhen GIs impose minimum quality standards (and consumers are aware of them),2

the cost of establishing reputations for high quality diminishes and so does the pre-mium consumers need to pay.The debate regarding the proper use and legislation regarding GIs is on-going,

but, as Joslin (2006) puts it, it is clear that GIs are here to stay. Indeed, GIs arebecoming more common in ‘new world’ countries (North America, South Amer-ica, Australia) as well as in Europe. Markets with dual (private-collective) reputa-tion structure are becoming increasingly common. It is therefore relevant toinvestigate whether the economic incentives associated with private and collectivereputations can be studied independently of each other (as is done in most of theexisting literature), or whether some significant interaction arises when the reputa-tion structure is dual.

2A significant stream of literature, referenced in Menapace and Moschini (2010), considersthe case in which GIs set minimum quality standards. Provided that consumers are aware of

the minimum standards, then GIs help producers in credibly signalling quality to inexperi-enced consumers. In the current article, we consider the more general case in which consum-ers infer that the quality of two producers within the same region is correlated. Rather than

acquiring information ex ante and then deciding on whether to buy, we model a world inwhich consumers learn ex post from their multiple experiences. In our opinion, this processfits better the case of agricultural products which are repeatedly purchased at a relatively lowcost.

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We study producers’ incentives to invest in quality when firms have their own pri-vate brand names but also share a common name and reputation. To do so, we simu-late a dynamic game in which profit-maximising firms invest in quality to maximisetheir returns from private and collective reputations. Model parameters are cali-brated using data from the California wine industry, tying the simulation to an expe-rience good market.3 The primary objectives are two-fold: (i) to study how the(intra-regional) quality-reputation dynamics may differ from markets where reputa-tions are either exclusively private or collective; and (ii) to investigate how market-specific or product-specific characteristics may alter the incentives in markets withdual reputations. Given the presence of both types of reputation, our model (concep-tually) nests the private name only model of Shapiro (1982, 1983) and the collective-only model of Winfree and McCluskey (2005) as special cases. The former was thefirst to use a dynamic optimization framework to model markets with private namesand showed that reducing consumers’ ability to assess product quality weakens theincentives to invest in it. The latter showed how collective reputations are essentiallypublic good resources, and as such are subject to the tragedy of the commons.Our study contributes to the literature on several fronts. First, a general theoreti-

cal representation of the firm’s decision process under the assumed dual structure ofreputation is developed. We then consider the case of a regional planner maximisingthe profits of the whole production district, providing insights for the analysis ofproducer and industry (district) welfare. Under this setting, the implicit assumptionis that all firms in a region collaborate, or a single decision maker owns the com-plete taxonomy of private and collective names)4. Regardless of the interpretation,however, we maintain the assumption of price-taking behaviour for each firm (inthe case of collaboration) or within each marketing unit (in the case of a single firmwith multiple products or brands). We show that under such a structure, the publicgood benefits of collective reputation are internalised, and more efficient investment(in terms of maximising returns to the region and firm) results. Conversely, we showthat a lack of cooperation among a fixed number of competing firms results is effi-ciency losses relative to this outcome.Second, we study how information lags (i.e. the ‘speed of consumer learning’

from Shapiro, 1982) and price-range market segments (determining the ‘cost ofbeing wrong’ in Landon and Smith, 1998) interact in determining equilibrium repu-tations and industry welfare. We show that, under specific conditions, steady-stateprivate reputations can be either stronger or weaker than the common collectivereputation when firms share the same production technology and face the sameprice incentives. Finally, we consider the case in which the investment in quality ofone agent, referred to as a reputation leader, affects collective reputation more thanthe other firms in the region. The rationale is that, given a positive cost of learningand forming quality expectations, some consumers may consider the quality of thegoods produced by a specific firm as a good indicator or predictor of the quality of

3We consider wine as an experience good for the purposes of this analysis. However, onecould make the argument that wine is a combination of an experience good and a credencegood (perhaps stemming from advertising). If that is the case, then the analysis is more com-

plicated and not all of our results will hold. A theoretical analysis of collective and firm repu-tations of a combination of experience and credence goods is beyond the scope of this paper.4 This would be the case for multi-brand or multi-product firms such as Nestle or Kraft.

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the whole district. This, we find, has a non-trivial effect on quality investments andoverall efficiency of the district.

2. Theoretical Model and Solution Mechanism

The theoretical framework developed here is a dynamic game to account for strate-gic behaviour between producers. We seek to model the case in which: (i) a fixed,large number of N risk-neutral producers in a production district maximise theirown net present value of profits over an infinite time horizon, subject to the evolu-tion of beliefs about regional and firm reputations; (ii) all firms produce a fixed,constant quantity, but each firm i chooses its quality level, which is costly5; and(iii) firm and collective reputations in each time period are determined via (deter-ministic) Markov processes, which are partially controlled by producers. Assump-tion (ii) is consistent with the model in Winfree and McCluskey (2005), in which anexogenous price curve p(R) is related to (collective) reputation R, but firms do notcompete for market share in the quantity dimension. As in Shapiro (1983), weabstract away from pricing decisions by firms on the basis of market power, andconcentrate on the incentives related to investment in quality, which leads to afirm-specific reputation and region-specific collective reputation, which in turnjointly determine price.It is assumed that, when firms compete, each producer makes a quality invest-

ment decision taking the response functions of the others as given (a la Cournot).Assuming a discount factor equal to d for each firm, we model the maximisationproblem solved by firm i as:

Vðri; r�i;RÞ ¼ maxqi�0

X1t¼0

dt½piðri;t;RtÞ � ciðqi;tÞ�

s:t: ri;tþ1 ¼ ri;t þ cbiðqi;t � ri;tÞrj;tþ1 ¼ rj;t þ cbjðq�j;tðri; r�i;RÞ � rj;tÞ8j 6¼ i

Rtþ1 ¼ Rt þ c wiqi;t þXj6¼i

wjq�j;tðri; r�i;RÞ � Rt

!;

ð1Þ

where ri is the private reputation state variable for firm i, r)i represents the (vectorof) private reputations of all the other firms in the district, and R is the region’s col-lective reputation. Indicating a (discrete) time period with t, the cost of producingat quality level qi,t is captured by the function ci(qi,t), while the market price of theproduct depends on reputations according to pi(ri,t, Rt).The state-transition equation ri;tþ1 ¼ ri;t þ cbiðqi;t � ri;tÞ portrays how, on the con-

sumer side, private firm reputations are updated (on average) based on the discrep-ancy between reputations and current quality output. The parameter c simulates theinformation lag between the time of production and the time when the quality levelis revealed. This can be thought of as the market or product-specific ‘speed of

5 The presence of collective reputation implies that firms in the production region may sharea comparative advantage relative to firms outside of the production region. Such comparativeadvantage could be exogenous. Since our focus is limited to a single production region, thequality choice is fully endogenous.

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consumer learning’ of Shapiro (1982). bi � (0,1) captures firm-specific brand visibil-ity. Cross-firm differences in bi may be determined by multiple factors such asmedia coverage, expert reviews or firm size.6

The transition equations rj;tþ1 ¼ rj;t þ cbjðq�j;tðri; r�i;RÞ � rj;tÞ8j 6¼ i represent thepaths of the private reputations of other firms in the industry and are defined asfunctions of the state-contingent control q�j;tðri; r�i;RÞfor firm j such that this controlmaximises the net present value of firm j’s profits given that the other agents pursuetheirs. Overall, the structure of the model is one where each firm can observe pri-vate (and collective) reputations, and anticipates that each firm will play a Nashstrategy subject to the evolution of the complete system.The state-transition equation for collective reputation, Rtþ1 ¼ Rt þ c

�wiqi;t

þPj6¼i

wjq�j;tðri; r�i;RÞ � Rt

�, follows the specification inWinfree andMcCluskey (2005).7

This equation provides the mechanism whereby consumers’ expectations regardingaggregate (average) regional quality enter the model as a weighted average of the firm-specific reputations, with full endogeneity implying wi ‡ 0 and

Pi

wi ¼ 1. While previ-ous work has set the influence of firm quality on collective reputation to the reciprocalof the number of firms in the region, there is no reason to necessarily believe, a priori,that wi = 1 ⁄N. The existence of one or more ‘reputation leaders’, for which wi > 1 ⁄N,corresponds to a situation in which a sizable number of consumers consider the perfor-mance of a particular firm as a good indicator of the quality of the whole region. Thiscould be due, for example, to a larger market share of the reputation leader, its earlyentrance in the market, or expected trickle-down effects of technological ⁄managerialleadership to the other firms in the region (all of which are exogenous in the model).The simplifying assumptions of exogeneity of the speed of consumer learning (c),

firm visibility (bi), and reputation leadership (wi) parameters are consistent with thestream of literature we are extending (notably Shapiro, 1982; and Winfree andMcCluskey, 2005). In reality, these assumptions may not hold in the long run, asfirms may be able to increase their visibility or take actions to affect their influencein the collective reputation, perhaps by investing in advertisement, expanding mar-ket share, or by other means. Explicitly modelling these processes would introduceadditional factors over which firms optimise without substantially adding insightinto investment quality decisions (conditional on visibility, reputation leadershipand speed of consumer learning).8

Also consistent with prior literature, we proxy the evolution of consumers’ beliefsand behaviour via the state-transition equations (which describe how consumersupdate their quality expectations) and the price function pi(ri,t, Rt), which capturesequilibrium price as aggregate willingness to pay for a specific reputation level.Given many firms and consumers and so long as all the relevant characteris-tics ⁄attributes are embedded in the measures of expected quality, indexed by ri and

6Here, we take these parameters as exogenous.7 Strictly speaking, Winfree and McCluskey (2005) assumed uniform weighting (i.e., wk ¼ 1

N)of each firms’ investment decision.8An anonymous reviewer suggested that firm visibility and reputation leadership, eventhough they are different concepts, may very well be correlated. This is certainly possible,and could be modelled by choosing appropriate values for the exogenous parameters repre-senting these dimensions.

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R, then the price function pi(ri,t, Rt) can be thought of as a hedonic price relation-ship, which firms consider as an exogenous determinant of their quality choices.9 Inother words, the price function provides a reduced-form shortcut to capture fromreal data how consumers learn and value quality when both private and collectivereputations are at play.10 It should also be noted that this relationship captures adegree of heterogeneity across the consuming population in terms of the informa-tion they posses about a given product and ⁄or differences in tastes and preferences.The Markov-perfect equilibrium for this discrete-time, N-agent game is thus char-

acterised by a set of N simultaneous Bellman equations of the form:

Viðri;r�i;RÞ¼maxqi�0

(piðri;RÞ�ciðqiÞþdVi

r1þcb1 q�1ðr1; . . . ;rN;RÞ�r1

� �;

r2þcb2 q�2ðr1; . . . ;rN;RÞ�r2� �

; . . . ;riþcbi½qi�ri�; . . . ;

rNþcbNðq�Nðr1; . . . ;rN;RÞ�rNÞ;Rþc wiqiþXj6¼i

wjq�j ðr1; . . . ;rN;RÞ�R

" #!):

ð2Þ

The unknowns in the system are the (closed-loop) policy functions q�i ðri;r�i;RÞandthe firm-specific value functions Vi(ri,r)i,R). Given the dimensionality of the prob-lem and the complexity of the mathematical solution, numerical analysis is used tosolve the game and characterise the key results. Following Miranda and Fackler(2002), the solution is approximated using a 9-node Chebychev polynomial approxi-mation to the unknown value function. The approximation is then used to representthe policy functions and simulate results.11

To reduce the dimensionality of the game in the simulation exercises, the numberof firms is restricted to two.12 Regardless of the ‘duopoly in reputation’ setup, it isstill assumed that firms have no market power, and the only way a firm can influ-ence product prices is by affecting its reputation via quality output. In other words,we model an incentive structure consistent with that of a market with many firmsand dual reputation structure, but choose a two firm illustration for tractability. Itis understood that, because of the public good nature of collective reputations,reducing the number of firms in the district increases equilibrium qualities and repu-tations, moving them closer to the industry-wide optimal quality investment of theregional planner (Winfree and McCluskey, 2005). Accordingly, our interpretation ofthe results is qualitative rather than quantitative.

9 The case of market power is not considered here, and thus the model best describes markets

in which there are many firms and production districts (e.g. wine). This is consistent with themodels of private reputations presented by Shapiro (1983) and collective reputation presentedby Winfree and McCluskey (2005).10We thank an anonymous reviewer for this intuition.11 The software of choice for our simulation was the CompEcon toolbox in MATLAB. Inter-ested readers may refer to the Appendix for relevant first-order analytical conditions of the

joint reputation game and the industry planning problem.12 This eases the complexity of programming, diminishes simulation running time and simpli-fies the graphical representation and interpretation of our results.

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3. Function Parameterization

Numerical dynamic programming techniques require specific functional forms forimplementation. Instead of assuming a functional form and a set of parameters, weutilise a California wine dataset to estimate a flexible hedonic model capturing how,in equilibrium, quality output and reputations relate to product prices.13 Reputa-tions play a pivotal role in wine markets, and as such, the wine industry offers avalid framework within which reputation dynamics can be studied, while obtainingsome reasonably general results.The dataset consists of 9,261 observations obtained from the Wine Spectator

(issues from 1992 to 2003) spanning ten vintages (1991–2000) of blind tasting qual-ity,14 scores (SCORE) for California red wines (see Table 1). Each observationincludes the producing winery, the American Viticultural Area (51 AVA in total),the vintage, and the price (CPI adjusted to the 2003 base year). The chosen specifi-cation is a quadratic form with an interaction term:

Plikt ¼ aþ b1~rit þ b2~r2it þ b3

~Rkt þ b4~R2kt þ b5

~Rkt~rit; ð3Þ

where Plikt is the price of the lth wine produced by winery i from region k in year tand ~r and ~R are proxies for private and collective reputations, respectively. Mimick-ing the state-transition equations in the theoretical model, we compute these reputa-tion proxies as moving average processes of previous quality rating scores.15

Table 1

Descriptive statistics of dependent and independent variables

PRICE* SCORE ~r ~R

N� 9,261 9,261 7,717 9,074

Mean $37.18 86.54 86.65 86.25Min $6.05 60 62.00 74.67p25 $19.76 84 85.00 85.42p50 $27.12 87 87.00 86.24

p75 $39.78 89 88.48 87.68Max $2,140 99 96.63 91.00

*CPI adjusted to 2003.

�Differences in number of observations across variables are to be attributed to non-AVAwines, scarcely populated series of quality ratings or missing data.

13 This model is a modification of the model by Costanigro et al. (2010).14A justification for the use of wine ratings as proxies for quality is that they are blind qual-ity assessments by experts, exogenous to prices.15More formally, and using the subscript i for the wine, j for the winery and k for theregions, the kth AVA reputation is defined as ~Rkt ¼ 1

2

�~Rkðt�1Þ þ avg

k

�SCOREijkðt�1Þ

��, where t

is the issue year of the Wine Spectator magazine, and avgk

the average operator applied to all

wines produced in the kth AVA, rated in period t)1. The analogous private reputation con-struct relative to the jth firm is ~rjt ¼ 1

2

�~rjðt�1Þ þ avg

j

�SCOREijkðt�1Þ

��. The first observation of

each series is missing, and the second is calculated using the average quality score of the firstyear in which a winery ⁄AVA appears in the dataset, producing 6,115 complete observations.

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Following Costanigro et al. (2010), the hedonic model in (3) is estimated via quan-tile regression (Koenker and Bassett, 1978) at different conditional quantiles (the15th, 50th, and 75th), in order to capture the changing structure of the reputationdynamics across wines in different price segments. While the wide range of pricesobserved in the wine market is somewhat unique, simulation results based on the dif-ferent pricing functions can be (roughly) interpreted as illustrating the incentive struc-ture in markets for cheap, medium and expensive products. Consistent withCostanigro et al. (2010), we expect private reputation to become more valuable (rela-tive to collective), the more expensive is the product. The intuition is that the increasedcognitive and search effort necessary to form quality expectations for the large num-ber of firm names is justified only when the price of the good is high enough.In quantile regression, parameters estimates are obtained by solving the minimiza-

tion problem: minb2<p

PNi¼1

qs

�yi � x0ib

�, where qs represents a function which, by asymmet-

rically weighting residuals, yields the sth conditional quantile 2 ½0; 1�, y is theregressand, x are the regressors, and p specifies the number of parameters to be esti-mated. Since the weighting function differs across quantiles, our estimations producethree sets of benchmark parameters, which may be interpreted as distinct subsets ofthe market with differing: (i) magnitudes of the marginal effects of reputation changes(both private and collective); (ii) relationships between the marginal relative effects ofprivate vs. collective reputations.16 Regression results are reported in Table 2.Given that the minimum ⁄maximum private and collective reputation measures

observed in the sample are ri 2 ½62:00; 96:63�8i and R 2 ½74:66; 91:00�, our results

Table 2

Pricing equations for the low, median and high price segments (quantile regression results)

Quantile 15 Quantile 50 Quantile 75

~r )20.96*** (3.17) )56.62*** (3.55) )108.38*** (12.65)~r2 0.04** (0.01) 0.18*** (0.02) 0.47*** (0.06)~R )23.02*** (5.43) )56.66*** (5.17) )98.38*** (13.07)~R2 0.05 (0.04) 0.19*** (0.03) 0.41*** (0.08)~R � ~r 0.18*** (0.04) 0.32*** (0.03) 0.37*** (0.07)Constant 1,766.38*** (248.50) 4,659.23*** (281.51) 8,548.18*** (699.18)N = 6,115Price 19.76 27.12 39.78

Mean r 85.00 87.00 88.48Mean R 85.42 86.24 87.68Marg r� $1.12 $2.81 $7.17

Marg R� $1.78 $3.54 $6.80

Standard errors in parentheses.**Significant at 5%, ***Significant at 1%.

�Marginal effects evaluated at means.

16 In the simulations that follow, it is assumed that all firms in a production district face theprice function for that quantile for all time periods in the simulation; that is, for each quan-tile q, pqi ðri;t;RtÞ ¼ pqðri;t;RtÞ8i; t, or equivalently, firms take their price function as given atthe beginning of the planning horizon, and do not or cannot migrate across quantiles.

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suggest that the predominant relationships are pr(ri,R) > 0, pR(ri,R) > 0,prr(ri,R) > 0, pRR(ri,R) ‡ 0, and prR(ri,R) > 0, for all quantiles. With the excep-tion of the private-collective cross effects, which are perhaps ambiguous on apriori grounds,17 all signs meet theoretical expectations (see Rosen, 1981, on the‘economics of superstars’ for an argument supporting the increasing marginalbenefit of reputation), with the proviso that the complementary relationshipbetween collective and private perceptions of quality might be a wine-industryspecific result. Examined across quantiles, empirical results show that the mar-ginal impact of an increase in reputation is generally greater for wines in thehigh-price market segment.In contrast to the price data, information on the cost side of the market is

unavailable. Therefore, we calibrate a cost function that ensures a unique steady-state equilibrium falling within the range of the observed data for the median quan-tile results reported in Table 2. For all firms in the production district, we assume alinear marginal cost function of the form c¢i(qi) = c¢(qi) = a1 + a2qi, such that themarginal cost of quality investment is increasing in quality.18 While we make noclaims as to the representativeness of this function for the industry as a whole, itallows for a numerical solution to the problem, as well as offering a first-orderapproximation to the underlying form of the cost functions. Again, the reader iscautioned that more attention should be paid to qualitative model indications,rather than the specific quantitative results.Based on these assumptions, the functional forms relevant for the simulation of

our two-player game, are: c¢(qi) = )323.571 + 3.7857qi for all quantiles, andprðri;RÞ ¼ �56:62þ 0:36ri þ 0:32R, and pRðri;RÞ ¼ �56:66þ 0:38Rþ 0:32ri,i = 1,2, for the median quantile. Marginal price functions for the 15th and 75thconditional quantiles can be derived from Table 2, and it is assumed that all firmsdiscount the future with a factor of d = 0.95.19

4. Results

4.1. Policy response function and general incentives (median quantile)

To illustrate the fundamental incentives of each firm in the dual reputation scenario,we first consider the case of fully homogeneous firms (that is b1 = b2 and w1 = w2).Figure 1 presents the policy (best response) function of Firm 1, assuming uniformspeed of adjustment parameters (c = 0.2, b1 = b2 = 1), and no reputation leader(w1 = w2 = 0.5). In this and all the subsequent figures, the vertical axis measuresquality (or, considering our data, the corresponding wine spectator score). Note thatthe overall speed of adjustment parameter is less than one, indicating a lag betweeninvestment in quality and consumers’ updating of reputations. In the first panel, wepresent a three-dimensional cross section in which Firm 1’s optimal quality investmentis mapped against the private reputation of Firm 1 and Firm 2 while collective

17 The only novel empirical result relates to the finding that, for California wineries, privateand collective reputations are complements.18 The adoption of identical marginal cost functions seems reasonable for firms operating inthe same production district.19 This implies an approximate interest rate of 5.3%.

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reputation is held constant at the node closest to the steady-state value.20 In the lowerpanel, Firm 1’s reputation and collective reputation vary, while Firm 2’s reputation isheld constant. These graphs thus show firm i’s investment decision is conditional onthe values of the state variables at the time of the decision, with slopes indicating themarginal response to a change in one of the state variables.In each case, we see that optimal investment in quality is increasing in own pri-

vate reputation, the other firm’s reputation, and the collective reputation, thoughthe magnitudes differ. The first panel, which holds collective reputation constant,shows that Firm 1’s investment decision is relatively more responsive to its own rep-utation than that of Firm 2, as given by the slope of the optimal investment surface.In the second panel, given the parameterization of the model, it can be seen that

9694

9290

88

Private Rep Firm 1 Private Rep Firm 2

Private Rep Firm 1 Collective reputation

8684

82 8284

8688 90

9294

9

86.2

86.4

86.6

86.8

87

87.2

87.4

86.2

86.4

86.6

86.8

87

87.2

87.4

Opt

imal

qua

llity

inve

stm

ent

Opt

imal

qua

llity

inve

stm

ent

Optimal Policy Rule, Firm 1, Reputation Game, Collective Rep = 86.8462

Optimal Policy Rule, Firm 1, Reputation Game, Firm 2 Rep = 86.8462

85

85.5

86.5

87.5

88

87

86

9694

9290

8886

8482 82 84

8688 90

9294

9

85

85.5

86.5

87.5

88

87

86

Figure 1. Policy response functions of Firm 1. Homogenous firms, w1 = w2 = 0.5, c = 0.2,

b1 = b2 = 1. First panel: Firm 1 Optimal Policy Rule, Collective Rep. Fixed. Second panel:Firm 1 Optimal Policy Rule, Firm 2 Rep. Fixed

20At solution nodes, the solution to the value functions embodied in the Bellman equationsare exact; off these nodes, mean errors are of the magnitude 2(10)9).

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when Firm 2’s reputation is fixed near the steady state level, there is approximatelyan equal response by Firm 1 to an increase in own reputation and collective reputa-tion. In both cases, the slope of the value function (not shown) implies that r)i andR have positive marginal values,21 but the investment response is not fully symmet-ric: a unit increase in the Firm 2’s reputation or the collective reputation will not bematched by a corresponding increase in investment by Firm 1. Though it is larger isthe case of the collective reputation due to the dilution of the corresponding bene-fits. To simplify, under a dual reputation structure, returns from private reputationsmitigate the free-riding behaviour associated with common-property resources,though this internalisation is not complete. This result is analogous to Carriquiryand Babcock’s (2007) findings for the case of a duopoly with collective reputations.Figure 2 illustrates the paths to the steady states and the role played by the pricing

equations, again for the case of homogenous firms. Initial private reputations are setat low level for Firm 1 and high for Firm 2 (r1 < R < r2). Regardless of the initialconditions, firm homogeneity implies that private reputations, collective reputations,and quality investment all converge to a common steady state. Also note that whenthe system is in equilibrium, reputations and quality choices coincide

��rs1 ¼ �qs

1 ¼�rs2 ¼ �qs

2 ¼ �Rs�. The speed of adjustment parameters (c and bi) determine the amount

of time required to reach the steady-state, with higher parameter values inducing arapid approach. The main result here is that the equilibrium quality and reputationsincrease from the low to the high conditional quantiles (Figure 2). While this result isconsistent with theoretical expectations (see figure III in Shapiro, 1983), in our simula-tions it is driven by the empirical estimation of the pricing function, rather than by apriori choices of parameters. An interpretation is that, since consumers are willing topay more for good reputations when facing high product prices (the cost of ‘beingwrong is higher’), in the higher price segments producers realise greater returns frominvesting in quality. This, in turn, increases the equilibrium quality and reputations.

4.2. Equilibrium quality, efficiency and polar cases

Based on theoretical expectations, two principal factors will influence investments inquality when private and collective reputations coexist: the degree to which consumers

Quantile 15 Quantile 50 Quantile 75

r1r1r1

r2 r2r2

RR

R

Figure 2. Paths to steady state for three conditional quantile price functions. Homogenousfirms, w1 = w2 = 0.5, c = 0.2, b1 = b2 = 1

21Given the price function, this marginal value (co-state) is not only positive, but increasingin r)i and R, though this result is more pronounced once heterogeneity is introduced.

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are able to immediately assess quality (as in Shapiro, 1982), and the ‘public good’dynamics arising from the presence of a collective name (which implies an inefficientinvestment in quality, as shown in Winfree and McCluskey, 2005).22 By specifyingalternative parameters for the simulation the effects of these specific market condi-tions or product characteristics on investment in quality can be investigated.We consider two polar scenarios to be used as benchmarks. In the first, the dual

reputation competitive scenario represented by equation (1) is modified to modelthe decisions of a regional planner maximising industry-wide profits. The intent hereis to identify how much more quality investment (with respect to competitive out-comes) would be made by the planner, representing producers fully cooperating andsustaining cooperation (or the amalgamation of all firms into a single monopoly).In the second case, firm visibility parameters are set to zero and firms are left tomaximise their own profits, thereby modelling the case of an industry with only col-lective reputations (or a monopoly with no separate brands).23

The regional planner will invest in quality so that the marginal cost of investment foreach firm equals the discounted marginal benefits for the industry, thereby includingthe total contribution to both private and collective reputations. In the dual reputationstrategic game, each firm also considers the marginal value of their own and collectivereputations, but positive externalities accruing to other firms are not internalised. Inthe collective-only model, these marginal benefits are smaller still, as the inability toinfluence private reputations ðVi;rið�Þcbi ¼ 0Þ induces even less investment.Figure 3 illustrates the results by juxtaposing, for various parameterizations, the

equilibrium reputations under the regional planner (dual reputation cooperative),the corresponding strategic game (dual reputation non-cooperative), and the collec-tive-only game (collective non-cooperative).24 As expected, the level of investmentin quality is increasing in the aggregate ‘speed of adjustment’ term, cbi: the longerthe time lag between quality investment and the realisation of the associatedresponse in revenues, the more firms will discount the value of reputations and pro-

22 In this case, ‘inefficiency’ is defined as a deviation from the optimal levels of investment ofFirm 1 and Firm 2 jointly, resulting in a lower net present value of net benefits for the regionthan is possible; that is, a different solution than that of the industry planner ⁄monopolist

model in the Appendix. As such, the accounting stance is from the standpoint of producersin the region. On the consumer side, we assume a non-autarkic region such that a full portfo-lio of reputation structures are represented in the market; i.e. regardless of regional producer

behaviour, all consumers have access to products of varying private and public reputations atthe market price.23 In more detail, the regional planner’s solution is obtained by maximising the sum of profits

across firms, subject to the equations of motion (see Appendix) and exogenous pricing struc-ture. The parameterization of the collective-only model is slightly more problematic: whilesetting b1 = b2 = 0 serves the purpose of dampening to zero the marginal benefits from pri-

vate reputation, for the sake of comparison we must set the private reputation constant atsome level in the pricing equation (it would be misleading to simply truncate the pricingfunction to Pikt ¼ aþ b3

~Rkt þ b4~R2kt) and the point chosen will influence results. In order to

keep the results as conservative as possible, private reputations for each firm are set at the

‘optimal’ steady state levels obtained in the regional planner scenario.24Note that because the firms are homogenous in this simulation, in the long-run private andcollective reputations converge.

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duce at lower quality. While differences are relatively small at steady state, largervalues of cbi induce a much more rapid convergence to the solution.The ratios between the two non-cooperative outcomes and the regional planner

solutions (in percentage terms in Figure 3) provide a measure of industry losses dueto lack of cooperation. Interestingly, even though the magnitude of the investmentin quality is increasing in the speed of adjustment, inefficiency losses are largestwhen consumers discover quality instantaneously (c = b1 = b2 = 1), and each firmimmediately sets quality investment to the long-run steady-state level.25 Conversely,the inefficiency is smaller when quality is difficult to observe. The interpretation isthat, when reputations are hard to build because of exogenous factors, returns frominvesting in quality are not capitalised in either pricing function, and there is simply

85

85.5

86

86.5

87

87.5

γ = βi = 1 γ = 1,βi = 0.05 γ = 0 .2,βi = 1 γ = 0 .2,βi = 0 .05

Dual Rep. cooperative Dual Rep. noncooperative Collective noncooperative

99.21%

99.55%

99.44%99.43%

98.40% 99.02%99.50%98.79%

Figure 3. Equilibrium reputations ⁄quality for games with dual (cooperative, non-coopera-

tive) and collective only (non-cooperativea) reputation structures. Ratios between cooperativeand non-cooperative outcomes are in percentages. Speed of adjustment decreases from theleft ðc � bi ¼ 1Þ to the right quadrant ðc � bi ¼ 0:01Þ. Homogeneous firmsb ðb1 ¼ b2Þ, median

quantile pricing equation. (a) private reputations are set constant at the dual cooperativeequilibrium. (b) homogenous firms imply that �r1 ¼ �R ¼ �r2 (see Figure 2)

25 The fact that equilibrium outcomes are quite close to 100% is a direct consequence ofreducing to two the number of firms in the district. The magnitude of the inefficiency will bemuch more significant when more than two firms are present, but the relative efficiency rank-ings across the different scenarios will remain unchanged.

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not much to lose from lack of cooperation. From a policy standpoint, this suggeststhat regulators wishing to increase product quality should first increase transparencyand consumers’ ability to recognise quality, and only subsequently target producers’free-riding behaviour.

4.3. Reputation leaders and quality laggards

We now relax the assumption of firm homogeneity to study the reputation dynamicsinduced by differential availability of information regarding quality performance andconsumer perceptions. Two cases are considered: one in which consumers can moreeasily update their expectations on the quality output of certain firms (which isdepicted by allowing for variation across bi) and one in which consumers use the qual-ity of a specific firm as an indicator or predictor of the quality of the entire district(variations in wi).

4.4. Differing firm visibilities

Sources of information that are used to form quality expectations include the con-sumer’s experience, expert reviews, and advertisement. In many cases, theseelements might vary across firms. Alternatively, consumers may be exposed more tothe products of certain firms (e.g. when market share is not equally divided amongfirms or there is a dominant firm). Figure 4 presents the case in which Firm 1 is lessvisible than Firm 2 (b1 < b2). The primary result here is that differences in these(exogenous) firm-specific parameters induce non-convergent steady state reputa-tions, specifically �rs1<

�Rs<�rs2.26 This shows that heterogeneity in output quality

within a region is not necessarily due to unequal access to production technology,but rather may be the result of demand-side conditions related to consumers’ differ-ential updating and learning. Also visible in Figure 4 is that, as the chosen pricingsegment increases, the steady-state collective reputation also increases, and so doesthe deviation of each agent’s private reputation from the collective level. As the fig-

Quantile 15 Quantile 50 Quantile 75

Figure 4. Paths to steady state for three conditional quantile price functions. Heterogeneous

firms with different visibility parameters, w1 = w2 = 0.5, c = 0.2, b1 = 0.05, b2 = 1

26Obviously, a similar (but trivial) result can be obtained assuming heterogeneity only inmarginal costs.

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ure shows, in the higher quantile the less-visible firm invests well below the collec-tive reputation level. That is, lower investment becomes more pronounced in thehighest pricing segment, where the returns from reputations are greatest.

4.5. Reputation leaders

We defined a reputation leader as one for whom quality performance has a promi-nent weight (wi > 1 ⁄N) in determining consumers’ expectations about the qualityof a region. This section investigates the incentive structure and efficiency outcomesinduced by the presence of a reputation leader, maintaining the assumption thatFirm 1 and Firm 2 are the only source of information used in developing the collec-tive reputation (w1 + w2 = 1).Figure 5 shows the equilibrium firm and collective reputations of the dual reputa-

tion strategic game (several parameterizations); and compares them to the regionalplanner (cooperative) solution. From left to right, the reputation leadership of Firm 1increases, while firm homogeneity is imposed in all other aspects. Results highlighthow the regional planner will asymmetrically increase the investment of the reputationleader, and decrease the follower’s. In the competitive versions of these games we see asimilar behaviour, yet the investment of the leader becomes increasingly sub-optimal

84.5

85

85.5

86

86.5

87

87.5

88

88.5

89

w1 = 0.50, w2 = 0.50 w1 = 0.75, w2 = 0.25 w1 = 0.95, w2 = 0.05

Firm 1 cooperative Collective cooperative Firm 2 cooperative

Firm 1 noncooperative Collective noncooperative Firm 2 noncooperative

99.21%

98.37%

99.52%

98.80%

98.29%

99.77%

98.98%

Figure 5. Equilibrium reputations ⁄quality for cooperative outcomes (Firm1, collective,Firm2), non-cooperative outcomes (Firm1, collective, Firm2) and ratios between cooperative

and non-cooperative outcomes (in percentages). Reputation leadership increases from the left(w1 = 0.5) to the right quadrant (w1 = 0.95). Dual reputation structure, median quantile

pricing equation and instantaneous speed of adjustment (c*bi = 1)

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as his ⁄her weight on the collective reputation grows larger; while the opposite is truefor the follower. In summary, the presence of a reputation leader increases the collectivereputation, but also the overall level of inefficiency27 and the associated industry losses.In the parameterization with instantaneous updating and the highest level of rep-

utation leadership (w1 = 0.95) the investment of Firm 2 is almost irrelevant, andthe collective reputation responds to the actions of the leader much as if it were itsown firm reputation. Thus, it is somewhat counterintuitive that the presence of areputation leader increases the inefficiency of the overall market due to public gooddynamics.28 The economic explanation is that, while reputation leadership influencesthe evolution of the collective reputation via the relative weights in the state equa-tion, a similarly proportional distribution of the resulting benefits does not occur,and every firm in the district receives an equal share.29 A regional planner imposes

84

86

88

90

92

94

96

Quantile 15 Quantile 50 Quantile 75

Firm 1 cooperative Collective cooperative Firm 2 cooperative

Firm 1 noncooperative Collective noncooperative Firm 2 noncooperative

99.3399.93

98.30

99.77

93.79

98.81

99.36

98.37

94.02

Figure 6. Equilibrium reputations ⁄quality for cooperative outcomes (Firm 1, collective, Firm2), non-cooperative outcomes (Firm 1, collective, Firm 2) and ratios between cooperative and

non-cooperative outcomes (in percentages) in the presence of a reputation leader(w1 = 0.95). Conditional quantile pricing function increases from the left (0.15) to the rightquadrant (0.75), dual reputation structure and instantaneous speed of adjustment (c*bi = 1)

27 Just as before, slower speeds of adjustment and visibility decrease quality but increase effi-

ciency (not shown in figure). The primary result is qualitatively unaffected.28 Firm 1 faces a per-unit loss of $6.46 (earning $29.00 per bottle compared to $22.54) andFirm 2 loses $3.65 (earning $24.65 vs. $21.00).29 This, we argue, is quite realistic, and applies to the cases of firm and regional reputation,firms and variety, or more generally firms and commodity produced (as in the brand vs. gen-eric advertisement literature).

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a very asymmetric quality investment policy to account for the sizable spilloversresulting from the leader’s investment. On the other hand, in a competitive settingthe reputation leader sees things quite differently: the high weight on collective rep-utation implies a large cost share of maintaining good (optimal) collective reputa-tion, yet the firm is unable to collect all the benefits, which accrue to the district asa whole. The externality arising from the public good dimension of the problem istherefore exacerbated, and the leader under-invests by a relatively large margin,driving the collective reputation efficiency down. However, since it is optimal forthe follower to invest relatively less in the cooperative solution, the relative effi-ciency of this firm is actually highest across the three scenarios. Finally, Figure 6shows that, consistent with previous reasoning, the inefficiency induced by a reputa-tion leader is minimal in the cheaper pricing segments, and largest in the high priceones.

5. Discussion and Conclusions

We have used differential game theory to study how and why profit-maximisingfirms invest in quality when price premia for good reputations are associated withboth private and collective names, and these reputations evolve in accordance withindividual firm behaviour. Previous research has typically focused on either privateor collective reputations independently, disregarding the interactions inherent indual reputation markets.To ground results to markets for experience goods, wine data are used to empiri-

cally calibrate the functional relationships between product prices and reputations.Equilibrium outcomes from a variety of parameterizations (each representing alter-native market conditions) are compared and contrasted with the industry-wide(monopoly) optimal investment in quality. Results were then used to qualitativelygauge the efficiency (in terms of relative quality) of non-cooperative outcomes, andthus the potential industry gains from cooperation.Consistent with theoretical predictions and previous literature, our results show

that equilibrium quality and reputations increase as it becomes easier for con-sumers to learn about quality and form their expectations. Similarly, resultsshow that without coordinated action, industry-wide investment in quality will beinefficient – the classic public good result arising from the diffused ownership ofthe collective name. Interestingly, inefficiencies owed to public good dynamicsare found to be larger in transparent markets, where reputations are quicklyformed and updated, and there are thus larger potential gains from investing inquality.The use of multiple pricing functions, specific to market price segments, yielded

another set of results. First, the optimal quality investment is found to increaseacross conditional price quantiles. That is, regardless of comparative advantage (i.e.cost functions), identical firms will choose to produce at higher quality when enter-ing the high-price segment. However, the relative efficiency of the non-cooperativeoutcomes decreases in the price quantiles. Our interpretation of these results some-what reverses the causality between product quality and prices. Consumers are will-ing to pay more for good reputations when buying expensive items, because thecost of experiencing poor quality is higher. This creates an incentive for producersto invest more, fulfilling the prophecy that high prices signal high quality. However,it is precisely in these markets, where the potential gains from good reputations are

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sizeable, that the tragedy of the commons is most pronounced, with greater damageto the producers who are unable to cooperate.Another set of results highlights how dual reputation structures, with their combi-

nation of private and public incentives, are inherently prone to intra-regional con-troversies. First, we find that diverging steady states in private reputations, aboveand below the collective reputation level, can be due to differences in firm visibility,rather than comparative advantage for quality. Thus, a less visible firm may beaccused of free-riding on the efforts of the others (which is technically untrue: everyfirm in our model behaves in the same way given its exogenous visibility). Second,we find that the equilibrium collective reputations increase in the presence of a rep-utation leader. However, the discrepancy between the optimal (cooperative) invest-ment and the competitive solution increases with the magnitude of reputationleadership, and it is the leader who could be accused of not doing enough to sustainthe good name of the region.It is curious that, against the common ‘little guys vs. the big guy’ mantra, it may

make economic sense for the follower(s) to subsidise the quality investment of thereputation leader, and share more of the collective reputation costs. Admittedly, thisresult is conditional on the exogeneity of the firm visibility and leadership weightparameters in the reputation-transition equations, which is a maintained assumptionin this analysis. In reality, this may not be the case: at least in the long run, the fol-lowers might be able to modify their firm visibility (the bi) or take actions to affecttheir influence in the collective reputation (the wi), perhaps by investing in advertis-ing, expanding market share, or by other means. However, it is not clear that itwould be in the best interest of the follower to do so, since the returns from collec-tive reputation are much higher in the presence of a reputation leader; and, given achoice, firms would much rather invest in their own firm visibility than in assumingthe thankless role of the regional reputation leader.Thus, a promising (if complicated) avenue to expand this work is to first under-

stand how reputation leadership and own firm visibility are related (here they areindependent), and then embed that information in a model with endogenousweights and visibilities. Another possible line of work is to investigate alternativemarket structures. Here, we extended the reputation literature that assumes a com-petitive environment, with price premia as the incentive necessary to persuade firmsto invest in quality when the associated returns to quality are lagged. This isreflected in the exogenous hedonic specification of the price function adopted. Thissetting could be modified to consider a true duopoly or monopolistic competitionmodel of regions (or multi-brand parent firms) with different cost functions. Undersome assumptions regarding the distribution of consumers’ preference for quality,this approach would expand the monopolistic competition literature (e.g. see Motta,1993) to consider the case in which firms compete in quality and price, and perhapsobtain some results regarding how collaborative action within a production districtmay affect consumer welfare.

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Appendix: First-Order Conditions of the Problems

Joint, non-cooperative game with both private and collective reputations

The first-order conditions for each player i in the non-cooperative game are derivedfrom the Kuhn-Tucker and Envelope Theorems applied to the Bellman equation(Miranda and Fackler, 2002):

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�c0ðqiÞþd½Vi;rið�ÞcbiþVi;Rð�Þcwi�¼0

Vi;rið�Þ¼prið�ÞþdVi;rið�Þð1�cbiÞþdXj 6¼i

Vi;rjð�Þcbjqj;rið�ÞþdVi;Rð�ÞXj6¼i

cqj;rið�Þwj

Vi;rjð�Þ¼dVi;rjð�Þ½1þcbjðqj;rjð�Þ�1Þ�þdXk 6¼i;j

Vi;rkð�Þcbkqk;rjð�ÞþdVi;Rð�ÞXj 6¼i

cqj;rjð�Þwj8j 6¼ i

Vi;Rð�Þ¼pRð�ÞþdXj6¼i

Vi;rjð�Þcbjqj;Rð�ÞþdVi;Rð�Þ 1þcXj6¼i

qj;Rð�Þwj�1 !" #

;

plus the equations of motion for each state variable.In essence, these conditions suggest that is it optimal for each firm to invest such

that the current-period marginal cost of investment is equal to the marginal benefitof doing so, with this marginal benefit defined as the (discounted) increase in valuefrom both private and collective reputation, with the discount depending on the dis-count rate, the speed of adjustment parameters, and the weight of own reputationon the collective.

Industry planner model ⁄monopolist with both private and collective reputations

In contrast, the first-order conditions for the regionally optimal solution characte-rise the solution to the Bellman equation

Jðr;RÞ ¼ maxq�0

(XNi¼1ðpiðri;RÞ � ciðqiÞÞ þ dJi

r1 þ cb1½q1 � r1�; r2 þ cb2½q2 � r2�; . . .

rN þ cbNðqN � rNÞ;Rþ cXi

wiqi � R

" #!);

and are defined as:

� c0ðqiÞ þ d Jrið�Þcbi þ JRð�Þcwi½ � ¼ 08iJrið�Þ ¼ pi;rið�Þ þ dJrið�Þð1� cbiÞ8iJRð�Þ ¼

Xi

pi;Rð�Þ þ dJRð�Þð1� cbiÞ:

Note that in contrast to the non-cooperative game problem, the regionally opti-mal solution accounts for the full effect of collective reputation through the equa-tion for JRð�Þ, and that investment in firm-specific reputations takes this intoaccount without any strategic interaction effects.

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