Abstract
We analyze a market with two product alternatives that differ in quality. Consumers choose between these products based on consumer reviews and their own experience. We examine how the market share of the superior product is affected by (i) the number of reviews obtained by consumers; and (ii) the type of information conveyed in these reviews. We find that when consumers randomly sample reviews from the entire population, an increase in the number of reviews can decrease the market share of the superior product. This, however, is not the case when consumers seek out reviews on each product. Further, we find that the market share of the superior product can be significantly lower when reviews convey subjective satisfaction compared to when they convey objective payoffs. This effect depends on the degree of heterogeneity in consumer expectations.
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Notes
Some other examples of markets that may have this feature are the services of medical doctors, car mechanics, and lawyers.
Ellison and Fudenberg (1995) do not consider equal-reviews sampling, endogenous switching, nor do they consider the use of a stars rating system.
Ellison and Fudenberg (1995) say the following about their study, “We have not been able to completely determine the long-run dynamics of our model. Rather than simplify the model further, we have chosen to provide a partial characterization.”(p. 101) The computational approach enables us to provide a more complete characterization of the outcomes with a more realistic model. See Judd and Page (2004) who advocate a computational approach for this and other reasons.
It may appear that Izquierdo and Izquierdo (2007) consider a single product. However, their setup can be interpreted as one with the following two characteristics: (1) there are two products, one that has uncertain quality and another that has a known and certain quality that is normalized to zero; and (2) the product with uncertain quality has higher average quality, but consumers are not aware of this fact. With this interpretation, market failure in their model occurs when consumers consume the lower quality product.
Lamberson and Page (2008) do not explicitly talk about payoffs. However, they have a variable referred to as “feedback”, which can be interpreted as the consumer’s payoff.
Ellison and Fudenberg (1995) have a continuum of agents, whereas we have a finite population.
In our model \( \theta _{H} \) and \( \theta _{L} \) are constant over time; that is, there are no product-specific, population-wide shocks. In contrast, in Ellison and Fudenberg (1995) \( \theta _{H} \) and \( \theta _{L} \) are random; \(\theta _{H} - \theta _{L} \) equals \( \theta > 0 \) with probability \( p \) and \( -\theta \) with probability \( (1-p) \). In their model, product \( H \) is superior in the sense that \( p > 1/2 \).
This assumption is changed in Sect. 4, where it is assumed that those who are more dissatisfied are more likely to consider a switch.
A potential switcher obtains a new sample in every time period that she becomes a potential switcher.
One could assume that sampled reviewers report a weighted average of their past payoffs instead of only their most recent payoff. As long as the reviewers report the (weighted average) payoff for the most recently consumed product only, our results continue to hold.
Note that this assumes that a potential switcher places the same weight on her own payoff as she places on other reviewers’ payoffs. One could consider a situation where a potential switcher places a higher weight on her own payoff. This is an interesting alternative to consider in future work.
We used Python and C programming languages for this purpose. The code is available upon request from the authors.
We believe that 5,000 time periods is sufficient because: One, for the parameter combinations considered, the market share of \( H \) converges by time period 5,000. Two, even if one model time period corresponds to as short as one calendar day, which means that the product is consumed once everyday, 5,000 time periods corresponds to about 14 calendar years. In practical terms, we believe that what happens beyond a 14 year time horizon is unlikely to be relevant for most policy planning purposes. For example, for questions such as whether regulatory intervention is necessary for promotion of the higher quality product, or what quality level a firm should provide, it may not be very helpful to know what happens beyond a 14 year horizon.
The probability that these inequalities are satisfied is given by the probability that \( \bar{U}_{H} - \bar{U}_{L} > 0 \), where \( \bar{U}_g \) is the sample average payoff from product \( g \in \{H, L\}\). Given the model assumptions, \( \bar{U}_{H} - \bar{U}_{L} \sim N \left( \theta _{H} - \theta _{L}, \frac{\sigma ^2}{k^2 + (X-k)^2} \right) \) when there are \( X \) reviewers and \( k \) of these \( X \) reviewers are \( L \) reviewers. When one additional reviewer is sampled, the variance of this distribution decreases: it either becomes \( \left( \frac{\sigma ^2}{k^2 + (X+1 - k)^2} \right) \) when the additional reviewer is an \( H \) reviewer, or \( \left( \frac{\sigma ^2}{(k+1)^2 + (X - k)^2} \right) \) when the additional review is an \( L \) reviewer. This decrease in variance implies an increase in the probability that \( \bar{U}_{H} - \bar{U}_{L} > 0 \).
As can be seen from Eq. 2, an \( H \) potential switcher chooses \( H \) with certainty when \( k = 0 \). However, the probability she chooses \( H \) is less than 1 when \( k > 0 \).
We tried \( P = 500, 1{,}000 \); \( \alpha = 0.01, 0.1, 0.5, 1 \); \( \sigma = 10, 30\); and \( (\theta _H, \theta _L) \) pairs (100, 75), (250, 225), (375, 350), (1,000, 975). Not surprisingly, the larger the \( \alpha \) the sooner the U-shaped pattern appears. Also, we found that for \( \sigma = 10 \) an increase in \( N \) has little effect on \( m_{H} \), while for \( \sigma = 30 \) the U-shaped relationship between \( N \) and \( m_{H} \) is more pronounced than for the base case of \( \sigma = 20 \). In the interest of space, these robustness checks are not presented in the paper but are available from the authors upon request.
This feature also holds for the other parameter combinations we tried but that are not presented here.
This assumes that it is socially optimal to produce and consume only \( H \), i.e., \( U_{H} - c_{H} > U_{L} - c_{L} \), where \( c_{i} \) is the constant marginal cost of alternative \( i \), where \( i \in \{H, L\} \).
To check for the robustness of the findings we also compared \( m_{H} \) across the two sampling procedures for \( \sigma = 10, 30 \); \( \alpha = 0.01, 0.5, 1 \); and \( (\theta _{H}, \theta _{L} ) \) = (250, 225), (375, 350) and (1,000, 975). We changed one parameter at a time with other parameters left at their base value. For example, when \( \sigma \) was set to 10, all the other parameters were at their base level. In the interest of space, we have not presented these results for the different \( \sigma \), \( \alpha \) and \( (\theta _{H}, \theta _{L}) \) values, but they can be requested from the authors.
In the interest of space, these robustness checks are not presented in the paper but are available from the authors upon request.
As in the previous subsection, we checked whether these conclusions hold for all possible parameter combinations formed with \( \gamma = 0.01, 0.05, 0.1, 0.5, 0.9 \) and \( A = 25, 90, 150\).
In addition to rating on a discrete scale, many consumers also provide written descriptions of their experience with the product. These descriptions can provide payoff-relevant information in addition to that provided by a rating on a 5-star scale, and hence can affect choices made by potential switchers. In this paper, however, we do not take account of these verbal descriptions. We think it is important to first examine the difference between the stars rating system and the objective payoff communication because if this difference is not large, a study of how verbal descriptions additionally affects \( m_{H} \) is not warranted.
This rule, along with restriction to maximum of 5 stars implicitly means that there is a threshold level \( T_{6} = \infty \).
We considered the same set of \( A \) and \( \gamma \) combinations as considered in Sect. 4.1; these are all possible combinations formed using values \( \gamma = 0.01, 0.05, 0.1, 0.5, 0.9 \) and \( A = 25, 90, 150 \). For \( \sigma \) we considered values \( \sigma =10, 30 \). In the interest of space, these robustness checks are not presented in the paper but are available from the authors upon request.
Recall that a threshold value of \( T = [T_{1}, T_{2}, T_{3}, T_{4}, T_{5}] \) means that a consumer awards \( k \) stars to product \( g \) consumed by her in time period \( t \) if \( T_{k} \le U_{igt}/A_{it} < T_{k+1} \).
In the interest of space, these robustness checks are not presented in the paper but are available from the authors upon request.
We ran simulations for the same set of \( A \), \(\gamma \) and thresholds values as in the previous sections. These results are available upon request from the authors.
We investigated the statistical significance of the difference in \( m_{H} \) across the objective payoff communication and the stars rating system (for both random sampling and equal-reviews sampling) for the following cases: (i) the base case, (ii) \(\sigma = 10 \), (iii) \(\sigma = 30 \) and (iv) \( \gamma = 0.01\). We found that differences in \( m_{H} \) of 0.3 to 1.4 percentage points are sufficient for statistical significance at the 1 % level.
We ran simulations for \( A = \) 25 and 150 in addition to the base level of 90. For thresholds, in addition to the base level of \( T = [0, 0.7, 0.9, 1.0, 1.1] \), we simulated \( m_{H} \) for \( T = \) [0, 0.75, 0.95, 1.1, 1.25], [0, 0.6, 0.75, 0.9, 1], [0, 1, 1.2, 1.4, 1.6], [0, 0.2, 0.4, 0.6, 0.8] and [0, 0.65, 0.75, 1.1, 1.2]. The results for these cases are available upon request from the authors.
See the second paragraph of Sect. 5, where we discuss two ways in which subjective communication results in loss of relevant information.
The fact that there is little subjectivity in reviews when \( \gamma \) is small is due to the assumption that the initial expected payoff, \( A \), is the same across all consumers. If we were to relax this assumption then a smaller \( \gamma \) would not necessarily imply less subjectivity. In this case, the difference in \( m_{H} \) across objective payoff communication and the stars rating system would likely be large even for small values of \( \gamma \).
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We appreciate the helpful comments from our fellow 2013 Southern Economics Association session participants and 2014 Eastern Economics Association participants
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Bhole, B., Hanna, B.G. Word-of-Mouth Communication and Demand for Products with Different Quality Levels. Comput Econ 46, 627–651 (2015). https://doi.org/10.1007/s10614-014-9453-8
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DOI: https://doi.org/10.1007/s10614-014-9453-8