Pricing algorithms have been widely used in online marketplaces for a long time. Amazon illustrated this trend almost a decade ago, performing over 2.5 million daily pricing changes, in contrast with competitors Best Buy and Walmart, who made 52,956 and 54,633 daily price changes, respectively (CMA 2018). Amazon is still one of the world's largest online marketplaces, processing an outstanding average of 18 orders per second and changing prices every 10 minutes (Huzenkova 2023). Amazon's pricing method, known as Amazon dynamic pricing or repricing, uses an algorithm to constantly modify prices. This system analyzes all pricing information available on Amazon's platform and around the internet. When the algorithm finds a lower price outside of Amazon, it adjusts Amazon's pricing to match the external prices (Huzenkova 2023).
In 2022, Turkish Competition Authority (TCA) announced its publication of e-commerce market survey (TCA 2022), emphasizing the importance of digitalization in marketplaces. Additionally, TCA started an investigation on e-commerce marketplace, stating that the findings were sufficient enough to initiate an investigation on companies that apply automated pricing mechanism (TCA 2023). These developments in the Turkish e-commerce industry raised interest in the use of algorithms and their impact on the Turkish economy. Whereas the scope or direction of the investigation is not clear because of confidentiality considerations, we have adopted an economic approach to algorithmic usage within Turkish online marketplaces.5 For this reason, we chose to collect data from Trendyol, a well-known e-commerce platform in Türkiye.6
4.1 Data
Data was gathered from the Trendyol website (t_marketplace) over a period extending from March 2023 to January 2024, utilizing web scraping techniques. Given that t_marketplace encompasses millions of products, our analysis was deliberately narrowed to focus exclusively on breakfast items, specifically ‘milk’ and ‘cereal’. This specific focus was driven by the intent to examine a globally recognized product category, whose competitive dynamics could potentially be extrapolated to a broader context. The data collection was conducted on a daily basis, encompassing a range of features:
- Time: The precise timestamp of data collection.
- Search criteria: Ranking of products based on various search filters like most favorite, best seller, suggested, etc.
- Page number: The webpage number where the product is listed.
- Brand owner: The brand associated with the product.
- Merchant: The retailer or seller offering the product.
- Sale Price: The retail price of the product at the time of data collection.
- Unit: The quantity or volume of the product sold.
- Unit Price: Sale price divided by the unit sold.
- Average rating: The mean rating awarded to the product by consumers.
- Rating Count: The total number of ratings received by the product.
- Coupon: Indication of whether the product is offered with a discount or promotion.
- Same day shipping: Information on whether the product is eligible for same-day shipping.
- Free shipping: Status of shipping charges, whether there are extra fee or not.
- Video content: Availability of video content describing the product's features.
-
In our study, we conducted an analysis of two distinct breakfast products, namely ‘milk’ (Panel A) and ‘cereal’ (Panel B). Since these products can be sold by multiple merchants, we used two different dataset where Dataset 1 has the unique merchant feature and Dataset 2 has the unique brand feature.7 This distinction is important because it allows us to measure intra-brand as well as inter-brand competition with respect to unique merchant criteria.
After initial filtering, Panel A contains 938,297 rows and Panel B contains 214,571 rows of information on respective products. Since these products displayed in different sections of the page multiple times, average of these information calculated on a daily basis. At the same time, differentiated products that are featured distinctly from the base product eliminated by using a second filter. For example, milk with almond flavor or gluten free are excluded from the dataset in order to capture a more homogenized product type for milk. Same criteria applied to the Panel B. At the same time, rows that contain null values more than 5 columns dropped from the dataset. To address the null values in the columns labeled "average rating", "rating count", "coupon", "promotion", "same day shipping", "free shipping", and "video content" for each unique product, forward and backward fill techniques were applied. However, rows featuring null values in the "unit price" column were excluded from the dataset. Finally, unit prices above the 95th percentile and below the 5th percentile were excluded from the dataset since these products either has specific features that require high/low pricing or has been inactive for a certain amount of time. Following these filtering, 103,786 rows (Dataset 1) & 104,034 rows (Dataset 2) rows remained in Panel A where 27,499 rows (Dataset 1) & 27,466 rows (Dataset 2) remained in Panel B.
It is important to highlight that boolean columns with “true” and “false” values were transformed into binary representations of ones and zeros, which were then averaged on a daily basis. Furthermore, due to the highly confidential nature of firm-level cost data, which is not publicly accessible, we incorporated alternative data sources such as Consumer Price Index (CPI) of food, the Producer Price Index (PPI), PPI of dairy, and animal feeds, in addition to the monthly production levels of milk. Our utilization of a regularization technique, which inherently reduces or eliminates the significance of redundant variables that could lead to multi-collinearity, allows us to confidently include multiple cost-related variables on the right-hand side of our equation. Furthermore, we introduced three dummy variables into our analysis: “election”, “reference raw milk price announcement”, and “competition authority investigation (on e-commerce platforms) announcement”.
4.2 Descriptive Statistics
Our dataset is comprised of two distinct panels: Panel A, which focuses on milk products, and Panel B, dedicated to cereal. Each panel was reconstructed using the unique merchant feature, as explained in Section 4.1.
Table 1: Descriptive Statistics for Panel A: Milk and Panel B:Cereal - 11
|
Panel A: Milk
|
Panel B: Cereal
|
Dataset 1
(Unique Merchant Feature)
|
Dataset 2
(Unique Brand Feature)
|
Dataset 1
(Unique Merchant Feature)
|
Dataset 2
(Unique Brand Feature)
|
Date Start
|
2023-03-28
|
2023-03-28
|
2023-03-28
|
2023-03-28
|
Date End
|
2024-01-04
|
2024-01-04
|
2024-01-04
|
2024-01-04
|
Unique # of Products
|
1540
|
1364
|
973
|
514
|
The observation period spans approximately 9 months, beginning with 2023-03-28 and ending with 2024-01-04. We have 1540, 1364, 973, and 514 unique products for Panels A and B, which vary in terms of merchant and brand features. the dataset is as follows:
Table 2: Descriptive Statistics for Panel A: Milk and Panel B:Cereal - 2
|
Panel A: Milk
|
Panel B: Cereal
|
Dataset 1
|
Dataset 2
|
Dataset 1
|
Dataset 2
|
Unit
Price
|
Avg. Rating
|
Rating Count
|
Unit
Price
|
Avg. Rating
|
Rating Count
|
Unit
Price
|
Avg. Rating
|
Rating Count
|
Unit
Price
|
Avg. Rating
|
Rating Count
|
Obs.
|
103,786
|
103,786
|
94,334
|
104,034
|
104,034
|
95,348
|
27,499
|
27,499
|
25,392
|
27,466
|
27,466
|
26,353
|
Mean
|
73.981
|
4.431
|
80.112
|
73.950
|
4.431
|
79.978
|
99.203
|
4.401
|
10.076
|
99.232
|
4.404
|
10.016
|
Median
|
71.990
|
4.444
|
77.926
|
71.990
|
4.446
|
77.839
|
88.400
|
4.513
|
9.248
|
88.400
|
4.534
|
9.301
|
Std. dev.
|
38.158
|
0.329
|
147.545
|
38.224
|
0.329
|
146.336
|
50.196
|
0.494
|
19.765
|
50.205
|
0.498
|
19.021
|
Min
|
12.930
|
1.667
|
1
|
12.930
|
1.667
|
1.000
|
18.330
|
2.250
|
1
|
18.330
|
2.250
|
1
|
Max
|
174.980
|
4.960
|
4221
|
174.980
|
4.960
|
4221
|
230.050
|
4.967
|
287
|
230.050
|
4.967
|
287
|
For milk in Panel A, Dataset 1 has 103,786 observations with an average unit price of 73.981 and an average rating of 4.431 out of 5. The median values nearly match to the mean, implying a symmetric distribution. The standard deviation for price is 38.158, and for rating it is 0.329, indicating that pricing fluctuation is moderate and rating variability is low. The average rating count is 80.112, with a standard deviation of 147.545, demonstrating significant diversity across products. Dataset 2 shows similar statistics with the same number of observations and the same mean, median, maximum, and minimum values for both unit price and rating.
For cereal in Panel B, Dataset 1 has 27,499 observations, an average unit price of 99.203, and an average rating of 4.401 out of 5. The median price is 88.4, little lower than the mean, while the median rating is 4.513, slightly higher than the average. The standard deviation for price is 50.196, and for rating it is 0.494, indicating that price has a bigger variability than milk while rating has a comparable variability. The average rating count is 10.076, with a standard deviation of 19.765, indicating a high variability for rating count statistics. Dataset 2 in Panel B has 27,466
Possible algorithmic pricing techniques are described by several authors. Wieting and Sapi (2021, p.21) categorized these patterns in five groups:
- Price jitter up and down: This refers to a sudden, transitory increase (jitter up) or decrease (jitter down) in the seller's pricing.
- Rockets and feathers: Price rises quickly, followed by a slow, gradual decline, frequently returning to the beginning level.
- Balloons and rocks: Prices rise gradually and steadily to a particular point before rapidly falling back to their former level.
- Alternating price: Prices fluctuate either upward or downward for a longer but temporary period within predetermined limitations before returning to a level near to the initial one.
- Random jumps: Prices undergo rapid and unpredictable changes.
Aparicio and Misra (2023) finds pricing fluctuations caused by artificial intelligence for a wide range of US online grocery items, including cereals, painkillers, personal care products, and snack foods. The authors note a significant variability in prices over short periods when retailers employ pricing algorithms (Aparicio and Misra 2023, p.105). Brown and MacKay (2021, p.9-16) indicates three facts about online prices, by providing examples. These facts are “online retailers update prices at regular intervals”, “retailers with the fastest pricing technology quickly react to price changes of slower rivals”, “consistent with the use of automated pricing algorithms, and firms with faster pricing technology have persistently lower prices for identical products”.
For example, the dataset comprises 1,540 separate products (as specified for Panel A, Dataset 1), all of which compete in the same market. Figure 1 depicts the natural logarithms of the unit price series for unique milk products.8
Figure 1 shows that majority of online unit pricing for the products in Panel A are highly synchronistic. Despite the differences in date ranges when compared to our dataset, this finding is consistent with the results reported in the Central Bank of the Republic of Türkiye’s (CBRT) study on the food retail sector (CBRT 2023). In this report, CBRT analyzes the dynamics of price changes in the food retail sector, stating that UHT (Ultra-high Temperature) milk prices vary across supermarkets and these retailers frequently change their prices. Furthermore, CBRT states that these price modifications occur at similar periods and maintain similar price levels. Finally, the report states that there is an increasing tendency to price rival UHT milk products at similar price levels, lowering the coefficient of variation in prices, and that there is economic evidence of price synchronization across supermarkets for UHT milk products, with a Fisher-Konieczny (FK) index value of 0.74 (CBRT 2023, p.11-12).9
Daily shifts in prices in Panel A appear to reflect a highly volatile market. However, as previously stated, the majority of these price variations are generated by algorithms using strategies such as ‘price jitter up and down’, ‘alternating price’, and/or ‘random jumps’. Figure 2 depicts various types of price fluctuations.
The quantity of price changes is a significant feature in distinguishing between algorithmic and human pricing. Although we will dive into more detail about this in the following section, the distinction is crucial because we do not have concrete, legal evidence that is publicly available. A major contributor to this phenomenon is ethical and legal sanctions, which can have a severe impact on the operations of an organization.
4.3 The Method, Assumptions and Hypothesis
Understanding the competitive dynamics within a market requires a thorough understanding of pricing strategies. Pricing dynamics are complex, especially in typical brick-and-mortar businesses. In dynamic business environments, where demand structure elements change rapidly, firms must act quickly to align with the developing dynamics of demand. This is especially true in online marketplaces, where the convergence of millions of products and billions of consumers produces a distinct and fast-paced business-related reality.
Beginning with pricing strategy, there exists a multitude of approaches that can be implemented within a market context. Ellickson and Misra (2008, p.813) describe pricing strategies in three groups: The initial method is the Everyday Low Price (EDLP), which reduces reliance on promotional pricing strategies such as temporary price cuts. In this method, prices are maintained at a consistently low level across all product categories. Another technique is the promotional pricing strategy, often known as Hi-Lo Pricing, which is characterized by frequent price drops. The final method is a hybrid model that incorporates components from both the EDLP and Hi-Lo Pricing strategies. In their study, Ellickson and Misra (2008) found that large firms usually adapts a mixture of pricing strategy, whereas approximately fifty percent of small firms use promotional pricing strategy Ellickson and Misra (2008, p.814).
Algorithms can be constructed to automatically adopt certain pricing strategies, offering an automated approach to pricing decision-making. For example, Deck and Wilson (2003, p.210-211) underlines three pricing strategies: (a) Undercut Algorithm: This algorithm, which is used in both brick-and-mortar and online retail sectors, determines pricing by monitoring competitor prices and then undercuts the lowest price by a given percentage, such as 1%. The author cites Books.com's pricing strategy as an example of how this tactic is used. (b) Low-Price Matching Algorithm: This algorithm, automates the process of matching low prices. Its use is thought to increase the chance of tacit collusive pricing, in which prices are automatically modified to match the lowest in the market. (c) Trigger Algorithm: This method involves first establishing a price and then modifying it if a competitor's price goes below a predetermined level. The pricing will be set at an alternative rate for the remaining periods. For example, grim trigger strategy is used to set a price above competitive level, punishing agents that does not conform with this strategy.
Algorithmic pricing and the patterns are mostly observable through graphical representations.
Chen et. al. (2016) analyzed Amazon’s Buy Box algorithm and modeled it as a prediction problem. The authors hypothesized that merchants that use algorithmic pricing are more likely to base their prices, at least in part, on those of other sellers. They proposed that if a seller has a high correlation with the target price (matching it at either the lowest, second lowest, or Amazon’s price) and makes a significant number of price changes, this provides greater proof of algorithmic pricing. On the other hand, if such a trend of frequent price modifications is not detected, the correlation is considered accidental. Using different change threshold (10 and 20), they found that when the change threshold is set above 20, 38% of all sellers use algorithmic pricing.
In the same vein, Wieting and Sapi (2021) analyzes algorithms in a marketplace called Bol.com. The researchers classed sellers as algorithmic based on observed behaviors, specifically setting a threshold for minimal price adjustments and correlations with several benchmarks, including the lowest price, second-lowest price, and others. However, their conclusion implies that the total number of price changes recorded over a given time period is the most reliable way for identifying algorithmic sellers (Wieting and Sapi 2021, p16).
Also Cavallo (2018, p.6-15) highlights that online sellers change their pricing significantly more frequently than traditional brick-and-mortar retailers. The author goes saying that the increased frequency of price adjustments in the online domain may be due, in part, to the usage of automated pricing algorithms. This shows that the digital architecture of online retail enables more dynamic and flexible pricing methods based on algorithmic inputs.
In this study, we adopt a similar approach while assessing algorithmic pricing strategies. Given that the main objective is not to determine which sellers use algorithmic pricing, we depend on the findings of aforementioned authors who have investigated algorithmic pricing in online platforms and tend to make the following assumptions in our analysis of finding an integrated strategy for detecting instances of algorithmic collusion.
Assumption 1: The likelihood of being an algorithmic seller grows with the number of price changes it makes.
As mentioned earlier, our primary goal in this study is to capture the possible algorithmic collusion instances by presenting an integrated strategy.
In this study, we use a two-stage model to assess the effects of algorithmic pricing on collusive behavior.
In the first stage, all dual combinations of unique products are defined with combination without replacement approach.10 Following that, the distance between ln(unit price) of these series is computed using the 'area' measure11 and compared it with the number of price changes that firms employed. This comparison is done by computing the Pearson product-moment correlation coefficients.
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)
Calculations in this regard are conducted by setting up three-day windows and one-day tracking for all product combinations. Pearson correlation coefficients are computed for all product combinations within these time periods. A positive coefficient suggests a positive association between price distance and price movements, implying competitive affinities, as price dispersion is more common in competitive markets. On the other hand, a negative coefficient suggests collusive affinity, as collusive firms prefer uniform price over the competitive level.12
Assumption 2: As the Pearson correlation coefficient approaches -1, the likelihood of perfect negative linear correlation increases, indicating a collusive outcome; as it approaches +1, the likelihood of perfect positive linear correlation increases, indicating a competitive outcome.
In the second stage, a machine learning model is created to estimate the Pearson correlation coefficients. For this task, we used ‘Elastic Net’ model (Zou and Hao 2009), which is a combination of both L1 and L2 regularization technique. The authors demonstrate through simulations that the adaptive elastic-net handles the collinearity problem better than previous oracle-like approaches, resulting in significantly enhanced finite sample performance.
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)
where MSE denotes the Mean Squared Error between true values of y and the predicted y, α is the regularization parameter that scales the penalty part of the loss function, L1 ratio is the mixing parameter between L1 and L2 regularization, θi is the ith coefficient of the model and m is the number of all features. With α equals to zero, Elastic Net model becomes a standard Ordinary Least Squares (OLS) model.
The Elastic Net model's estimator is determined in two steps using the lasso (L1 regularization) and ridge (L2 regularization) regression techniques. It initially identifies the ridge regression coefficients before moving on to the second stage, which involves shrinking the coefficients with a lasso. This method subjects the coefficients to two forms of shrinkages. The naive elastic net's double shrinkage results in low predictability and substantial bias. To account for these impacts, coefficients are rescaled by multiplying by (1+λ2).13
The Elastic Net model is preferred because it delivers variable selection and regularization simultaneously. It is a clear benefit for our study, as we seek to uncover the underlying nature of algorithmic pricing. In this commitment, we are attempting to absorb all conceivable factors that may affect Pearson correlation coefficients while also determining the exact coefficient for algorithmic agents.
In our regression model, we use several quantiles (0.95, 0.90, 0.70 and 0.50) to define price change frequencies as high and low in order to identify high frequency sellers as algorithmic sellers per Assumption 1, and regress high frequency price change category among other variables to see its net effect on collusive outcomes. Our model is represented as follows:14
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)
where denoted by ρ, represent the correlation coefficient quantifying the relationship between alterations in distance and price in specific time windows and independent variables are
- PHF: Periodic high frequency price changes,
- DHF: Periodic high frequency distance changes,
- PLF: Periodic low frequency price changes,
- DLF: Periodic low frequency distance changes,
- ∆Ravg: Absolute difference in average rating,
- ∆Rcount: Absolute difference in rating count,
- ∆C: Absolute difference in coupon availability,
- ∆SD: Absolute difference in same day shipping availability,
- ∆FS: Absolute difference in free shipping availability,
- ∆VC: Absolute difference in video content availability,
- CPIfood: The Consumer Price Index of food,
- PPI: The Producer Price Index,
- PPIdairy: PPI of dairy,
- PPIfeeds: PPI of animal feeds,
- Mprod: Monthly production levels of milk,
- Edummy: Election dummy,
- Rdummy: Reference raw milk price announcement dummy,
- CAdummy: The Turkish Competition Authority investigation announcement dummy.
At this point, we will develop our main hypothesis as:
Hypothesis: In light of the Assumption 1 and 2, algorithmic pricing has no effect on pricing decisions, indicating a zero coefficient for the high frequency price changes (PHF).
4.4 Results and Discussion
In order to capture the effect of algorithms on price distances (area measure), we have created 5886 dual combination (Panel A, Dataset 1), 10296 dual combination (Panel A, Dataset 2), 528 dual combination (Panel B, Dataset 1) and 946 dual combination (Panel B, Dataset 2) of price series. Also we have obtained different distance measures such as Partial Curve Mapping (PCM), Area Method, Discrete Frechet distance (FD) and Dynamic Time Warping (DTW).15 As stated in Assumption 2, positive correlation statistics indicate competitive dynamics, whereas negative correlation values indicate collusive behaviors. The strength of these indications increases as the correlation values approach +1 or -1.
Table 3: Correlation Coefficients in Different Measures (All Dataset)
|
Panel A: Milk
|
Panel B: Cereal
|
|
Dataset 1
|
Dataset 2
|
Dataset 1
|
Dataset 2
|
Obs.
|
5,886
|
10,296
|
528
|
946
|
Correlation Coef.
(pcm&price change)
|
0.129
|
0.190
|
0.003
|
-0.083
|
Correlation Coef. (area&price change)
|
0.159
|
0.219
|
0.023
|
-0.034
|
Correlation Coef. (fd&price change)
|
0.182
|
0.294
|
0.021
|
0.053
|
Correlation Coef. (dtw&price change)
|
0.159
|
0.219
|
0.023
|
-0.034
|
Table 3 represents the correlation coefficients between total distance in different metrics and total price changes for all dual combinations of price series. Dataset 1 contains 5,886 dual combinations of milk in Panel A and the correlation coefficients range from 0.129 to 0.182. Dataset 2 has 10,296 observations with usually higher correlation coefficients ranging from 0.190 to 0.294 for the same measures. For cereal in Panel B, Dataset 1 consists of 528 dual combinations with very low correlation coefficients, indicating a weak relationship between the variables. Dataset 2 has negative correlation coefficients for the pcm, area, and dtw measures, but a positive value for the fd measure. Overall, the results demonstrate that the correlation coefficients between total distance and total price changes across various combinations of price series are positive and around zero. Only the fd measure yields controversial results, with negative correlation coefficients. To maintain consistency, we will use the “area” measure for the remainder of our distance analysis.
For the goal of exploring algorithmic pricing, we divided our dataset into quantiles using different thresholds. For this reason, we have looked into the correlation between high and low frequency price changes using different quantiles of the data, specifically 95th, 90th, 70th, and 50th quantiles. The results are presented in the following table:
Table 4: Correlation Coefficients in Area Measure (All Dataset, High Frequency Price Changes and Low Frequency Price Changes)
Price Distance Measure: Area
|
|
Panel A: Milk
|
Panel B: Cereal
|
|
Dataset 1
|
Dataset 2
|
Dataset 1
|
Dataset 2
|
Corr. All
(distance & price change)
|
0.159
|
0.219
|
0.023
|
-0.034
|
High Frequency (HF) Quantile: 0.95 <= q <= 1
Low Frequency (LF) Quantile: 0 <= q < 0.95
|
Corr. HF
(distance & price change)
|
0.167
|
-0.174
|
Nan
|
0.356
|
Corr. LF
(distance & price change)
|
0.077
|
-0.003
|
0.106
|
0.044
|
High Frequency (HF) Quantile: 0.90 <= q <= 1
Low Frequency (LF) Quantile: 0 <= q < 0.90
|
Corr. HF
(distance & price change)
|
0.239
|
-0.127
|
-0.262
|
0.347
|
Corr. LF
(distance & price change)
|
0.080
|
-0.002
|
0.087
|
0.126
|
High Frequency (HF) Quantile: 0.70 <= q <= 1
Low Frequency (LF) Quantile: 0 <= q < 0.70
|
Corr. HF
(distance & price change)
|
0.171
|
0.258
|
0.150
|
-0.272
|
Corr. LF
(distance & price change)
|
-0.009
|
0.040
|
0.041
|
0.240
|
High Frequency (HF) Quantile: 0.50 <= q <= 1
Low Frequency (LF) Quantile: 0 <= q < 0.50
|
Corr. HF
(distance & price change)
|
0.196
|
0.233
|
-0.032
|
-0.133
|
Corr. LF
(distance & price change)
|
0.103
|
0.033
|
0.173
|
0.044
|
Table 4 illustrates the relationship based on the criteria involving high and low frequency price changes. For example, adopting 90th percentile as the threshold, high frequency price changes have positive correlation coefficients for Panel A: Dataset 1 (0.239) and Panel B: Dataset 2 (0.347), indicating a positive relationship with the distance measure. On the other hand, high frequency price changes have negative correlation coefficients for Panel A: Dataset 2 (-0.127) and Panel B: Dataset 1 (-0.262). The variations in the results make it more difficult to understand the results. It is crucial to note at this point that basic correlation coefficient analysis ignores the fact that coefficients vary over time. For this reason, further modifications were introduced to the data frame.
After elimination of inactive sellers, who has less than a total of 3 price changes, all series partitioned into three days time frames with one day tracking. A total of 264 rows of correlation coefficient, and columns of periodic distance (total area distance between all dual price series within each time frame), periodic price changes (total price changes of all series within each time frame) and other related variables are included in the data frame for both Panel A and Panel B. Correlation coefficients between total price changes and distance within these three days time frames constitute our model’s dependent variable. Figure 3 presents the distance series created for this purpose.
By creating time frames, our model became more realistic as time can be a factor in determining the correlations among price series. It is also appropriate to analyze collusive behavior with respect to the other factors in a time-series framework.
For the regression analysis, we employed the elastic net model, which combines the ridge (l2 regularization) and lasso regression (l1 regularization) techniques. We tried several alpha and l1 regularization values to find an ideal model that balances low bias and low variance features. Model selection criteria take into account both minimum mean squared errors and an absolute score difference of less than 5% between the training and test sets. Although Panel A: Dataset 1 had the highest training, test, and cross validation scores, we can still get insights from other groups. The primary issue is that we are not attempting to fully explain the dependent variable (correlation coefficient), but rather to capture the effects of algorithmic pricing on those correlation coefficients. Since we are using rigid parameters to regularize the model, any irrelevant coefficient is asymptotically reduced to zero, resulting in a regression model with minimal bias and variance. A summary table presented in Table 5:16
Table 5: Summary Regression Results
|
PHF
|
PLF
|
∆Ravg
|
∆Rcount
|
∆FS
|
PPI
|
Mprod
|
Ed
|
Rd
|
CAd
|
Panel A: Milk
|
Dataset 1 1
|
HF Q: 0.95
|
0.021
|
-0.089
|
-0.103
|
0.030
|
0.057
|
0.144
|
-0.034
|
0.002
|
-0.007
|
0.003
|
HF Q: 0.90
|
0.002
|
-0.080
|
-0.116
|
0.036
|
0.059
|
0.130
|
-0.044
|
0.002
|
-0.009
|
0.003
|
HF Q: 0.70
|
-0.015
|
-0.067
|
-0.118
|
0.051
|
0.039
|
0.133
|
-0.039
|
0.002
|
-0.008
|
0.004
|
HF Q: 0.50
|
-0.027
|
-0.058
|
-0.122
|
0.027
|
0.066
|
0.145
|
-0.-036
|
0.002
|
-0.006
|
0.003
|
|
Dataset 2 2
|
HF Q: 0.95
|
0.020
|
-0.066
|
-0.000
|
-0.000
|
-0.004
|
0.000
|
-0.017
|
0.003
|
0.001
|
-0.002
|
HF Q: 0.90
|
0.017
|
-0.067
|
-0.009
|
-0.000
|
-0.000
|
0.000
|
-0.029
|
0.001
|
0.003
|
-0.004
|
HF Q: 0.70
|
-0.000
|
-0.059
|
-0.016
|
-0.000
|
-0.000
|
0.000
|
-0.044
|
0.001
|
0.000
|
-0.006
|
HF Q: 0.50
|
-0.012
|
-0.050
|
-0.021
|
-0.000
|
-0.000
|
0.000
|
-0.051
|
0.000
|
0.001
|
-0.008
|
|
Panel B: Cereal
|
Dataset 1 3
|
HF Q: 0.95
|
0.000
|
0.001
|
-0.000
|
-0.000
|
-0.000
|
0.000
|
0.006
|
0.000
|
0.000
|
0.000
|
HF Q: 0.90
|
0.018
|
0.000
|
-0.010
|
-0.000
|
-0.000
|
0.000
|
0.003
|
0.000
|
0.005
|
0.000
|
HF Q: 0.70
|
0.004
|
0.000
|
-0.000
|
-0.000
|
-0.000
|
0.000
|
0.007
|
0.000
|
0.000
|
0.000
|
HF Q: 0.50
|
0.005
|
-0.000
|
-0.000
|
-0.000
|
-0.000
|
0.000
|
0.006
|
0.000
|
0.000
|
0.000
|
|
Dataset 2 4
|
HF Q: 0.95
|
-0.000
|
0.005
|
-0.000
|
-0.000
|
-0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
HF Q: 0.90
|
-0.000
|
0.010
|
-0.000
|
-0.000
|
-0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
HF Q: 0.70
|
0.002
|
0.002
|
0.000
|
-0.000
|
-0.001
|
0.000
|
0.000
|
0.000
|
0.000
|
0.001
|
HF Q: 0.50
|
0.003
|
0.000
|
-0.000
|
-0.000
|
-0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
1 Mean Training Score: 64.32, Mean Test Score: 60.33, Mean MSE: 0.083, Mean Cross Validation Score (Std.): 54.45 (7.47)
2 Mean Training Score: 45.88, Mean Test Score: 40.94, Mean MSE: 0.078, Mean Cross Validation Score (Std.): 34.67 (7.38)
3 Mean Training Score: 15.50, Mean Test Score: 10.66, Mean MSE: 0.096, Mean Cross Validation Score (Std.): 20.73 (7.91)
4 Mean Training Score: 6.58, Mean Test Score: 1.63, Mean MSE: 0.086, Mean Cross Validation Score (Std.): 13.96 (9.33)
Table 5 summarizes our findings and both Panel A and B provide additional insights for the theory of market and production. At this point, we would like to highlight the following insights:
First, Panel A shows a systematic relationship between algorithmic pricing and competitive dynamics. The PHF coefficient rises in proportion to the high frequency price change threshold. In other words, price dispersion grows with the possibility of being an algorithmic seller, rejecting our null hypothesis that “no effect on pricing decisions”. Although multiple inferences might be drawn from studying and modeling pricing levels and presenting a concentrated market environment, we consider this finding as competitive rather than collusive in accordance with Assumption 2 and standard antitrust law and economics perspectives.
Second, differences in quality (∆Ravg) have a negative influence on competitiveness because they negatively affect the connection between distance and price fluctuations.17 This finding can be linked to the algorithm's pricing strategy of following the most praised product's pricing strategy, resulting in collusive pricing despite differences in quality measures. At the same time, consumers may make irrational and suboptimal decisions, particularly in markets that have numerous competing items Yalçın (2016). As a result, producer surplus increases in expense of consumer’s benefits.
Third, uht milk production (Mprod) consistently provides negative coefficients in Panel A. This result is controversial because production is believed to enhance competition in conventional economic and market theory. However, we observe negative impact on price levels, indicating that the increase in production leads to more collusive pricing schemes within the market. Although it is difficult to find the underlying reason for this occurrence, one reason might be the fast response of algorithmic pricing to the dynamically changing demand levels. In conventional economic theory, supply line shifts toward with the assumption of static demand, leading a price reduction with the increasing levels of quantity. However, it might not be the case for dynamic markets where algorithms make the pricing decisions. Moving forward, Mprod appears to be increasing competitiveness in the cereal market by providing positive values. As the most important complementary product for breakfast cereals, its impact on the surrounding market is unsurprising, as it enhances consumption while also reinforcing the need to provide cereal products.
These effects are important because each represents a different characteristics of the market and production theory. Effects of the algorithms (PHF) represents competitive or collusive dynamics that affect wealth distribution. Differences in quality (∆Ravg) represents the quality feature that shapes both pricing decisions and consumer’s utility functions. Production (Mprod) is the essential part of business decisions and economic theory that enables firms to create production and cost functions, allocate resources and define capacity constraints.18 Figure 4 summarizes the aforementioned findings in an illustrative way:
Our findings contribute to the findings of Chen et. al. (2016), suggesting that algorithmic sellers use target strategies such as lowest price, Amazon price and second lowest price. Algorithmic pricing allows firms to receive more feedback, and win Buy Box more frequently and likely suggesting higher sales volumes and more revenue (Chen et. al. 2016). Furthermore, Wieting and Sapi (2021, p.30-33) finds that Buy Box price decreases by 9% if the monopolist seller is algorithmic, compared to a traditional seller. In this vein, Brown and MacKay (2021, p.14) states that “firms with faster pricing technology have persistently lower prices for identical products”, indicating an advantage for fast responsive algorithms against slower ones. Although the authors interpret this effect as a factor for “softening competition”, looking from a shorter horizon and including the ease of selling a product in online marketplaces this finding may be found competitive in line with our study. At this point, in order to evaluate the effects of algorithmic pricing, it is important to define market characteristics as well as algorithm’s working principle, objective function and the different levels of usage among competitors.19