{'fraction_non_alphanumeric': 0.022833723653395786, 'fraction_numerical': 0.0117096018735363, 'mean_word_length': 4.685524126455907, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Cardinality Bundling Under Oligopoly – a Simulation Model

The analysis of the putative effect of proposed mergers of mobile telecommunications operators has reached unprecedented levels of complexity, typically now running into hundreds of pages whereas in 2007 the European Commission was able to approve a 4-to-3 merger in The Netherlands on the basis of 18 pages of analysis. At the heart of this analysis is the structure of the industry, based on the number of firms. This paper takes a new approach in which we explicitly focus on the fact that for mobile operators today, the main product (with the possible exception of the handset subsidy) is data bundles. In the presence of heterogeneous consumer valuations, firms choose bundle sizes and prices. The structural focus of our analysis is the effect of the number and range of bundles offered, in addition to the number of firms, on form profits and consumer surplus. Future work will incorporate the dimension of time as in practice data bundles with various periods of validity are offered in the market. 
 
We construct a discrete model in which optimal pricing strategies for firms are determined in a Stackelberg-type competition model. There are finitely many consumers and finitely many firms. Firms determine their quasi-optimal pricing strategy in sequence by using simulation to each select a fixed number of bundles of a single product to offer. Bundles differ in their price and size. There is assumed to be no product differentiation among the firms and consumers have randomized willingness to pay and select their optimal purchase(s) by maximizing their individual consumer surplus. Some customers may choose to purchase nothing at all. 
 
First, we select distributions for the firms' choices and for the consumer valuations that allow for outcomes that are typically observed in an oligopoly market like mobile network data. The finite number of consumers can be thought of discrete groups of types of consumers. This is not entirely dissimilar to the user baskets often used (low, moderate and high volume users) in merger analysis. 
 
Second, we investigate the effect on consumer and total welfare of a change in the number of firms using our Monte Carlo simulation. Prices and quantities as well as customer valuations are discrete variables and we purposely eschew an attempt to find an analytical solution. 
 
The model builds on models where a single firm determines bundling prices and strategies (e.g. Spence, 1980; Schmalensee, 1984; Hitt and Chen, 2005;, Wu et al., 2018; Ye, et al., 2019; Bucarey, et al, 2021), by incorporating competitive interaction (e.g. Mantovani and Vanderkerckhove, 2016). The novelty of our model is the ability to calibrate it to provide insights across a wide range of distributions of customer willingness-to-pay, other consumer preference characteristics and market structures (number of firms). The model is informative for both competition authorities assessing merger proposals, and for firms engaged in cardinality bundle pricing or contemplating market entry. 
 
A key finding is that in this model, a reduction of the number of firms from 4 to 3 has no effect on consumer surplus. We also see that when the model runs with 4 firms, it quite often happens that an equilibrium state is reached where one of the firms fails to make any sales at all. This was not observer in the case of 3 firms.