Simulating Nash Equilibrium Market Outcomes with Bayesian Analysis of Choice-Based Conjoint Data

The implemented model constrains the beta coefficients for price and budget. Both are restricted to positive values only, which makes the model much more realistic. Usually one would assume the price coefficients to be negative only, however in the BLP-type specification there is a reward for not using up the entire budget. Hence,
${\beta _{price}}$
must be positive (Pachali et al. 2017b). In some cases, it makes sense to additionally impose ordinal constraints on the betas among brands. This would be beneficial if there were a clear and strict preference for individual specifications of the products in question (i.e. a higher quality ceteris paribus is always more desirable). For this particular beer data set, this cannot reasonably be justified, since there is no objective order of beers. The research question whether a merger between Heineken and Amstel would yield an incremental profit beyond the sum of the individual profits can now be answered by changing the ownership matrix so that those three beers belong to the same owner and thus not price compete anymore. This market is now a duopoly with two players (Heineken together with Amstel vs. Estrella) and referred to as the merge competition scenario. Table 1 displays the weighted average price and the producer surplus before and after the merger and quantifies the absolute and relative difference between those two scenarios. While
${\bar p}$
increases by 3.3%, the producer surplus even increased.