Peter Kurz | Searcharxiv

arXiv2026

Discrete Choice and Competitive Reactions: End-to-End Simulation with the R Package cash

Although discrete choice (choice-based conjoint) analysis has become a widely used technique for the elicitation of consumer preferences and hence a foundation for product design, to the best of our knowledge, there exists neither free and open-source nor commercial software that covers the game-theoretic simulation of competitive reactions among firms based on discrete choice models to improve decision making beyond traditional product (line) optimization. The R package cash (conjoint + Nash) does not only provide functions to fill this gap but comprises an entire simulation pipeline including the upstream processes of discrete choice analysis itself. cash ranges from preference generation, choice design, error and response simulation, through Bayesian model estimation and evaluation, to Nash equilibrium computation. Doing so, it partly draws from established R packages concerned with discrete choice analysis. While the structure of cash generally aims towards end-to-end simulation as well as simulation of competitive dynamics based on real data, all its key elements mentioned above may be of use independently of each other.

econ.EM↗

arXiv2025

Computing Nash equilibria for product design based on hierarchical Bayesian mixed logit models

Despite a substantial body of theoretical and empirical research in the fields of conjoint and discrete choice analysis as well as product line optimization, relatively few papers focused on the simulation of subsequent competitive dynamics employing non-cooperative game theory. Only a fraction of the existing frameworks explored competition on both product price and design, none of which used fully Bayesian choice models for simulation. Most crucially, no one has yet assessed the choice models' ability to uncover the true equilibria, let alone under different types of choice behavior. Our analysis of thousands of Nash equilibria, derived in full and numerically exact on the basis of real prices and costs, provides evidence that the capability of state-of-the-art mixed logit models to reveal the true Nash equilibria seems to be primarily contingent upon the type of choice behavior (probabilistic versus deterministic), regardless of the number of competing firms, offered products and features in the market, as well as the degree of preference heterogeneity and disturbance. Generally, the highest equilibrium recovery is achieved when applying a deterministic choice rule to estimated preferences given deterministic choice behavior in reality. It is especially in the latter setting that incorporating Bayesian (hyper)parameter uncertainty further enhances the detection rate compared to posterior means. Additionally, we investigate the influence of the above factors on other equilibrium characteristics such as product (line) differentiation.

econ.EM↗