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Data-Driven Behaviour Estimation in Parametric Games

Anna M. Maddux, Nicolò Pagan, Giuseppe Belgioioso, Florian Dörfler

TL;DR

The paper addresses learning the underlying utilities of agents in multi-agent games from observed behavior, whether in equilibrium or in sequential action data. It introduces a data-driven inverse-game-theoretic inference method that computes all parameter vectors $\Theta_i$ that best rationalize the observations, yielding polyhedral solution sets. The approach is computationally efficient and accommodates both Nash equilibrium profiles and better-response trajectories. In a Coca-Cola vs. Pepsi advertising competition case, it infers firms' beliefs about market-share evolution from historical expenditures, achieving lower irrationality relative to standard fits such as $L_2$ or OLS and highlighting practical applicability to marketing strategy analysis.

Abstract

A central question in multi-agent strategic games deals with learning the underlying utilities driving the agents' behaviour. Motivated by the increasing availability of large data-sets, we develop an unifying data-driven technique to estimate agents' utility functions from their observed behaviour, irrespective of whether the observations correspond to equilibrium configurations or to temporal sequences of action profiles. Under standard assumptions on the parametrization of the utilities, the proposed inference method is computationally efficient and finds all the parameters that rationalize the observed behaviour best. We numerically validate our theoretical findings on the market share estimation problem under advertising competition, using historical data from the Coca-Cola Company and Pepsi Inc. duopoly.

Data-Driven Behaviour Estimation in Parametric Games

TL;DR

The paper addresses learning the underlying utilities of agents in multi-agent games from observed behavior, whether in equilibrium or in sequential action data. It introduces a data-driven inverse-game-theoretic inference method that computes all parameter vectors that best rationalize the observations, yielding polyhedral solution sets. The approach is computationally efficient and accommodates both Nash equilibrium profiles and better-response trajectories. In a Coca-Cola vs. Pepsi advertising competition case, it infers firms' beliefs about market-share evolution from historical expenditures, achieving lower irrationality relative to standard fits such as or OLS and highlighting practical applicability to marketing strategy analysis.

Abstract

A central question in multi-agent strategic games deals with learning the underlying utilities driving the agents' behaviour. Motivated by the increasing availability of large data-sets, we develop an unifying data-driven technique to estimate agents' utility functions from their observed behaviour, irrespective of whether the observations correspond to equilibrium configurations or to temporal sequences of action profiles. Under standard assumptions on the parametrization of the utilities, the proposed inference method is computationally efficient and finds all the parameters that rationalize the observed behaviour best. We numerically validate our theoretical findings on the market share estimation problem under advertising competition, using historical data from the Coca-Cola Company and Pepsi Inc. duopoly.
Paper Structure (4 sections, 2 figures)

This paper contains 4 sections, 2 figures.

Table of Contents

  1. Conclusion
  2. Appendix
  3. Proof of Proposition \ref{['prop:1']}
  4. Proof of Proposition \ref{['LP_reformulation']}

Figures (2)

  • Figure 2: Coke's and Pepsi's irrationality, expressed by violations of the better-response conditions in \ref{['better-response']}, over the time horizon. Resulting irrationality from the OLS regression fit (black line), the $L_2$-based variant (red line), and from our estimation method (grey line).
  • Figure 3: Coke’s and Pepsi’s beliefs on market share evolution of Coke. The true market share evolution (blue line), the OLS regression fit (black line), the fit from the $L_2$-based variant (red line) and the fit from the polyhedral solution set (grey region).