<p>This study analyzes optimal pricing strategies in a duopoly market where customers differ in their preferences toward congestion. We consider two customer types: type-P customers, whose utility increases with aggregate demand, and type-N customers, whose utility decreases with aggregate demand. We formulate a Nash price competition model with linear demand and heterogeneous firm quality, and derive closed-form equilibrium prices, demands, and profits. We also compare the competitive equilibrium with the cooperative, joint revenue-maximizing solution. The analysis shows that customer composition and the relative strength of positive and negative network effects substantially shape equilibrium outcomes. In particular, under symmetric price sensitivities, a larger proportion of type-N customers raises equilibrium prices and profits, whereas a larger proportion of type-P customers intensifies price competition. The results further show that the higher-quality firm consistently dominates its rival. Moreover, when congestion aversion is sufficiently strong and quality asymmetry is not too large, competitive prices can rise above cooperative prices, enabling competitive pricing to attain revenues close to the cooperative benchmark. These findings provide practical guidance for pricing in service markets where congestion affects customer choice.</p>

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Optimal pricing with heterogeneous congestion preferences in duopoly markets

  • Kimitoshi Sato,
  • Nako Iwaji

摘要

This study analyzes optimal pricing strategies in a duopoly market where customers differ in their preferences toward congestion. We consider two customer types: type-P customers, whose utility increases with aggregate demand, and type-N customers, whose utility decreases with aggregate demand. We formulate a Nash price competition model with linear demand and heterogeneous firm quality, and derive closed-form equilibrium prices, demands, and profits. We also compare the competitive equilibrium with the cooperative, joint revenue-maximizing solution. The analysis shows that customer composition and the relative strength of positive and negative network effects substantially shape equilibrium outcomes. In particular, under symmetric price sensitivities, a larger proportion of type-N customers raises equilibrium prices and profits, whereas a larger proportion of type-P customers intensifies price competition. The results further show that the higher-quality firm consistently dominates its rival. Moreover, when congestion aversion is sufficiently strong and quality asymmetry is not too large, competitive prices can rise above cooperative prices, enabling competitive pricing to attain revenues close to the cooperative benchmark. These findings provide practical guidance for pricing in service markets where congestion affects customer choice.