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Dynamic Optimization and Learning: How Should a Manager Set Prices When the Demand Function is Unknown?

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  • Alexandre X. Carvalho
  • Martin L. Puterman

Abstract

This paper considers the problem of changing prices over time to maximize expected revenues in the presence of unknown demand distribution parameters. It provides and compares several methods that use the sequence of past prices and observed demands to set price in the current period. A Taylor series expansion of the future reward function explicitly illustrates the tradeoff between short term revenue maximization and future information gain and suggests a promising pricing policy referred to as a one-step look-ahead rule. An in-depth Monte Carlo study compares several different pricing strategies and shows that the one-step look-ahead rules dominate other heuristic policies and produce good short term performance. The reasons for the observed bias of parameter estimates are also investigated. Neste artigo, nós estudamos o problema de escolher preços sequencialmente, de forma a maximizar a receita esperada, em um ambiente onde os parâmetros da função de demanda são desconhecidos, e o horizonte de vendas é finito. Vários métodos de otimização seqüencial são discutidos, onde os preços e as vendas resultantes anteriores são utilizados para determinar o preço no período atual. Expansões de Taylor são empregadas para construir aproximações da função valor, explicitando a relação de compromisso entre maximização de receita no curto-prazo e maior ganho de informação para obter maior receita agregada no longo-prazo. A partir dessas expansões, nós derivamos estratégias promissoras, denominadas políticas de one-step look-ahead que combinam otimização e aquisição de informação dinamicamente. Simulações de Monte Carlo são apresentadas, onde constatamos a superioridade das políticas de one-step look-ahead, quando comparadas a diversas outras regras de otimização seqüencial. Finalmente, nós discutimos problemas de endogeneidade, onde fazemos um paralelo com a teoria de controle adaptativo, e discutimos a validade das regras de one-step look-ahead, mesmo quando endogeneidade é observada.

Suggested Citation

  • Alexandre X. Carvalho & Martin L. Puterman, 2015. "Dynamic Optimization and Learning: How Should a Manager Set Prices When the Demand Function is Unknown?," Discussion Papers 0158, Instituto de Pesquisa Econômica Aplicada - IPEA.
    • Handle: RePEc:ipe:ipetds:0158
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    References listed on IDEAS

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