Bayesian Production/Inventory Competition with Unobserved Lost Sales

Shuang He (), Pujie Shi () and Jian Zhang ()
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Shuang He: Beijing Jiaotong University
Pujie Shi: Inner Mongolia University of Finance and Economics
Jian Zhang: Inner Mongolia University of Finance and Economics

A chapter in LISS 2020, 2021, pp 1037-1056 from Springer

Abstract: Abstract We study the multi-period production/inventory competition problem of two substitutable products which are operated by two manufacturers respectively. The aggregate demand distribution form of products is known but one parameter is unknown before selling season. At each period, the manufacturers first update the estimates of the unknown parameters using the historical sales data, then they check the inventory levels and make the production/inventory decisions accordingly. Finally, the aggregate demand is realized and satisfied by the available products. One manufacturer’s unsatisfied demand switch to the rival and is satisfied by the rival’s left products if available. The unsatisfied switching demand is lost and unobserved, the unsold products incur a holding cost. The manufacturers compete for the substitute demand by making production/inventory decisions. We model the competition problem as a dynamic Bayesian game with three-dimension state-space. We reduce the dimension of state-space under certain conditions. We prove that there exists a unique Nash equilibrium in each period and show that the produce-to policy is the equilibrium production strategy. Finally, we conduct numerical experiments to examine how the model parameters impact on the equilibrium strategy and payoffs, and to generate some managerial insights.

Keywords: Production competition; Bayesian game; Nash equilibrium; Produce-up-to policy (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-33-4359-7_71

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DOI: 10.1007/978-981-33-4359-7_71

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