Stackelberg equilibria in a multiperiod vertical contracting model with uncertain and price-dependent demand
AbstractIn this paper, we consider Stackelberg games in a multiperiod vertical contracting model with uncertain demand. Demand has a distribution with a mean and variance that depend on the current retail price, and this dependence may vary from period to period. We focus on a class of problems in which the market has a memory-based scaling of demand, and the mean scaling is a function of previous retail prices. This leads to a strategic game in which the parties must balance high immediate profits with reduced future earnings. We propose a complete solution to this multiperiod Stackelberg game, covering cases with finite and infinite horizons. The theory is illustrated by using a Cobb-Douglas demand function with an additive, normally distributed random term, but the theory applies to more general settings.
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Bibliographic InfoPaper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2012/2.
Length: 27 pages
Date of creation: 27 Feb 2012
Date of revision:
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Stackelberg game; multiperiod vertical contracting model; price-dependent demand;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-03-28 (All new papers)
- NEP-COM-2012-03-28 (Industrial Competition)
- NEP-IND-2012-03-28 (Industrial Organization)
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2011/14, Department of Business and Management Science, Norwegian School of Economics.
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