Stochastic Optimal Control for Online Seller under Reputational Mechanisms
In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (store). This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in order to maximize her profit, and further that this switch can be identified through the seller’s reputation. We show that for each seller there is an optimal reputation, i.e. , the reputation at which the seller should switch her state in order to maximize her total profit. We design a stochastic behavioral model for an online seller, which incorporates the dynamics of resource allocation and reputation. The design of the model is optimized by using a stochastic advertising model from  and used effectively in the Stochastic Optimal Control of Advertising . This model of reputation is combined with the effect of online reputation on sales price empirically verified in . We derive the Hamilton-Jacobi-Bellman (HJB) differential equation, whose solution relates optimal wealth level to a seller’s reputation. We formulate both a full model, as well as a reduced model with fewer parameters, both of which have the same qualitative description of the optimal seller behavior. Coincidentally, the reduced model has a closed form analytical solution that we construct.
References listed on IDEAS
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- Patrick Bajari & Ali Hortaçsu, 2004. "Economic Insights from Internet Auctions," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 457-486, June.
- Paul Resnick & Richard Zeckhauser & John Swanson & Kate Lockwood, 2006.
"The value of reputation on eBay: A controlled experiment,"
Springer;Economic Science Association, vol. 9(2), pages 79-101, June.
- Resnick, Paul & Zeckhauser, Richard & Swanson, John & Lockwood, Kate, 2003. "The Value of Reputation on eBay: A Controlled Experiment," Working Paper Series rwp03-007, Harvard University, John F. Kennedy School of Government.
- Daniel Houser & John Wooders, 2006. "Reputation in Auctions: Theory, and Evidence from eBay," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(2), pages 353-369, 06.
- Ram C. Rao, 1986. "Estimating Continuous Time Advertising-Sales Models," Marketing Science, INFORMS, vol. 5(2), pages 125-142. Full references (including those not matched with items on IDEAS)
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