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Pricing under a multinomial logit model with non linear network effects

Maldonado, Felipe and Berbeglia, Gerardo and Hentenryck, Pascal Van (2020) Pricing under a multinomial logit model with non linear network effects. Working Paper. arXiv. (Unpublished)

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Abstract

We study the problem of pricing under a Multinomial Logit model where we incorporate network effects over the consumer's decisions. We analyse both cases, when sellers compete or collaborate. In particular, we pay special attention to the overall expected revenue and how the behaviour of the no purchase option is affected under variations of a network effect parameter. Where for example we prove that the market share for the no purchase option, is decreasing in terms of the value of the network effect, meaning that stronger communication among costumers increases the expected amount of sales. We also analyse how the customer's utility is altered when network effects are incorporated into the market, comparing the cases where both competitive and monopolistic prices are displayed. We use tools from stochastic approximation algorithms to prove that the probability of purchasing the available products converges to a unique stationary distribution. We model that the sellers can use this stationary distribution to establish their strategies. Finding that under those settings, a pure Nash Equilibrium represents the pricing strategies in the case of competition, and an optimal (that maximises the total revenue) fixed price characterise the case of collaboration.

Item Type: Monograph (Working Paper)
Additional Information: 18 pages plus 9 pages appendix, 7 figures. Working paper, to be submitted
Uncontrolled Keywords: cs.GT; cs.MA
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 06 Jul 2021 20:12
Last Modified: 06 Jan 2022 14:25
URI: http://repository.essex.ac.uk/id/eprint/30708

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