Competitive Pricing in Participation-Dependent Social-Learning Markets

We consider a market comprising two competing service providers and a collection of users who can choose to subscribe to one provider or the other. The market is assumed to evolve over two subscription periods, while the users’ subscription decisions are based on the reviews of the earlier users, the prices set by the providers, and their own private preference parameter. In this context, we are interested in investigating the nature of the pricing policy adopted by the service providers. Towards this direction, employing the framework of stochastic games, we proceed to first solve the second-period pricing problem using information about the evolution of the market during the first-period. Specifically, given the first-period reviews about the QoS (Quality of Service) performance of the service providers, we characterize the solution to the second-period problem in terms of Nash equilibrium (NE) prices. We then derive an explicit expression for the NE prices by identifying the providers’ best-response functions. Next, using the form of the second-period NE prices we solve the overall two-period problem. In particular, for a given pair of pricing policies, we derive an integral-form expression for the expected revenue accrued by the providers over the two subscription periods. The revenue expression can be solved numerically to obtain the overall solution in terms of (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $</tex-math> </inline-formula>-approximate) NE pricing policy. Finally, we conduct a detailed numerical study to understand the performance of the market at the proposed Nash equilibrium pricing policy. Specifically, we identify two possible market scenarios (namely, true-belief and false-belief) that arise depending on whether the users’ belief about the providers’ capacity is correct. Interestingly, our results demonstrate that, under both market scenarios, a natural revenue-sharing compromise emerges between the providers across the two subscription time periods.