Modeling competitive markets : retailers and ride-hailing platforms

This work broadly focuses on modeling competition within a marketplace, with two areas of application. First, we study the design of loyalty programs within the setting of a competitive retail duopoly, and second, we model competition between ride-hailing platforms, focusing on conditions that give rise to equilibria other than a ``race to the bottom'' price and further develop theory for driver strategy based on ride request rejections. We first optimize the design of a frequency reward program against traditional pricing in a competitive duopoly, where customers measure their utilities in rational economic terms. We assume two kinds of customers: myopic and strategic. Every customer has a prior loyalty bias toward the reward program merchant, a parameter drawn from a known distribution, indicating an additional probability of choosing the reward program merchant over the traditional pricing merchant. Under this model, we characterize the customer behavior: the loyalty bias increases the switching costs of strategic customers until a tipping point, after which they strictly prefer and adopt the reward program merchant. Subsequently, we optimize the reward parameters to maximize the revenue objective of the reward program merchant. We show that under mild assumptions, the optimal parameters for the reward program design to maximize the revenue objective correspond exactly to minimizing the tipping point of customers and are independent of the customer population parameters. Moreover, we characterize the conditions for the reward program to be better when the loyalty bias distribution is uniform - a minimum fraction of population needs to be strategic, and the loyalty bias needs to be in an optimal range. If the bias is high, the reward program creates loss in revenues, as customers effectively gain rewards for ``free'', whereas a low value of bias leads to loss in market share to the competing merchant. Second, we present a model to study competition between ride-hailing platforms. Riders maximize their utility which is decreasing in price and waiting time, while drivers wish to maximize earnings. Platforms compete over prices, and all agents can choose to participate in both platforms simultaneously or instead remain within a single platform. We investigate whether competition leads to a ``tragedy of the commons'' and market failure as the platforms compete over the shared resource of open cars. We present a combination of theoretical results with numerical case studies, using parameters estimated from Uber data, as well as simulations. Our theoretical analysis shows that in all equilibria, riders and drivers will use both platforms and prices will be equal; market failure is always a possibility, but under certain conditions, the possibility of rapid deterioration of market throughput gives rise to equilibria that deter the platforms from undercutting each other's prices. This result is also supported by numerical analysis and simulations. Surprisingly, we observe that under natural conditions on the utility of the riders, namely if riders are not very sensitive to waiting times, the loss of efficiency due to competition could be small. We also further model strategic behavior of the drivers where they can reject trips with long-pick up times. We show the existence and uniqueness of the equilibrium under standard assumptions. We observe that even if the platforms choose sub-optimally low prices, the equilibrium induced by these strategic drivers could maintain high throughput.

Advisor: Saberi Amin 
Ashlagi Itai 
Goel Ashish