A stochastic generalized Nash equilibrium model for platforms competition in the ride-hail market

TL;DR

This paper develops a distributed stochastic algorithm to find equilibrium pricing strategies for competing ride-hailing platforms under market uncertainties, avoiding the need for extensive sampling and ensuring convergence under mild conditions.

Contribution

It introduces a novel Tikhonov-regularized stochastic algorithm for solving SGNEPs in ride-hailing markets, with practical advantages in sampling and convergence guarantees.

Findings

Algorithm converges to Nash equilibrium under monotonicity.

No need for increasing sample size during stochastic approximation.

Validated on a numerical ride-hailing market instance.

Abstract

The presence of uncertainties in the ride-hailing market complicates the pricing strategies of on-demand platforms that compete each other to offer a mobility service while striving to maximize their profit. Looking at this problem as a stochastic generalized Nash equilibrium problem (SGNEP), we design a distributed, stochastic equilibrium seeking algorithm with Tikhonov regularization to find an optimal pricing strategy. Remarkably, the proposed iterative scheme does not require an increasing (possibly infinite) number of samples of the random variable to perform the stochastic approximation, thus making it appealing from a practical perspective. Moreover, we show that the algorithm returns a Nash equilibrium under mere monotonicity assumption and a careful choice of the step size sequence, obtained by exploiting the specific structure of the SGNEP at hand. We finally corroborate our results on a numerical instance of the on-demand ride-hailing market.