  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.
