Autonomous vehicles will be an integral part of ride-sharing services in the future. This setting differs from traditional ride-sharing marketplaces because of the absence of the supply side (drivers). However, it has far-reaching consequences because in addition to pricing, players now have to make decisions on how to distribute fleets across network locations and re-balance vehicles in order to serve future demand. In this paper, we explore a duopoly setting in the ride-sharing marketplace where the players have fully autonomous fleets. Each ride-service provider (RSP)'s prices depend on the prices and the supply of the other player. We formulate their decision-making problems using a game-theoretic setup where each player seeks to find the optimal prices and supplies at each node while considering the decisions of the other player. This leads to a scenario where the players' optimization problems are coupled and it is challenging to find the equilibrium. We characterize the types of demand functions (e.g.: linear) for which this game admits an exact potential function and can be solved efficiently. For other types of demand functions, we propose an iterative algorithm to compute the equilibrium. We conclude by providing numerical insights into how different kinds of equilibria would play out in the market when the players are asymmetric. Our numerical evaluations also provide insights into how the regulator needs to consider network effects while deciding regulation in order to avoid unfavorable outcomes.

翻译：自动驾驶车辆将成为未来网约车服务的重要组成部分。与传统网约车市场不同，这一情景因缺乏供应方（司机）而具有根本性差异。然而，这带来了深远的影响——除了定价之外，参与者还需决定如何在不同网络节点间分配车队并进行车辆再平衡，以应对未来需求。本文探讨了网约车市场中双寡头垄断的情景，其中参与者拥有完全自动驾驶车队。每个乘车服务提供商的定价取决于竞争者的定价与供应量。我们采用博弈论框架来构建其决策问题，使每个参与者在考虑对方决策的同时，寻求每个节点上的最优定价与供应量。这导致参与者间的优化问题相互耦合，难以求解均衡。我们刻画了存在精确势函数且可高效求解的博弈需求函数类型（如线性需求函数）。针对其他类型需求函数，我们提出了一种迭代算法以计算均衡值。最后，通过数值分析揭示了参与者不对称时市场中不同类型均衡的演化规律。数值评估还为监管者提供了启示：在制定监管规则时需考虑网络效应，以避免不利结果。