Autonomous vehicles will be an integral part of ride-sharing services in the future. This setting is different 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 depends 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 solve for 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 heuristic 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 or when there are regulations in place.

翻译：自动驾驶汽车将成为未来共享出行服务的重要组成部分。这一情境与传统共享出行市场有所不同，因为在其中缺少供给侧（司机）。然而，这带来深远影响：除了定价之外，参与者现在还需决定如何将车队分布至网络中的不同位置，并重新平衡车辆以服务未来需求。本文探讨了共享出行市场中双寡头垄断的设定，其中参与者拥有完全自动化的车队。每家出行服务提供商的价格取决于另一家的价格和供应量。我们利用博弈论框架构建其决策问题：每个参与者在考虑另一参与者决策的同时，寻求每个节点上的最优价格和供应量。这导致参与者的优化问题相互耦合，求解均衡具有挑战性。我们刻画了能承认精确势函数且可高效求解的此类博弈的需求函数类型（例如线性函数）。对于其他类型的需求函数，我们提出一种迭代启发式算法来计算均衡。最后，我们通过数值分析，提供关于当参与者不对称或存在监管时，不同均衡如何在市场中演化的见解。