We study Emergency Medical Services (EMS) in emerging economies, which are mostly still decentralized. Randomly arriving customers can request service from multiple service providers (duplicate orders) and choose the one that provides quicker service. Such customer behavior plays off providers deliberately against each other; and they, in turn, strategically define their service regions. To our knowledge, this setting, where customers pit service providers against each other dynamically and temporally, has not been studied before, and we present the first paper on this topic. We consider a stylized non-cooperative game with two service providers, each with one server, located at either end of a Hoteling line. Demand is temporally Poisson and spatially uniform. Providers' strategically choose service regions to maximize their utility accounting for stochasticity and associated opportunity costs. %This simplified model is quite complex with interesting and novel properties. We observe that provider behaviors are coupled, that is, the joint idle probability component is {\em not independent}. We analyze this using renewal theory, and find that the dependence between the servers is `limited'. This leads us to a significantly more tractable approximation of the joint idle probability, which is close to the exact joint probability. We then show that the approximate utility functions of a provider, given a fixed strategy of the competitor, are unimodal. We prove this game admits a symmetric \emph{pure strategy} Nash Equilibrium, and that this approximate equilibrium is an $\epsilon-$Nash equilibrium of the exact system. Providers, thus, can choose service regions that overlap and compete for customers, as is seen in reality. We compare this setting with two single order systems. We benchmark this system against a fully centralized EMS, and compute the Price of Anarchy (PoA), and show it is bounded by a small constant depending on the game parameters. As centralization is not achievable, we next compare with a decentralized single-order system (where EMSs still compete). Providers in aggregate are worse off under duplicate orders, in terms of utilities and number of customers served. Customers being strategic leads to similarly strategic decisions on the part of providers, whose service ranges (mostly) turn out to be shorter under duplicate orders. The customer perspective is more nuanced -- customers if served may experience shorter response times under duplicate orders; but ultimately, they have fewer provider options; and because of some placing duplicate orders, many others are dropped. Duplicate orders often deteriorate service equity along the line, with some regimes as exceptions. Policymakers should carefuly consider equity vs access tradeoffs for these exceptions. We also show that the gap between the duplicate order and single order systems can (only) be partially bridged using bargaining mechanisms that improve both provider and customer performance metrics.
Read full abstract