Taxi driver learns dynamic multi-market equilibrium

2018-04-11Taxi is a valuable part of urban transportation and industrial organization, where taxi drivers are both ride service providers and independent contractors. This paper studies the street-hail taxi industry, where each taxi in service is seen as a multi-market firm, every street segment is a distinct market, and firms allocate service time across the street network. We generalize the model into a game of multi-market competition among firms of equal capacity, and prove that the game has pure-strategy Nash equilibrium (PSNE), which is (1) symmetric, (2) essentially unique in that marginal player payoffs are uniform across all invested markets, and (3) globally asymptotically stable under gradient adjustment process and imitative learning. The aggregate strategy at equilibrium maximizes a ""potential function"", and it differs from the social optimal strategy for most forms of production functions. With 868 million trip records of all 13,237 Medallion taxis (yellow cab) in New York City from 2009 to 2013, we validate that taxi drivers' behavior conform to this equilibrium under fixed traffic speeds and taxi demand. Consistent with the equilibrium, marginal segment income is constant over time-of-day in each shift. With the launch of Street Hail Livery (green cab) in late 2013, which increases street-hail vehicles out of core Manhattan, we observe a decrease in yellow cab pickups beyond East 96th Street and West 110th Street