On the Convergence of the Shapley Value in Parametric Bayesian Learning Games

Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian learning games where players perform a Bayesian inference using their combined data, and the posterior-prior KL divergence is used as the characteristic function. We show that for any two players, under some regularity conditions, their difference in Shapley value converges in probability to the difference in Shapley value of a limiting game whose characteristic function is proportional to the log-determinant of the joint Fisher information. As an application, we present an online collaborative learning framework that is asymptotically Shapley-fair. Our result enables this to be achieved without any costly computations of posterior-prior KL divergences. Only a consistent estimator of the Fisher information is needed. The framework's effectiveness is demonstrated with experiments using real-world data.

Toward Large-Scale Agent Guidance in an Urban Taxi Service

Empty taxi cruising represents a wastage of resources in the context of urban taxi services. In this work, we seek to minimize such wastage. An analysis of a large trace of taxi operations reveals that the services' inefficiency is caused by drivers' greedy cruising behavior. We model the existing system as a continuous time Markov chain. To address the problem, we propose that each taxi be equipped with an intelligent agent that will guide the driver when cruising for passengers. Then, drawing from AI literature on multiagent planning, we explore two possible ways to compute such guidance. The first formulation assumes fully cooperative drivers. This allows us, in principle, to compute systemwide optimal cruising policy. This is modeled as a Markov decision process. The second formulation assumes rational drivers, seeking to maximize their own profit. This is modeled as a stochastic congestion game, a specialization of stochastic games. Nash equilibrium policy is proposed as the solution to the game, where no driver has the incentive to singly deviate from it. Empirical result shows that both formulations improve the efficiency of the service significantly.