RABIH SALHAB - Research Overview

Understanding the interplay between individual and collective behaviors in large populations of interacting decision makers is an important and under-explored challenge in decision science and control theory. This interplay constitutes a crucial step towards developing efficient policies that govern global behavior in systems of practical interest, such as designing optimal pricing strategies and information filters to shape the distribution of a large number of competing taxi drivers in a city and making optimal marketing investments in large markets of socially influenced strategic consumers. Current models face many challenges that limit their applicability. On the one hand, aggregate models, though simple, elegant, and computationally tractable, fall short of capturing asymmetric information structures, strategic interactions among individuals, individual behavioral biases, population heterogeneity, and aggregation of distributed information. On the other hand, while agent-based models overcome the aforementioned shortcomings, they easily become intractable. My research focuses on bridging the gap between aggregate and agent-based models in large populations of interacting decision makers.

In particular, I am pursuing two research directions. First, I develop abstract agent-based models that have applications in microeconomics, robotics, advertising, transportation systems, and smart grids. I use tools from mean-field games (MFG) theory to leverage models' symmetries and develop tractable solutions that anticipate the aggregate behavior. Second, I study aggregation of information in large social networks.

without_q_stoch.mp4

A group of players choosing between -10 and 10 without social effect.

hight_q_stoch.mp4

A group of players choosing between -10 and 10 under a strong social effect.

Collective Stochastic Discrete Choice Problems

(Click here for our presentation at the mean field games workshop, IPAM - UCLA)

The emergence of collective choices from interdependent individual choices is an abundant phenomenon in human and animal social organizations. This work aims at developing tractable models to understand the relation between individual and collective choices in large populations of interacting, heterogeneous, and strategic decision makers. More specifically, we consider a large group of agents who are moving in a state/opinion space from their initial opinions to ultimately settle on a finite set of predefined alternatives while minimizing effort and trying to conform with the average opinion. This work has practical applications in modelling opinion dynamics and crystallization of final choices in elections; understanding biological collective decision making mechanisms, such as honey bees choosing a nectar site; and controlling a multi-agent robot team to visit multiple sites of interest and perform collective tasks, such as search and rescue.

We address the following research questions:

What optimal strategy guides an agent to select under peer pressure and least effort one of the alternatives?
What minimal information set is required to make an optimal choice of alternative?
Can one anticipate the distribution of choices among the alternatives?
Does the population split between the alternatives in a unique or multiple ways?
How do the agents' cooperative and non-cooperative behaviors shape the distribution of choices?

paths.mp4

A group of drivers serving randomly appearing customers. The blue and red dots are the vacant and busy cars, respectively. The green circles are the probability distribution of the customers.

Ride-sharing Problems

Emerging ride-sharing services such as Uber or Lyft match a group of drivers providing rides with customers through an online ride-sharing platform (RSP). This business model faces a number of fundamental challenges due to the self-interested and independent nature of drivers as decision makers. As independent contractors, drivers choose the area they wish to serve, if they accept or reject rides, and when they start and stop working. With no direct control over the drivers, the RSP can only use financial incentives and select the information it provides to the drivers and customers to improve the quality of service and balance supply and demand. The goal of this work is to understand the dynamics and economics of ride-sharing services, taking into account the self-interested nature and strategic behavior of participating agents. This includes analyzing and predicting the reaction of competing drivers to the information provided by the RSP, which is a combination of request statistics, prices at various locations and times, and estimation of the state of road network.

Non-Bayesian Social Learning over Networks

People form beliefs over various political, economic, environmental, and social issues. With insufficient and heterogeneous sources of information, they engage in communication with their social clique to learn the truth. For example, consumers learn the quality of a product from others' personal experiences before making a purchase. This work studies the learning process under different behavioral assumptions. In particular, we consider a non-Bayesian learning model over a social network where a group of agents receive private signals about an unknown parameter. We presume two behavioral assumptions. The first assumes communication constraints in that agents can only share samples from their beliefs with their neighbors. This is in contrast with standard models of sharing the full belief, i.e. probability distribution over the entire set of parameters. The second assumption is limited cognitive power, based on which individuals incorporate their neighbors' samples into their beliefs following a simple DeGroot-like social learning rule which suffers from redundancy neglect and imperfect recall of the past history.

Marketing Models

Understanding the dynamics of large markets of interacting consumers is a key step in designing optimal marketing investments. The aggregate marketing models are computationally tractable, but they fail to model market heterogeneity in consumer sensitivity to prices and social pressure, consumer strategic behavior, and consumer behavioral biases. This project aims to build tractable agent-based models in two different contexts-markets with online rating systems and diffusion of innovation-and obtain new insights that are tied to the consumer strategic forward-looking behavior and market heterogeneity.