This is Jessica. Previously I posted about interface-induced equilibria in strategic settings, which I find interesting in light of the potential for behavioral induced feedback loops when presenting people with model predictions (e.g., performative prediction), and the fact that there’s not a lot of research on the effects of interfaces (such as visualizations) in strategic settings. Related to this, in some recent work, Paula Kayongo, Glenn Sun, Jason Hartline and I ran an initial experiment looking into what we call ‘visualization equilibrium’, where we took a simple congestion game and had participants choose between two locations, A and B, where their earnings from each choice they made was governed by a payoff function that accounted for how many other participants also chose that location. In most trials they also saw a visualization which they could use as a prediction of what might happen, e.g., a bar chart labeled as showing how many people had chosen each location in a prior iteration of the game with the same number of people. In one set of conditions, we told the participants that only they had access to this visualization, but in another ‘public visualization’ set, they were told that the visualization was available to everyone else they were playing against.
We found that visualizing the Nash equilibrium of the game did not result in behavior at equilibrium; that required visualizing a slightly more even distribution over location A and B. We had included a condition where we varied the way the prior play was visualized to see whether visually emphasizing sampling error in the prediction would make it harder for participants to anticipate how other people would react to the public visualization, changing the outcome distribution. We saw only a little evidence of this though, in the form of slightly more people reporting that they switched their decision relative to when the visualization was available only to them when the visualization just showed point estimates. Overall the results were noisy, perhaps because the focus on initial play encouraged more random guessing or experimenting with strategies (participants didn’t get feedback on how they did to help them evaluate strategies), perhaps because the task felt too abstract or contrived.
So in some current work with Jason and Dongping Zhang, our goal is to study these kinds of effects in the context of taxi or rideshare networks. The idea is that the visualization could potentially coordinate driver behavior to reach some desirable steady state. E.g., imagine you’re a taxi driver. You might have some beliefs about where the most lucrative locations for pick-ups are based on your prior experience. How much better off could you and other drivers be if there’s a public information signal that aggregates information across drivers, so that you aren’t stuck making decisions based on limited prior experience? Or maybe there’s some hybrid signaling strategy that allocates a public visualization to some drivers and direct recommendations to others. From the perspective of the taxi or rideshare company, the goal is presumably for the public signal to help guide the system toward some desirable equilibrium, e.g., one that maximizes total revenue.
However, we’re running into challenges with modeling supply demand interaction. We’ve been working with a big origin-destination taxi and rideshare data set from Chicago, where we can distinguish trips by taxi ID and observe some censored trip-level information, such as pickup and drop locations and timestamps (rounded to the nearest 15 mins), fare, and trip duration. Ideally, we want to use the data to create a realistic problem setting for an experiment, one in which we can find an equilibrium of a region based on local supply and demand. This kind of OD data has limitations for studying equilibria though: for any given location during a time span, we can only observe the realized demand (i.e. the number of passengers who got picked up in that location at that time), and the approximated local supply (i.e. the number of taxi drivers who dropped off in in that location in the previous time period). We need a way to generate counterfactuals, i.e., how would changes in supply affect the total pickups for a location at a time?
We’ve spent some time browsing the transportation literature, but it seems fairly common to use the observed pickups to represent demand in a region, which doesn’t really help us. So I’m posting this in the hopes that maybe some readers have thoughts on reasonable models, from ridesharing or transportation applications or other domains with analogous data limitations, that could be applied to estimate the uncertainty in local pickups based on dynamically changing local supply.
Does your data have wait times (time between order and pickup)? This might be a measure of excess demand at least once you normalize for time of day. I’m not a transport economist though.
We don’t have information on requests, just time of pickup. But maybe that’s a feature some rideshare datasets would provide.
One thought is that demand in other parts of the city could provide useful variation. For example, the end of a baseball game or unusually high airport arrivals might draw drivers from downtown for reasons unrelated to local demand.
Nicola Rosaia (who is coming to Columbia Business School next year) seems like the right person to talk to. His job market paper used some kind of policy variation to solve this problem, but presumably has all the right references.
Thank for the tip, I am checking out Rosaisa’s work and it does look interesting. I like the idea of introducing some form of assumptions about how higher than usual pickups in some zones might translate to more unfulfilled demand in others.
To be clear:
You’re seeking: f(x) = g(x) + t, where g(x) is a linear function, representing the relationship between supply and demand, t is an error and you want to find when f(x) will diverge. That is, you already know when f(x) converges.
Then, you’re asking for examples/counter-factuals/data sets that would allow you to see when this linear function diverges, in practice? Is this right?
Am not 100% sure that this is related, but there is the phenomenon of the “hot hand fallacy”. This is a sports metaphor that means that the more a player or a team scores consecutively, the more likely it is to score. It’s been repeatedly shown that this is a fallacy because the player or team scoring often resembles something closer to a random walk, rather than a monotonic function.
To apply this to your supply and demand cases, it could be that an Uber driver thinks that because a stream of riders is coming into location x, it’s a “hot-hand”. In reality, it’s a random function.
So, formally, what you’re looking for is when f(x) resembles a diffusion equation. Right?
Thanks for the comments/questions. We’re going to try an approach someone suggested involving modeling pickups using a production function and relying on some assumptions and a prior over how requests convert to pickups, available drivers in a zone at a given time, etc.
Traditional transportation choice literature and academics may be able to provide insight and suggestions. The work of:
– David Hensher, U of Sydney
– Ken Train, UCB
– Daniel McFadden, UCB
If the work posted to their websites or in Google Scholar isn’t helpful, reaching out to them directly may address this query more directly.