Pragmatic algorithmic game theory

Abstract

Algorithmic Game Theory (AGT) studies problems at the interface between computer science and microeconomics. Research in this area typically attacks very general settings using theoretical tools. There are great advantages to such an approach: in particular, the field has amassed an impressive range of sweeping impossibility, optimality, and approximation results. However, sometimes it is very difficult to obtain a clean theoretical result that addresses a complex, real-world problem of interest. We can often say more about realistic problems if we're willing to be pragmatic. In particular, progress can often be made by leveraging one or both of the following forms of pragmatism: 1. Aiming to achieve good performance only on problems of interest, rather than in relatively unconstrained settings; and 2. Working with statistical rather than analytical tools, thereby defining problems of interest implicitly via a dataset and/or appealing to data-driven measures of performance. This talk will survey three broad problems that I have attacked using such pragmatic approaches in my own research. (There is, of course, a wide range of excellent work in this vein by others; however, surveying it is beyond the scope of this talk.) First, a central problem in AGT is reasoning about equilibrium behavior in games. A seminal result was that the identification of a sample Nash equilibrium is PPAD-complete even in two-player games, meaning that the problem is probably intractable in the worst case. However, it is nevertheless often still possible to reason about games of interest, because they often exhibit various structural regularities. I'll describe the Action Graph Game (AGG) formalism, and explain how restricting ourselves to games that are compact in this (general) language yields exponential performance improvements. AGGs are particularly interesting for AGT researchers because they can compactly model messy, realistic mechanisms like advertising auctions or voting systems. I'll discuss what can be gained by analyzing such mechanisms in this way, and introduce some general tools that researchers can use to easily leverage these techniques in their own work. A second problem at the core of AGT is market design. I'll focus here on the FCC's upcoming 'incentive auction', in which television broadcasters will be given the opportunity to sell their broadcast rights, remaining broadcasters will be repacked into a smaller block of spectrum, and the freed airwaves will be resold to telecom companies. The stakes for this auction are huge'projected tens of billions of dollars in revenue for the government'justifying the design of a special-purpose descending-price auction mechanism, which I'll describe. An inner-loop problem in this mechanism is determining whether a given set of broadcasters can be repacked into a smaller block of spectrum while respecting radio interference constraints. This is an instance of a (worst-case intractable) graph coloring problem; however, stations' broadcast locations and interference constraints are all known in advance. I'll explain how this information can be leveraged by machine learning methods to obtain a SAT-based algorithm that can very quickly solve nearly all repacking problems encountered in practice. Finally, I'll briefly discuss Kudu, a market for agricultural commodities that my collaborators and I have built to help smallhold farmers in Uganda.