Fall 2015

Robust Inference for Games via Theoretical Guarantees

Wednesday, November 18th, 2015 3:20 pm4:00 pm

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In the past decade the Economics literature has developed a unified approach to inference and prediction of strategic environments. This approach starts with a full theoretical model that characterizes the preferences of agents and the mechanism of interaction between them.
The Econometrician then infers the components of the theoretical model from the data and provides prediction for the new settings by computing a new equilibrium of the strategic model. The issue with this approach is that the initial step where the Econometrician recovers the preferences of the agents from the data boils down to an inversion of a nonlinear mapping that can be discontinuous and even set-valued. In the talk I will discuss the properties of this mapping for classes of simple games and demonstrate that even in cases where this mapping is invertible, the recovered pre-image is very sensitive to the specification of the model. I will also discuss that such poor behavior of the solution will be preserved even when one uses strong conditions to ``regularize" this mapping. All these problems will be further amplified in the prediction.
The approach of set inference provides a robust alternative to traditional inference. In this approach the Econometrician recovers an entire set of preferences of the agents in the interactions that are compatible with many possible specifications of the theoretical model. However, computation of such sets is difficult even in simple games. In my talk I discuss a new approach to inference that is based on the idea of the price of anarchy in Koutsoupias and Papadimitriou (1999). The idea of the approach is to bypass the set inference for the primitives of the model and instead directly infer the outcomes of interest such as welfare or revenue in the game. However, unlike the standard price of anarchy which is based on the ``worst case scenario"-based prediction for the outcomes, we propose to consider the bounds that are informed by the distribution of the data. I talk about the new notion of the empirical price of anarchy that yields the 
price of anarchy over all preferences of agents that could have generated the observable distribution of the data. I then discuss some connections between our notion of the empirical price of anarchy and Economic literature on set inference.
The talk will be based on the the recent work [Khan and Nekipelov, 2014] and [Hoy, Nekipelov and Syrgkanis, 2015].