Econometric Theory for Games Part 1 Introduction to

Econometric Theory for Games Part 1: Introduction to Econometrics and Econometrics of Discrete Bayesian Games Vasilis Syrgkanis Microsoft Research New England

Outline of tutorial • Day 1: • Brief Primer on Econometric Theory • Estimation in Static Games of Incomplete Information: two stage estimators • Markovian Dynamic Games of Incomplete Information • Day 2: • Discrete Static Games of Complete Information: multiplicity of equilibria and set inference • Day 3: • Auction games: Identification and estimation in first price auctions with independent private values • Algorithmic game theory and econometrics • Mechanism design for data science • Econometrics for learning agents

A Primer on Econometric Theory Basic Tools and Terminology

Econometric Theory •

Main Goals •

Estimator Properties of Interest •

General Classes of Estimators •

General Classes of Estimators •

Consistency of Extremum Estimators •

Asymptotic Normality • In practice, typically variance is computed via Bootstrap [Efron’ 79]: Re-sample from your samples with replacement and compute empirical variance

Econometric Theory for Games

Econometric Theory for Games •

Why useful? • Scientific: economically meaningful quantities • Perform counter-factual analysis: what would happen if we change the game? • Performance measures: welfare, revenue • Testing game-theoretic models: if theory on estimated quantities predicts different behavior, then in trouble

Incomplete Information Games and Two-Stage Estimators Static Games: [Bajari-Hong-Krainer-Nekipelov’ 12] Dynamic Games: [Bajari-Benkard-Levin’ 07], [Pakes-Ostrovsky. Berry’ 07], [Aguirregabiria-Mira’ 07], [Ackerberg-Benkard-Berry. Pakes’ 07], [Bajari-Hong-Chernozhukov-Nekipelov’ 09]

High level idea • At equilibrium agents have beliefs about other players actions and best respond • If econometrician observes the same information about opponents as the player does then: • Estimate these beliefs from the data in first stage • Use best-response inequalities to these estimated beliefs in the second stage and infer parameters of utility

Static Entry Game with Private Shocks •

Static Entry Game with Private Shocks •

Static Entry Game with Private Shocks •

Simple case: finite discrete states •

• [Newey-Mc. Fadden’ 94: Large Sample Estimation and Hypothesis Testing]

Continuous State Space and Semi. Parametric Efficiency

[Bajari-Hong-Kranier-Nekipelov’ 12] •

Semi-Parametric Two-Stage Estimation [Newey-Mc. Fadden’ 94, Chernozhukov et al ‘ 16]

Semi-Parametric Two-Stage Estimation [Newey-Mc. Fadden’ 94] For detailed exposition see: • [Newey 94, Ai-Chen’ 03] • Section 8. 3 of survey of [Newey-Mc. Fadden’ 94] • Han Hong’s Lecture notes on semi-parametric efficiency [ECO 276 Stanford]

General Dynamic Games [Bajari-Benkard-Levin’ 07], [Pakes-Ostrovsky-Berry’ 07], [Aguirregabiria-Mira’ 07], [Ackerberg-Benkard-Berry-Pakes’ 07], [Bajari-Hong-Chernozhukov-Nekipelov’ 09]

Steady-State Markovian Dynamic Games … … 1. 4. Private shocks i. i. d. , independent of state and private information to each player 2. • State probabilistically transitions to next state, based on prior state and on action profile 3. Each player receives payoff “shockless” discounted expected equilibrium payoff.

Dynamic Games: First Stage [Bajari-Benkard-Levin’ 07] •

Dynamic Games: First Stage [Bajari-Benkard-Levin’ 07] •

Dynamic Games: Second Stage [Bajari-Benkard-Levin’ 07] •

Recap of main idea • At equilibrium agents have beliefs about other players actions and best respond • If econometrician observes the same information about opponents as the player does then: • Estimate these beliefs from the data in first stage • Use best-response inequalities to these estimated beliefs in the second stage and infer parameters of utility

References •