Estimating dynamic games of oligopolistic competition: an experimental investigation

• DOI: http://doi.org/10.1111/1756-2171.12321
• Published date: 01 June 2020
• Author: Emanuel Vespa,Tobias Salz
• Date: 01 June 2020

RAND Journal of Economics

Vol.51, No. 2, Summer 2020

pp. 447–469

Estimating dynamic games of oligopolistic

competition: an experimental investigation

Tobias Salz∗

and

Emanuel Vespa∗∗

We evaluate standard assumptions in the estimation of dynamic oligopoly models with labora-

tory data. Using an entry/exit game, we estimate structural parameters under the assumption

that the data are generated by a Markov-perfect equilibrium and subsequently predict counter-

factual behavior. If behavior was collusive, however, the assumption would be violated and one

would mispredict counterfactuals. The laboratory allows us to compare predicted behavior to

true counterfactuals implemented as treatments. Our main finding is that prediction errors due

to collusion are modest in size. We also document a differentdeviation from equilibrium behavior

(inertia) that can lead to large prediction errors.

1. Introduction

Many empirical studies attempt to recover primitives of an economic model that are then

used to evaluate counterfactual scenarios. Identification of such primitives typically requires

assumptions (on functional forms, equilibrium selection, etc.), and if these are not met, param-

eter estimates and counterfactual policy recommendations can be inaccurate. In this article, we

illustrate how the laboratory can be used to evaluate the extent to which specific modelling as-

sumptions may generate counterfactual prediction errors. The exercise we propose involves four

steps. First, we implement a model of interest in the laboratory and obtain data resulting from

(subjects’) play under those primitives. Second, under standard identification assumptions,we

use the laboratory-generated data to structurally recover the primitives. Third, we compare the

true implemented primitives to the estimates. Fourth, we use the estimated primitives to predict

behavior in a counterfactual scenario. Crucially, for step four, we also implement the counter-

factual scenario directly in the laboratory allowing us to compare it to the counterfactual model

∗Massachusetts Institute of Technology;tsalz@mit.edu.

∗∗UC Santa Barbara; vespa@ucsb.edu.

For helpful discussions the authors would liketo thank John Asker, Isabelle Brocas, Colin Camerer, Juan Carrillo, Allan

Collard-Wexler,Guillaume Fréchette, Ali Hortaçsu, Kei Kawai, Robin Lee, Alessandro Lizzeri, Ryan Oprea, Ariel Pakes,

TomPalfrey, Stephen Ryan, Andrew Schotter, Ralph Siebert, Matthew Shum, Anson Soderbery,Charles Sprenger, Sever-

ine Toussaert,Matan Tsur, Georg Weizsäcker, Alistair Wilson,and Sevgi Yuksel. They are also grateful for the comments

from the Editor and two anonymous referees. Vespa is grateful for financial support from the UCSB Academic Senate.

© 2020, The RAND Corporation. 447

448 / THE RAND JOURNAL OF ECONOMICS

prediction. Specifically, we will focus our attention on a test of Markov perfection, an assump-

tion that rules out the possibility of collusion in our setting. Therefore, if behavior was in fact

collusive, parameters would be biased and counterfactuals mispredicted.

We study a dynamic game of oligopolistic competition. The primitives in these models are

often related to investments or fixedcosts and counterfactual policy scenarios might study merger

guidelines or other market interventions. The basic environment is one of repeated interactions,

with a state variable that evolves endogenously (e.g., the number of firms in the market in an

entry/exit model). The set of subgame-perfect equilibria (SPE) in dynamic games with an infinite

horizon can be large (Dutta, 1995) and often hard to characterize. Empirical studies often focus

on a subset of SPE known as Markov-perfect equilibria (MPE), where attention is restricted to

stationary Markov strategies. On the one hand, this restriction is extremely useful as it allows

for dynamic programming tools to solve for MPE and makes the model tractable. On the other

hand, there are circumstances where the assumption of Markov play may be too restrictive. In

fact, when the gains from collusion are large, behavior may not be properlycaptured by an MPE.

Support of collusion as an SPE typically requires the threat of credible punishments to deter

parties from otherwise profitable deviations. Hence, agents need to keep track of past play and

use history to condition their present choices. Stationary Markov strategies, however, condition

behavior only on the state variable, ignoring the particular history that led to the current state.

Consequently, collusive equilibria that are supported by a switch to a punishment phase upon

deviation cannot be enforced with a Markov strategy.

To test how restrictive the Markov assumption is for counterfactual predictions we imple-

ment a dynamic oligopoly model in the laboratory. The key treatment variable is a structural

parameter that affects whether collusion can be supported as an SPE or not. To provide a strin-

gent test, the gains from collusion are very high in some treatments.

There are two potential threats posed by a violation of the MPE assumption. First, it may

lead to biased estimates. Standard Monte Carlo simulations in our environment show that esti-

mates are strongly biased if the data are generated according to a collusive equilibrium. Second,

it may lead to biased counterfactual predictions. Monte Carlo simulations, again, confirm that

such counterfactual prediction error can be severe in our setting. Consider a baseline in which

the incentives to collude are low, and the data are actually consistent with an MPE. If the incen-

tives to collude are larger in the counterfactual scenario, the selected equilibrium may change.

The counterfactual might therefore not only entail a change in primitives but also in conduct, vi-

olating the ceteris paribus assumption of counterfactual comparisons. A Monte Carlo study can

help determine the extent of biases under specific assumptions on behavior, but it cannot resolve

which of the assumptions better captures human behavior. Our experimental exercise allows us

to study the consequences of human behavior without having to take an aprioristance on what

such behavior consists of. In this sense it is akin to a Monte Carlo study, except that the data are

generated by humans in a laboratory.

Our design is based on the seminal contribution of Ericson and Pakes (1995), an infinite-

horizon entry/exit game.1Each of two firms can be in or out of the market in each period and their

state (in/out) is publicly observable. Each period consists of two stages: the quantity stage and

the entry/exit stage. When both firms are in the market, they play a quantity-stage game. Each

firm can select a low or a high level of production, where high is associated with the stage-game

Nash equilibrium and low with collusion. A firm that is not in the market does not participate

in the quantity game and makes zero profits. If a firm is alone in the market, the optimal action

is to set the high quantity. In the entry/exit stage, firms decide whether they are in or out of the

market next period. Firms that are in the market choose whether to stay or exit to receive a scrap

value. Firms that are out decide whether to stay out or pay an entry fee to enter. Scrap values

and entry fees are privately observed and randomly drawneach period from common-knowledge

1To be precise, we implement a model that includes privately observed shocks to firms’ decisions, like in Bajari,

Benkard, and Levin (2007) and Aguirregabiria and Mira (2007).

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