Oblivious equilibrium for concentrated industries
| Author | Gabriel Y. Weintraub,Przemyslaw Jeziorski,C. Lanier Benkard |
| Published date | 01 October 2015 |
| DOI | http://doi.org/10.1111/1756-2171.12102 |
| Date | 01 October 2015 |
RAND Journal of Economics
Vol.46, No. 4, Winter 2015
pp. 671–708
Oblivious equilibrium for concentrated
industries
C. Lanier Benkard∗
Przemyslaw Jeziorski∗∗
and
Gabriel Y. Weintraub∗∗∗
This article exploresthe application of oblivious equilibrium (OE) to highly concentrated markets.
We define a natural extended notion of OE, called partially oblivious equilibrium (POE), that
allows for there to be a set of strategically important firms (the “dominant” firms), whose
firm states are always monitored by every other firm in the market. We perform computational
experiments that explore the characteristicsof POE, OE, and Markov perfect equilibrium (MPE),
and find that POE generally performs well in highly concentrated markets. We also derive error
bounds for evaluating the performance of POE for cases where MPE cannot be computed.
1. Introduction
There has been much recent work in industrial organization (IO) on empirical applications
of dynamic oligopoly models (e.g., Benkard, 2004; Collard-Wexler, 2013 [henceforth CW];
Fowlie, Reguant, and Ryan, in press; Goettler and Gordon, 2011; Jeziorski, 2014; Ryan, 2012;
Sweeting, 2013). The primary benefit of using a dynamic model is that such models allow us
to study the effects of a government policy on technological progress and on industry structure,
that is, the set of firms in the market, their technologies, and the products that they choose to
offer. In many applications, such as merger analysis or environmental and energy regulation,
these long-run effects can dwarf the short-run static effects, and thus analyzing them is of first-
order importance. The cost of doing a dynamic analysis is that the models are inherently more
complex. Indeed, this recent work was only made possible by the advent of new methods for
estimating dynamic oligopoly models (Bajari, Benkard, and Levin, 2007; Pakes, Ostrovsky, and
∗Stanford University and NBER; lanierb@stanford.edu.
∗∗University of California at Berkeley; przemekj@haas.berkeley.edu.
∗∗∗Columbia University; gweintraub@columbia.edu.
Wewould like to thank Ben Van Roy for numerous fruitful conversationsand valuable insights provided at the beginning
stages of this project. We are grateful to Allan Collard-Wexler for generously sharing his data and for helpful input.
This article has also benefitted from conversations with Ariel Pakes, Ali Yurukoglu, and seminar participants at various
conferences and institutions.
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Berry, 2007; Aguirregabiria and Mira, 2007; Pesendorfer and Schmidt-Dengler, 2003) that do
not require the econometrician to compute Markov perfect equilibria (henceforth, MPE) of the
underlying game being studied. This is important because MPE computation is subject to the
curse of dimensionality.
Despite this recent progress, there remain substantial hurdles in the empirical application of
dynamic oligopoly models. Even when it is possible to use these new methods to estimate the
model parameters without computing an equilibrium, equilibrium computation is still required
to analyze the effects of a counterfactual policy or environmental change. The result is that in
applications many modelling details are still heavilydictated by computational concerns, typically
at some expense to the credibility of the economic analysis.
In a recent article, Weintraub, Benkard, and VanRoy (2008) propose a method for analyzing
Ericson and Pakes (1995; hereafter, EP) style dynamic models of imperfect competition that is
intended to address some of these concerns. In that article, they defined a notion of equilibrium,
oblivious equilibrium (henceforth, OE), in which each firm is assumed to make decisions based
only on its own state and knowledgeof the long-run industr y state, but where firms ignore current
information about competitors’ states. The great advantage of OE is that their computation time
is not systematically related to the overall number of firms in the industry, and thus they are
much easier to program and compute than MPE, allowing researchers to analyze richer empirical
models. Although OE have some very appealing properties, they also havesome weaknesses. One
that has often been raised is the appropriateness of the OE assumptions for highly concentrated
markets. Because many of the most interesting policyquestions in IO focus on highly concentrated
markets, this is an important flaw.
In this article, we introduce an extension to OE designed to address this important case. We
define an extended notion of oblivious equilibrium that we call partially oblivious equilibrium
(POE) that allows for there to be a set of strategically important firms, that we call “dominant”
firms, whose firm states are always monitored by every other firm in the market. Thus, for
example, if there are two dominant firms, then in POE, each firm’s strategy will be a function of
its own state and also the states of both dominant firms. Such strategies allow for richer strategic
interactions than do oblivious strategies, which depend only on a firm’s own state, and our hope
is that POE will provide a better model of more concentrated markets than OE does. Moreover, if
entry and exit are modelled identically for dominant and (nondominant) “fringe” firms, then the
POE model nests both OE and MPE, where OE is a POE model with no dominant firms, MPE
is a POE model with all dominant firms, and where all other POE models represent intermediate
cases.
The extension primarily trades offricher strategic interactions against increased computation
time and memory requirements due to a larger state space. The state space for OE is of the order
of a one firm problem; the state space for POE with one dominant firm is of the order of a
two-firm problem; the state space for POE with two dominant firms is of the order of a three-firm
problem, and so forth. In all cases, for a fixed number of dominant firms, compute time and
memory requirements for POE (and OE) are not systematically related to the number of firms in
the overall industry. As a consequence, although POE take substantially more time to compute
than OE, it is still dramatically less than MPE.
POE can also be motivated as a behavioral model in its own right. It seems unrealistic that
firms would be able to follow strategies that are functions of more than a handful of competitor
firms. Strategies that are functions of all firms are high dimensional and highly complex, and
it is hard to imagine how firms would obtain enough information to compute them and execute
them. If firms follow strategies that are only functions of a few firms, it seems likely that their
strategies would include only themselves and the leading firms, ignoring less important fringe
firms. Additionally, if information is costly, then firms would only pay to learn the information
that is most relevant to them. In the models we consider, the most valuable information would
typically be the states of the leading firms. Finally, in many markets there are “leader” firms
whose actions are followed more closely than the other firms in the industry. Indeed, there are
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older literatures (Von Stackelberg, 1934; Kydland, 1979) that model the dominant firm in an
industry as moving first.
We perform a large number of computational experiments to evaluate how POE performs
in practice and to compare POE with OE and MPE. We find that in markets with medium to
high concentration, there is little difference between MPE and OE or POE with one, two,or three
dominant firms. POE is generally closer to MPE than OE is, but the differences are small. In these
cases, OE is clearly the best tool as it is the simplest to compute and would allow researchers
to use the most robust economic model, while providing results that are the same as the other
equilibrium concepts.
In very highly concentrated markets, markets with C2 >0.90, corresponding to approxi-
mately the top 1% of manufacturing industries in the United States, we find that OE sometimes
does not work well. (It is not typically close to MPE, in ways that seem undesirable.) We explore
the performance of POE in these cases and find that as long as turnover among leading firms is not
too unrealistically high, within or even exceeding the range observed in real-world markets (see
Sutton 2007), then POE with one or two dominant firms works welleven in the most concentrated
markets.
Another finding from our computational experiments is that the information structure of
the model can be quite important in determining firm behavior. In the POE model, dominant
firms’ states are tracked by all firms, whereas individual (nondominant) fringe firms’ states
are not tracked. Because dominant firms’ states are tracked, their actions have a direct impact
on other firms’ behavior, and they can more easily deter entry or investment by investing and
becoming large. As a result, we find that in POE, dominant firms generally invest more than
fringe firms, and this leads to them on average being larger and remaining large for longer. In
essence, being labeled as “dominant” causes the firm to in fact be dominant most of the time. This
asymmetry in behavior sets the POE model apart from the OE and MPE models, in which it is
typically assumed that all firms would behave the same way at the same state of the world. These
results also suggest using caution when simplifying firms’ strategies in equilibrium calculations
more generally. Although POE strategies are somewhat natural, and lead to behavior that is
not unrealistic, arbitrary restrictions of firms’ strategies to facilitate computation could lead to
unintended and unnatural firm behavior.
We also applyPOE to the empirical model of CW. We find that for the basic CW model OE
is fairly close to MPE, though it is not exactly the same. Adding dominant firms makes many
statistics closer to MPE, but we find that it takes four dominant firms to obtain results nearly the
same as MPE. We also explore what happens in the CW model as we make the discretization of
the state space finer. Coarse discretization of the state space is a common tool used in the empirical
literature to make dynamic models more tractable (e.g., Benkard,2004; Gowrisankaran and Town,
1997). The CW model is quite complex and thus, in order to compute MPE, the model discretizes
individual firm size states to just three points. Because OE and POE are computationally light,
we are able to solve the CW model on much finer state space grids. For our finest grid, the model
has 66 billion state points.
Wefind that there are some differences in the results as we make the size grid finer. The main
differences are that on the three point grid there are equal numbers of small and medium firms,
but on the finer grids there are nearly twice as many medium firms as small ones. Furthermore,
transition costs get much larger as firms are now changing size more often and thus paying more
transition costs. The intuition for this finding is that the coarse grid has the same effect as an
adjustment cost, so that on a coarse grid firms are unable to make fine adjustments to their size.
When the grid is made finer, firms adjust size more often and there are more medium-sized firms
and fewer small firms.
Webelieve that these results demonstrate an important trade-off facing empirical researchers
in this area. Using a computationally simple equilibrium concept such as POE allows the re-
searcher to use a richer economic model. Sometimes the economics of the model may be changed
less by using OE or POE in place of MPE than they would by simplifying the model to facilitate
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