Chemistry Reference
In-Depth Information
Chapter 5
Oligopolies with Misspecified and Uncertain
Price Functions, and Learning
The previous chapters have already dealt with the behavior of boundedly rational
firms in an oligopoly. Although the firms know the true demand relationship, we
have assumed that they do not know their competitors' quantity choices. Instead
they form expectations about these quantities and they base their own decisions on
these beliefs. In particular, we have focused on several adjustment processes that
firms might use to determine their quantity selections and we have investigated the
circumstances under which such adjustment processes might lead to convergence
to the Nash equilibrium of the static oligopoly game. However, the information that
firms have about the environment may be incomplete on several accounts. For exam-
ple, players may misspecify the true demand function or just misestimate the slope
of the demand relationship, the reservation price, or the market saturation point.
However, if firms base their decisions on such wrong estimates, they will realize that
their beliefs are incorrect, since the market data they observe (for example, market
prices or quantities) will be different from their predictions. Obviously, firms will
try to update their beliefs on the demand relationship and this will give rise to an
adjustment process. In other words, firms will try to learn the game they are play-
ing. Following this line of thought, in this chapter we study oligopoly models under
the assumption that firms either use misspecified price functions (Sect. 5.1) or do
not know certain parameters of the market demand (Sect. 5.2). The main questions
we want to answer are the following. If we understand an equilibrium in a game
as a steady state of some non-equilibrium process of adjustment and “learning,”
what happens if the players use an incorrect model of their environment? Does a
reasonable adaptive process (for example, based on the best response) converge to
anything? If so, to what does it converge? Is the limit that can be observed when the
players play their perceived games (close to) an equilibrium of the underlying true
model? Is the observed situation consistent with the (limit) beliefs of the players?
In Sect. 5.1 we consider a framework based on the idea of Leonard and Nishimura
(1999), who derive similar insights for a simple Cournot duopoly model with
decreasing reaction functions. We demonstrate that in situations where players
choose their actions based on a misspecified model of the environment, additional
self-confirming steady states may emerge, despite the fact that the Nash equilib-
rium of the game under perfect knowledge is unique. We will derive (sufficient)
conditions for the local and global stability of these steady states. For discrete time
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