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\begin{document}
\title{Hirshleifer Ch. 10 (micro)}
\author[1]{Clara Jace}%
\affil[1]{George Mason University}%
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\date{\today}
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As an oligopolist faces only a few competitors, each firm is in a
strategic situation. In choosing its own price or output, it needs to
consider how its rivals will individually react. This is complex since
each firm is dependent upon the other's behavior for their success.~
\section*{10.1~ Strategic Behavior: The Theory of
Games}
{\label{998558}}
A game, in a mathematical sense, is a way of picturing social
interactions. Two distinct elements must be kept in mind: (a) the
pattern of payoffs, and (b) the protocol of play. The pattern of payoffs
reflects the mix of shared versus opposed interests. The protocol of
play corresponds to the rules of the game.~
\subsection*{Patterns of Payoffs}
{\label{598244}}
The payoff matrix below reflects Paul Revere's famous ride. The redcoats
had to come by land or by sea, and their choice could be observed from
the steeple of Boston's Old North Church.~ Revere's task was to carry
the message (signaled by lanterns in the church steeple - ``one if by
land, two if by sea'') to the American defenders at Lexington and
Concord. The rows represent possible British strategies; the columns
represent American strategies. In each cell, the paired numbers are the
payoffs:
\par\null\par\null\par\null\par\null\par\null\par\null
Such a pattern of payoffs, where each cell adds up to 0, represents
totally divergent interests called a ``zero-sum game.'' The next table
displays the exact opposite, pure coordination.~ Here the players'
interests are in full accord:
\par\null\par\null\par\null\par\null\par\null\par\null
Intermediate cases can be blended in important ways. Below is the
classic Prisoners' Dilemma, where certain payoffs are coordinating and
certain are opposing.~
\par\null\par\null\par\null\par\null\par\null\par\null\par\null\par\null\par\null\par\null\par\null\par\null
The dilemma here is that each does better confessing, regardless of what
his accomplice does, though both could gain more by refusing to confess.
This is also the same situation that firms in cartels find themselves
in.~
\subsection*{Pure Strategies}
{\label{947016}}
In game theory, a solution is a prediction of the strategies that
rational players will select in the light of opponents' possible
choices. Solutions depend upon both the pattern of payoffs and the
protocol of play.~
\subsubsection*{Sequential Play: Each player makes a rational decision,
on the assumption that the opponent will choose rationally when it comes
to his or her
turn.~}
{\label{408042}}
With regard to sequential-move solutions, two important questions are:
(1) Who does better, the first or second mover? (2) Are these results
efficient? That is, does some other pair of choices yield payoffs better
for both parties, or at least one side without the other side being
worse off?
This sequence also introduces the idea of credible threats-- the fact
that to offer a credible threat, the player must be able to carry out
within the protocol and payoff of the game.~
\subsubsection*{Simultaneous Play: Under the simultaneous-move protocol
each player must make his or her choice without knowing what the
opponent has decided to
do.~}
{\label{233568}}
In game theory terminology, the strategy that both players choose is the
dominant strategy, resulting in dominant equilibrium. When neither side
has a dominant strategy, a broader solution concept for the
simultaneous-move protocol is the Nash equilibrium. To find the Nash
equilibrium, look for a cell in the payoff matrix such that, even if the
opponent's strategy were revealed, neither party would benefit from a
unilateral change of move. In other words, no player has an incentive to
alter his or her decision given the other's choice.~
\section*{10.2~ Duopoly - Identical
Products}
{\label{246750}}
Before we said that a monopolist can achieve profit-maximization by
either choosing the most profitable price or most profitable quantity
(because in the industry demand, the chosen price will determine
quantity and vice versa). Here, it makes a difference whether the firms
engage in quantity or price competition.~
\subsection*{Quantity Competition}
{\label{261270}}
Choosing a quantity, a monopolist would usually set MR equal to MC. The
collusive solution occurs when the two firms act together as a
collective monopolist/cartel to share the gain equally. If they cannot
collude, the opposite extreme if a competitive solution, where each firm
would behave as a price-taker using the decision rule MC = P.
Between these two solutions lies the Cournout solution, where there are
two underlying assumptions: (1) each firm recognizes that increasing its
own output reduces the market price, (2) however in making its own
output decision each firm assumes its competitor's is fixed. Thus each
decision maker chooses the highest available payoff given the decision
of the other. This outcome is similar to Nash equilibrium and~ would
include a reaction curve for the both duopolists.~
\subsection*{Price Competition}
{\label{146839}}
Rather than quantity, firms usually compete by quoting prices to
consumers. It turns out that this competition is more severe, since if
the products are identical, a firm that quotes a lower price doesn't
just take away part of his competitor's business but all of it.~
Here, the Nash equilibrium solution is called the Bertrand equilibrium:
each firm chooses a profit-maximizing price, given the other's price.
This leads to worse outcomes for the firms but better for consumers. If
there is sequential move protocol, the first mover (Stackelberg leader)
is at an advantage under quantity competition but disadvantage under
price competition.~
\section*{10.3~ Duopoly - Differentiated
Products}
{\label{787074}}
This is now more realistic, however, the same forces operation.~
When duopolists produce differentiated products, the Cournot and
Bertrand solutions will be a function of s, the index of similarity
between the two products. At one extreme (s = 1), the products are
identical and at the other, they are independent monopolists (s = 0).
For intermediate values, when quantity is the decision variable the
reaction curve will slope downward. When price is the decision variable,
it will be upward. Price competition is more severe and outcomes are
more favorable to consumers than the firm.~
\par\null
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