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\title{Summary of Experiment III for ``Duopoly Dynamics with a Barrier to Entry''}
\author{Jeff R. Campbell}
\date{\today}


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\begin{abstract}
This paper examines the effects of erecting a \emph{barrier} to entry in the short/medium run.  By using many of the equilibrium characteristics of the model found in ``Last In-First Out Dynamics'', several different versions of an experiment are conducted in order to the trace various effects of the parameters of the model.  The experiment finds that barriers to entry have significant effects in the short run on the size of an industry, with uncertainty having a strong influence on the size of this effect.
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\section{Introduction}
\indent\indent In order to illustrate the effects of a barrier to entry on the dynamics of a particular industry an experiment was created.  Using the equilibrium strategies found in ``Last In-First Out Dynamics'', two model industries are created; one experiencing a barrier to entry for the ``infant firm'' while the other industry exhibits no such barrier.  The difference in the \emph{expected} number of firms in the two model industries will serve as the illustrative statistic and will be the subject of the analysis.

A barrier to entry has two effects on the particular size of an industry.  Most intuitively a barrier to entry will deter entry by firms who have to endure this cost; lowering the number of firms serving an industry.  In addition, however, because a monopololist can now expect greater payoffs (from a wider set of demand states in which she will remain a monopolist) a barrier to entry may make lower demand states more endurable for the monopolist.  In effect, \emph{raising} the number of expected firms serving the industry.  

Because of the presence of these two opposing effects, an alternative version of the experiment was created in order to isolate the dynamics of each.  Instead of using the threshold rules determined by the equilibrium strategies given a barrier to entry, an alternative version is run where only the ``infant'' firm's policy decisions are altered.  In essence, a barrier to entry has been raised on the infant firm without allowing the first firm's decisions of entry/exit to be altered.  This version abstracts away from the possible entry/active ``encouragement'' effect a barrier to entry may have on a monopolist.

Figure (\ref{perm}) chart the impulse responses for each of the different versions of the experiment.  On the furthest left panel are the range of values of the ``innovation'' variance for the stochastic demand.  Proceeding to the right, are the range of values for the relative ``persistence'' of demand shocks.  Across the top are the particular values of the entry (sunk) costs for the first firm.

The following sections will outline each version of the experiment.  Section \ref{permbarrier} traces the effects of a permanent barrier to entry.  Section \ref{conclusion} concludes.



\section{Implementing a Permanent Barrier to Entry}\label{permbarrier}

\input{ac2bIIIperm}

\emph{say anything particular to this experiment in this section}


\section{Conclusion}\label{conclusion}
\indent\indent By conducting several different versions of a basic duopoly experiment, the short/medium run effects of barrier to entries have been examined.  As far as the number of firms expected to serve an industry, barrier to entries' clearly have substantial effects.  The particular stochastic nature of demand will influence the size and relative strength of these effects.  In general as the uncertainty of the demand process increases the relative effect of the barrier to entry decreases.  In addition, in the face of stronger persistence of demand shocks the influence of barrier to entry will also subside.

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