You could write a more “formal” academic applied paper. This would have
an introduction (research question/motivation) and a literature review.
Now for this class paper I’m not expecting any empirical results
necessarily. Instead the student could talk about what hypothesis he or
she wants to test to expand upon the literature. Discuss what data you
would obtain in an ideal world and what regressions you would run. If
the results of the regressions came out one way, what would that imply?
What if they came out the other way? What lessons would we learn or
insights would we gain. Then you can write a short conclusion that again
outlines why the topic is important and interesting, what others have
done, and what additional insights you would expect to gain by doing
your analysis.

2) The second broad approach is to write a bit more informal academic
applied paper where you do a game theoretic analysis of something you
have observed in the real world. Here you would write an introduction
where you briefly describe this observation (and why it is
interesting/important) and how you think we can gain insights using game
theory (Why does this occur? What does it predict will happen? Is it a
rational best response strategy?). Then you can go into more detail
about the game… describe who the players are, what the strategies each
player has are, and what you think the proper payoffs (at least the
ordinal ranking of them) should be (go into detail about why you are
making these assumptions). Then you can try to set up the game. If it is
best designed as a sequential move game, do it this way. If it is
simultaneous move, do it that way. Then use the tools of game theory to
solve the Nash EQ. You could do some variations on the game as well…
like say what if we now made the game that was simultaneous into a
sequential game (or vice versa). Or you could even assume perhaps one of
the players had incomplete information about the other player and hence
use a Harsanyi transformation to find a Bayesian Nash EQ.

To provide a couple of examples of these types of papers, I recall a
student wrote a really nice paper a few years ago looking at “price
dispersion,” which is the topic we will talk about on Tuesday. He was
particularly interested in a finding that I showed (will show) that
online websites that require more clicks before showing you the price of
the product (say a specific TV) charge lower prices for the same
product than websites that show you the price more quickly. He wrote a
fairly formal paper whereby he had a specific research question and he
then did an extensive literature review of recent papers discussing
price dispersion and applications of it in the real world. He then
described an analysis he would do if he had the time to assemble the
data. He described the regressions he would run and what the results
would suggest depending upon how they turned out. Ultimately, he
extended this into his plan B paper by actually carrying out this
analysis and getting data and running the regressions.

As another example, I recall a student from Nepal wrote a game academic
applied paper about the Nepalese noodle industry. He took more of the
second approach above. He did not have much or any of a literature
review, but instead he talked about the details of the Nepalese noodle
industry (like how many firms it had, how homogeneous the products were,
etc.) and then he discussed a specific strategy that was carried out in
that industry and he created a game theoretic model that explained why
this strategy occurred. He carefully laid out his assumptions about who
the players were, what the potential strategies were, and what he felt
the ordinal structure of the payoffs would be.
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