Publication: Essays in microeconomic theory
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2016-02
Defense date
2016-03-14
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Abstract
My thesis considers various aspects of microeconomic theory and focuses on the
different types of uncertainty that players can encounter. Each chapter studies
a setting with a different type of uncertainty and draws conclusions about how
players are likely to behave in such a situation.
The first chapter focuses on games of incomplete information and is joint work
with Peter Eccles. We provide conditions to allow modelling situations of asymmetric
information in a tractable manner. In addition we show a novel relationship
between certain games of asymmetric information and corresponding games
of symmetric information. This framework establishes links between certain games
separately studied in the literature. The class of games considered is defined by
scalable preference relations and a scalable information structure. We show that
this framework can be used to solve asymmetric contests and auctions with loss
aversion.
In the second chapter I move to situations in which information is almost complete.
In joint work with Peter Eccles, we consider the robustness of subgame perfect
implementation in situations when the preferences of players are almost perfectly
known. More precisely we consider a class of information perturbations where
in each state of the world players know their own preferences with certainty and
receive almost perfectly informative signals about the preferences of other players.
We show that implementations using two-stage sequential move mechanisms are
always robust under this class of restricted perturbations, while those using more
stages are often not.
The third chapter deals with a case of complete information and is joint work with Peter Eccles. We introduce the family of weighted Raiffa solutions. An individual
solution is characterised by two parameters representing the bargaining weight of
each player and the speed at which agreement is reached. First we provide a cooperative
foundation for this family of solutions, by appealing to two of the original
axioms used by Nash and a simple monotonicity axiom. Using similar axioms we
give a new axiomatization for a family of weighted Kalai-Smorodinsky solutions.
Secondly we provide a non-cooperative foundation for weighted Raiffa solutions,
showing how they can be implemented using simple bargaining models where offers
are intermittent or the identity of the proposer is persistent. This shows that
weighted Raiffa solutions have cooperative foundations closely related to those of
the Kalai-Smorodinksy solution, and non-cooperative foundations closely related
to those of the Nash solution.
The fourth chapter is closely related to the third chapter and is joint work with
Bram Driesen and Peter Eccles. It provides a non-cooperative foundation for asymmetric
generalizations of the continuous Raiffa solution. Specifically, we consider
a continuous-time variation of the classic Stahl-Rubinstein bargaining model, in
which each player's opportunity to make proposals is produced by an independent
Poisson process, and a definite deadline ends the negotiations. Under the assumption
that future payoffs are not discounted, it is shown that the payoffs realized
in the unique subgame perfect equilibrium of this game approach the continuous
Raiffa solution as the time horizon tends to infinity. The weights reflecting the
asymmetries among the players, correspond with the Poisson arrival rates of their
respective proposal processes
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Keywords
Incertidumbre, Microeconomía, Teoría de juegos