Essays on bilateral trade with discrete types
Author
Mohammadinezhad, Kamyar Kargar
Advisor
Pınar, Mustafa Çelebi
Date
2019-11Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
Bilateral trade is probably the most common market interaction problem and
can be considered as the simplest form of two sided markets where a seller and
a buyer bargain over an indivisible object subject to incomplete information
on the reservation values of participants. We treat this problem as a combinatorial
optimization problem and re-establish some results of economic theory
that are well-known under continuous valuations assumptions for the case of
discrete valuations using linear programming techniques.
First, we propose mathematical formulation for the problem under dominant
strategy incentive compatibility (DIC) and ex-post individual rationality
(EIR) properties. Then we derive necessary and sufficient conditions under
which ex-post efficiency can be obtained together with DIC and EIR. We also
define a new property called Allocation Maximality and prove that the Posted
Price mechanism is the only mechanism that satisfies DIC, EIR and allocation
maximality. In the final part we consider ambiguity in the problem framework
originating from different sets of priors for agents types and derive robust
counterparts.
Next, we study the bilateral trade problem with an intermediary who wants
to maximize her expected gains. Using network programming we transform
the initial linear program into one from which the structure of mechanism is
transparent. We then relax the risk-neutrality assumption of the intermediary
and consider the problem from the perspective of risk-averse intermediary. The
effects of risk-averse approach are presented using computational experiments.
Finally, we broaden the scope of the problem and discuss the case in which
the seller is also a producer at the same time and consider benefit and cost
functions for the respective parties. Starting by a non-convex optimization
problem, we obtain an equivalent convex optimization problem from which
the problem is solved easily. We also reconsider the same problem under
dominant strategy incentive compatibility and ex-post individual rationality
constraints to preserve the practicality of all obtained solutions.