3 research outputs found
Essays on the Computation of Economic Equilibria and Its Applications.
The computation of economic equilibria is a central
problem in algorithmic game theory. In this dissertation, we
investigate the existence of economic equilibria in several
markets and games, the complexity of computing economic
equilibria, and its application to rankings.
It is well known that a competitive economy always has an
equilibrium under mild conditions. In this dissertation, we study
the complexity of computing competitive equilibria. We show that
given a competitive economy that fully respects all the conditions
of Arrow-Debreu's existence theorem, it is PPAD-hard to compute an
approximate competitive equilibrium. Furthermore, it is still
PPAD-Complete to compute an approximate equilibrium for economies
with additively separable piecewise linear concave utility
functions.
Degeneracy is an important concept in game theory. We study the
complexity of deciding degeneracy in games. We show that it is
NP-Complete to decide whether a bimatrix game is degenerate.
With the advent of the Internet, an agent can easily have access
to multiple accounts. In this dissertation we study the path
auction game, which is a model for QoS routing, supply chain
management, and so on, with multiple edge ownership. We show that
the condition of multiple edge ownership eliminates the
possibility of reasonable solution concepts, such as a
strategyproof or false-name-proof mechanism or Pareto efficient
Nash equilibria.
The stationary distribution (an equilibrium point) of a Markov
chain is widely used for ranking purposes. One of the most
important applications is PageRank, part of the ranking algorithm
of Google. By making use of perturbation theories of Markov
chains, we show the optimal manipulation strategies of a Web
spammer against PageRank under a few natural constraints. Finally,
we make a connection between the ranking vector of PageRank or the
Invariant method and the equilibrium of a Cobb-Douglas market.
Furthermore, we propose the CES ranking method based on the
Constant Elasticity of Substitution (CES) utility functions.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64821/1/duye_1.pd