3,152 research outputs found
The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions
We show that the widely used homotopy method for solving fixpoint problems,
as well as the Harsanyi-Selten equilibrium selection process for games, are
PSPACE-complete to implement. Extending our result for the Harsanyi-Selten
process, we show that several other homotopy-based algorithms for finding
equilibria of games are also PSPACE-complete to implement. A further
application of our techniques yields the result that it is PSPACE-complete to
compute any of the equilibria that could be found via the classical
Lemke-Howson algorithm, a complexity-theoretic strengthening of the result in
[Savani and von Stengel]. These results show that our techniques can be widely
applied and suggest that the PSPACE-completeness of implementing homotopy
methods is a general principle.Comment: 23 pages, 1 figure; to appear in FOCS 2011 conferenc
Non-additive Security Games
We have investigated the security game under non-additive utility functions
Distributed Methods for Computing Approximate Equilibria
We present a new, distributed method to compute approximate Nash equilibria
in bimatrix games. In contrast to previous approaches that analyze the two
payoff matrices at the same time (for example, by solving a single LP that
combines the two players payoffs), our algorithm first solves two independent
LPs, each of which is derived from one of the two payoff matrices, and then
compute approximate Nash equilibria using only limited communication between
the players.
Our method has several applications for improved bounds for efficient
computations of approximate Nash equilibria in bimatrix games. First, it yields
a best polynomial-time algorithm for computing \emph{approximate well-supported
Nash equilibria (WSNE)}, which guarantees to find a 0.6528-WSNE in polynomial
time. Furthermore, since our algorithm solves the two LPs separately, it can be
used to improve upon the best known algorithms in the limited communication
setting: the algorithm can be implemented to obtain a randomized
expected-polynomial-time algorithm that uses poly-logarithmic communication and
finds a 0.6528-WSNE. The algorithm can also be carried out to beat the best
known bound in the query complexity setting, requiring payoff
queries to compute a 0.6528-WSNE. Finally, our approach can also be adapted to
provide the best known communication efficient algorithm for computing
\emph{approximate Nash equilibria}: it uses poly-logarithmic communication to
find a 0.382-approximate Nash equilibrium
Applications of Repeated Games in Wireless Networks: A Survey
A repeated game is an effective tool to model interactions and conflicts for
players aiming to achieve their objectives in a long-term basis. Contrary to
static noncooperative games that model an interaction among players in only one
period, in repeated games, interactions of players repeat for multiple periods;
and thus the players become aware of other players' past behaviors and their
future benefits, and will adapt their behavior accordingly. In wireless
networks, conflicts among wireless nodes can lead to selfish behaviors,
resulting in poor network performances and detrimental individual payoffs. In
this paper, we survey the applications of repeated games in different wireless
networks. The main goal is to demonstrate the use of repeated games to
encourage wireless nodes to cooperate, thereby improving network performances
and avoiding network disruption due to selfish behaviors. Furthermore, various
problems in wireless networks and variations of repeated game models together
with the corresponding solutions are discussed in this survey. Finally, we
outline some open issues and future research directions.Comment: 32 pages, 15 figures, 5 tables, 168 reference
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