625 research outputs found
Distributed Learning for Stochastic Generalized Nash Equilibrium Problems
This work examines a stochastic formulation of the generalized Nash
equilibrium problem (GNEP) where agents are subject to randomness in the
environment of unknown statistical distribution. We focus on fully-distributed
online learning by agents and employ penalized individual cost functions to
deal with coupled constraints. Three stochastic gradient strategies are
developed with constant step-sizes. We allow the agents to use heterogeneous
step-sizes and show that the penalty solution is able to approach the Nash
equilibrium in a stable manner within , for small step-size
value and sufficiently large penalty parameters. The operation
of the algorithm is illustrated by considering the network Cournot competition
problem
A numerical algorithm for finding solutions of a generalized Nash equilibrium problem
A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm
CONTAINER TRANSPORTATION NETWORK EQUILIBRIUM ANALYSIS CONSIDERING DRAFT OF VESSEL
This paper analyzes container transportation network equilibrium considering draft of vessels. Concept of load factor
(ďż˝) of ship is included in the model. Three players are considered, i.e. port administrator, ship companies (carriers),
and shippers. Interaction of these players leads to Nash equilibrium problem. The result of the model calculation indicates
that Hong Kong and Singapore port dominates container throughput in the world and the big vessel (3000 - 6000
TEU) is dominant in these ports. Conversely, the smaller port with depth less than 15 m dominated by 1000 TEU vessels.
The result is inline with the reality. The other finding from the study is 6000 TEU vessels can enter port with depth
less than 15 m such as port of Shanghai. Again, it is inline with reality. Validation of the model shows that coefficient of
determination (R2) is 0.95. It indicates the model provides good accuracy.
Keywords:
Container transportation, Nash Equilibrium, Networ
Multi-Leader Multi-Follower Model with Aggregative Uncertainty
We study a non-cooperative game with aggregative structure, namely when the payoffs depend on the strategies of the opponent players through an aggregator function. We assume that a subset of players behave as leaders in a Stackelberg model. The leaders, as well the followers, act non-cooperatively between themselves and solve a Nash equilibrium problem. We assume an exogenous uncertainty affecting the aggregator and we obtain existence results for the stochastic resulting game. Some examples are illustrated
Computing all solutions of Nash equilibrium problems with discrete strategy sets
The Nash equilibrium problem is a widely used tool to model non-cooperative
games. Many solution methods have been proposed in the literature to compute
solutions of Nash equilibrium problems with continuous strategy sets, but,
besides some specific methods for some particular applications, there are no
general algorithms to compute solutions of Nash equilibrium problems in which
the strategy set of each player is assumed to be discrete. We define a
branching method to compute the whole solution set of Nash equilibrium problems
with discrete strategy sets. This method is equipped with a procedure that, by
fixing variables, effectively prunes the branches of the search tree.
Furthermore, we propose a preliminary procedure that by shrinking the feasible
set improves the performances of the branching method when tackling a
particular class of problems. Moreover, we prove existence of equilibria and we
propose an extremely fast Jacobi-type method which leads to one equilibrium for
a new class of Nash equilibrium problems with discrete strategy sets. Our
numerical results show that all proposed algorithms work very well in practice
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