706 research outputs found
Finding Optimal Strategies in a Multi-Period Multi-Leader-Follower Stackelberg Game Using an Evolutionary Algorithm
Stackelberg games are a classic example of bilevel optimization problems,
which are often encountered in game theory and economics. These are complex
problems with a hierarchical structure, where one optimization task is nested
within the other. Despite a number of studies on handling bilevel optimization
problems, these problems still remain a challenging territory, and existing
methodologies are able to handle only simple problems with few variables under
assumptions of continuity and differentiability. In this paper, we consider a
special case of a multi-period multi-leader-follower Stackelberg competition
model with non-linear cost and demand functions and discrete production
variables. The model has potential applications, for instance in aircraft
manufacturing industry, which is an oligopoly where a few giant firms enjoy a
tremendous commitment power over the other smaller players. We solve cases with
different number of leaders and followers, and show how the entrance or exit of
a player affects the profits of the other players. In the presence of various
model complexities, we use a computationally intensive nested evolutionary
strategy to find an optimal solution for the model. The strategy is evaluated
on a test-suite of bilevel problems, and it has been shown that the method is
successful in handling difficult bilevel problems.Comment: To be published in Computers and Operations Researc
Pricing and Resource Allocation via Game Theory for a Small-Cell Video Caching System
Evidence indicates that downloading on-demand videos accounts for a dramatic
increase in data traffic over cellular networks. Caching popular videos in the
storage of small-cell base stations (SBS), namely, small-cell caching, is an
efficient technology for reducing the transmission latency whilst mitigating
the redundant transmissions of popular videos over back-haul channels. In this
paper, we consider a commercialized small-cell caching system consisting of a
network service provider (NSP), several video retailers (VR), and mobile users
(MU). The NSP leases its SBSs to the VRs for the purpose of making profits, and
the VRs, after storing popular videos in the rented SBSs, can provide faster
local video transmissions to the MUs, thereby gaining more profits. We conceive
this system within the framework of Stackelberg game by treating the SBSs as a
specific type of resources. We first model the MUs and SBSs as two independent
Poisson point processes, and develop, via stochastic geometry theory, the
probability of the specific event that an MU obtains the video of its choice
directly from the memory of an SBS. Then, based on the probability derived, we
formulate a Stackelberg game to jointly maximize the average profit of both the
NSP and the VRs. Also, we investigate the Stackelberg equilibrium by solving a
non-convex optimization problem. With the aid of this game theoretic framework,
we shed light on the relationship between four important factors: the optimal
pricing of leasing an SBS, the SBSs allocation among the VRs, the storage size
of the SBSs, and the popularity distribution of the VRs. Monte-Carlo
simulations show that our stochastic geometry-based analytical results closely
match the empirical ones. Numerical results are also provided for quantifying
the proposed game-theoretic framework by showing its efficiency on pricing and
resource allocation.Comment: Accepted to appear in IEEE Journal on Selected Areas in
Communications, special issue on Video Distribution over Future Interne
A Repeated Game Formulation of Energy-Efficient Decentralized Power Control
Decentralized multiple access channels where each transmitter wants to
selfishly maximize his transmission energy-efficiency are considered.
Transmitters are assumed to choose freely their power control policy and
interact (through multiuser interference) several times. It is shown that the
corresponding conflict of interest can have a predictable outcome, namely a
finitely or discounted repeated game equilibrium. Remarkably, it is shown that
this equilibrium is Pareto-efficient under reasonable sufficient conditions and
the corresponding decentralized power control policies can be implemented under
realistic information assumptions: only individual channel state information
and a public signal are required to implement the equilibrium strategies.
Explicit equilibrium conditions are derived in terms of minimum number of game
stages or maximum discount factor. Both analytical and simulation results are
provided to compare the performance of the proposed power control policies with
those already existing and exploiting the same information assumptions namely,
those derived for the one-shot and Stackelberg games.Comment: 25 pages, 5 figures, accepted for publication in IEEE Transaction on
Wireless Communicatio
Leadership in Singleton Congestion Games: What is Hard and What is Easy
We study the problem of computing Stackelberg equilibria Stackelberg games
whose underlying structure is in congestion games, focusing on the case where
each player can choose a single resource (a.k.a. singleton congestion games)
and one of them acts as leader. In particular, we address the cases where the
players either have the same action spaces (i.e., the set of resources they can
choose is the same for all of them) or different ones, and where their costs
are either monotonic functions of the resource congestion or not. We show that,
in the case where the players have different action spaces, the cost the leader
incurs in a Stackelberg equilibrium cannot be approximated in polynomial time
up to within any polynomial factor in the size of the game unless P = NP,
independently of the cost functions being monotonic or not. We show that a
similar result also holds when the players have nonmonotonic cost functions,
even if their action spaces are the same. Differently, we prove that the case
with identical action spaces and monotonic cost functions is easy, and propose
polynomial-time algorithm for it. We also improve an algorithm for the
computation of a socially optimal equilibrium in singleton congestion games
with the same action spaces without leadership, and extend it to the
computation of a Stackelberg equilibrium for the case where the leader is
restricted to pure strategies. For the cases in which the problem of finding an
equilibrium is hard, we show how, in the optimistic setting where the followers
break ties in favor of the leader, the problem can be formulated via
mixed-integer linear programming techniques, which computational experiments
show to scale quite well
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