22,345 research outputs found
Distributed convergence to Nash equilibria in two-network zero-sum games
This paper considers a class of strategic scenarios in which two networks of
agents have opposing objectives with regards to the optimization of a common
objective function. In the resulting zero-sum game, individual agents
collaborate with neighbors in their respective network and have only partial
knowledge of the state of the agents in the other network. For the case when
the interaction topology of each network is undirected, we synthesize a
distributed saddle-point strategy and establish its convergence to the Nash
equilibrium for the class of strictly concave-convex and locally Lipschitz
objective functions. We also show that this dynamics does not converge in
general if the topologies are directed. This justifies the introduction, in the
directed case, of a generalization of this distributed dynamics which we show
converges to the Nash equilibrium for the class of strictly concave-convex
differentiable functions with locally Lipschitz gradients. The technical
approach combines tools from algebraic graph theory, nonsmooth analysis,
set-valued dynamical systems, and game theory
Communication networks with endogenous link strength
This paper analyzes the formation of networks when players choose how much to invest in each relationship. We suppose that players have a fixed endowment that they can allocate across links, and in the baseline model, suppose that link strength is an additively separable and convex function of individual investments, and that agents use the path which maximizes the product of link strengths. We show that both the stable and efficient network architectures are stars. However, the investments of the hub may differ in stable and efficient networks. Under alternative assumptions on the investment technology and the reliability measure, other network architectures can emerge as efficient and stable
Energy-Aware Competitive Power Allocation for Heterogeneous Networks Under QoS Constraints
This work proposes a distributed power allocation scheme for maximizing
energy efficiency in the uplink of orthogonal frequency-division multiple
access (OFDMA)-based heterogeneous networks (HetNets). The user equipment (UEs)
in the network are modeled as rational agents that engage in a non-cooperative
game where each UE allocates its available transmit power over the set of
assigned subcarriers so as to maximize its individual utility (defined as the
user's throughput per Watt of transmit power) subject to minimum-rate
constraints. In this framework, the relevant solution concept is that of Debreu
equilibrium, a generalization of Nash equilibrium which accounts for the case
where an agent's set of possible actions depends on the actions of its
opponents. Since the problem at hand might not be feasible, Debreu equilibria
do not always exist. However, using techniques from fractional programming, we
provide a characterization of equilibrial power allocation profiles when they
do exist. In particular, Debreu equilibria are found to be the fixed points of
a water-filling best response operator whose water level is a function of
minimum rate constraints and circuit power. Moreover, we also describe a set of
sufficient conditions for the existence and uniqueness of Debreu equilibria
exploiting the contraction properties of the best response operator. This
analysis provides the necessary tools to derive a power allocation scheme that
steers the network to equilibrium in an iterative and distributed manner
without the need for any centralized processing. Numerical simulations are then
used to validate the analysis and assess the performance of the proposed
algorithm as a function of the system parameters.Comment: 37 pages, 12 figures, to appear IEEE Trans. Wireless Commu
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
We introduce a class of finite strategic games with the property that every
deviation of a coalition of players that is profitable to each of its members
strictly decreases the lexicographical order of a certain function defined on
the set of strategy profiles. We call this property the Lexicographical
Improvement Property (LIP) and show that it implies the existence of a
generalized strong ordinal potential function. We use this characterization to
derive existence, efficiency and fairness properties of strong Nash equilibria.
We then study a class of games that generalizes congestion games with
bottleneck objectives that we call bottleneck congestion games. We show that
these games possess the LIP and thus the above mentioned properties. For
bottleneck congestion games in networks, we identify cases in which the
potential function associated with the LIP leads to polynomial time algorithms
computing a strong Nash equilibrium. Finally, we investigate the LIP for
infinite games. We show that the LIP does not imply the existence of a
generalized strong ordinal potential, thus, the existence of SNE does not
follow. Assuming that the function associated with the LIP is continuous,
however, we prove existence of SNE. As a consequence, we prove that bottleneck
congestion games with infinite strategy spaces and continuous cost functions
possess a strong Nash equilibrium
- ā¦