Provider-Customer Coalitional Games

Efficacy of commercial wireless networks can be substantially enhanced through large-scale cooperation among involved entities such as providers and customers. The success of such cooperation is contingent upon the design of judicious resource allocation strategies that ensure that the individuals' payoffs are commensurate to the resources they offer to the coalition. The resource allocation strategies depend on which entities are decision-makers and whether and how they share their aggregate payoffs. Initially, we consider the scenario where the providers are the only decision-makers and they do not share their payoffs. We formulate the resource allocation problem as a nontransferable payoff coalitional game and show that there exists a cooperation strategy that leaves no incentive for any subset of providers to split from the grand coalition, i.e., the core of the game is nonempty. To compute this cooperation strategy and the corresponding payoffs, we subsequently relate this game and its core to an exchange market setting and its equilibrium, which can be computed by several efficient algorithms. Next, we investigate cooperation when customers are also decision-makers and decide which provider to subscribe to based on whether there is cooperation. We formulate a coalitional game in this setting and show that it has a nonempty core. Finally, we extend the formulations and results to the cases where the payoffs are vectors and can be shared selectively.

Zero-Sum Risk-Sensitive Stochastic Differential Games

We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs equations. Finally, we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

General-sum stochastic games: Verifiability conditions for Nash equilibria

Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair. (c) 2012 Elsevier Ltd. All rights reserved.

Spatial SINR Games of Base Station Placement and Mobile Association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

Ship-Mounted Real-Time Surface Observational System on board Indian Vessels for Validation and Refinement of Model Forcing Fields

A network of ship-mounted real-time Automatic Weather Stations integrated with Indian geosynchronous satellites Indian National Satellites (INSATs)] 3A and 3C, named Indian National Centre for Ocean Information Services Real-Time Automatic Weather Stations (I-RAWS), is established. The purpose of I-RAWS is to measure the surface meteorological-ocean parameters and transmit the data in real time in order to validate and refine the forcing parameters (obtained from different meteorological agencies) of the Indian Ocean Forecasting System (INDOFOS). Preliminary validation and intercomparison of analyzed products obtained from the National Centre for Medium Range Weather Forecasting and the European Centre for Medium-Range Weather Forecasts using the data collected from I-RAWS were carried out. This I-RAWS was mounted on board oceanographic research vessel Sagar Nidhi during a cruise across three oceanic regimes, namely, the tropical Indian Ocean, the extratropical Indian Ocean, and the Southern Ocean. The results obtained from such a validation and intercomparison, and its implications with special reference to the usage of atmospheric model data for forcing ocean model, are discussed in detail. It is noticed that the performance of analysis products from both atmospheric models is similar and good; however, European Centre for Medium-Range Weather Forecasts air temperature over the extratropical Indian Ocean and wind speed in the Southern Ocean are marginally better.

Zero-sum risk-sensitive stochastic games on a countable state space

Infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled Markov chains with countably many states are analyzed. Upper and lower values for these games are established. The existence of value and saddle-point equilibria in the class of Markov strategies is proved for the discounted-cost game. The existence of value and saddle-point equilibria in the class of stationary strategies is proved under the uniform ergodicity condition for the ergodic-cost game. The value of the ergodic-cost game happens to be the product of the inverse of the risk-sensitivity factor and the logarithm of the common Perron-Frobenius eigenvalue of the associated controlled nonlinear kernels. (C) 2013 Elsevier B.V. All rights reserved.

Zero-Sum Stochastic Games with Partial Information and Average Payoff

We consider a discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we present a pair of optimal strategies for both the players.

Application of Qualitative Imaging Methods to Electrical Performance-Aware Package Board Design

Package-board co-design plays a crucial role in determining the performance of high-speed systems. Although there exist several commercial solutions for electromagnetic analysis and verification, lack of Computer Aided Design (CAD) tools for SI aware design and synthesis lead to longer design cycles and non-optimal package-board interconnect geometries. In this work, the functional similarities between package-board design and radio-frequency (RF) imaging are explored. Consequently, qualitative methods common to the imaging community, like Tikhonov Regularization (TR) and Landweber method are applied to solve multi-objective, multi-variable package design problems. In addition, a new hierarchical iterative piecewise linear algorithm is developed as a wrapper over LBP for an efficient solution in the design space.

Efficient Adaptive Mesh Refinement for MoM-based Package-Board 3D Full-wave Extraction

The accurate solution of 3D full-wave Method of Moments (MoM) on an arbitrary mesh of a package-board structure does not guarantee accuracy, since the discretizations may not be fine enough to capture rapid spatial changes in the solution variable. At the same time, uniform over-meshing on the entire structure generates large number of solution variables and therefore requires an unnecessarily large matrix solution. In this work, a suitable refinement criterion for MoM based electromagnetic package-board extraction is proposed and the advantages of the adaptive strategy are demonstrated from both accuracy and speed perspectives.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. (C) 2015 Elsevier B.V. All rights reserved.

Accelerating method of moments based package-board 3D parasitic extraction using FPGA

In this article, a Field Programmable Gate Array (FPGA)-based hardware accelerator for 3D electromagnetic extraction, using Method of Moments (MoM) is presented. As the number of nets or ports in a system increases, leading to a corresponding increase in the number of right-hand-side (RHS) vectors, the computational cost for multiple matrix-vector products presents a time bottleneck in a linear-complexity fast solver framework. In this work, an FPGA-based hardware implementation is proposed toward a two-level parallelization scheme: (i) matrix level parallelization for single RHS and (ii) pipelining for multiple-RHS. The method is applied to accelerate electrostatic parasitic capacitance extraction of multiple nets in a Ball Grid Array (BGA) package. The acceleration is shown to be linearly scalable with FPGA resources and speed-ups over 10x against equivalent software implementation on a 2.4GHz Intel Core i5 processor is achieved using a Virtex-6 XC6VLX240T FPGA on Xilinx's ML605 board with the implemented design operating at 200MHz clock frequency. (c) 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:776-783, 2016