Results 1 
8 of
8
Coalitional game theoretic approach for secondary spectrum access in cooperative cognitive radio networks
 IEEE Transactions on Wireless Communications
, 2011
"... Abstract—In this paper, we exploit a novel setting for Cognitive Radio (CR) networks to enable multiple operators to involve secondary users (SUs) as cooperative relays for their primary users. In return, SUs get an opportunity to access spare channels for their own data transmission. Initially, we ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper, we exploit a novel setting for Cognitive Radio (CR) networks to enable multiple operators to involve secondary users (SUs) as cooperative relays for their primary users. In return, SUs get an opportunity to access spare channels for their own data transmission. Initially, we assume that the CR network supports payment transfer. Then, we formulate the system as a transferable utility coalitional game. We show that there is an operating point that maximizes the sum utility over all operators and SUs while providing each player a share such that no subset of operators and SUs has an incentive to break away from the grand coalition. Such operating points exist when the solution set of the game, the core, is nonempty. Subsequently, we examine an interesting scenario where there is no payment mechanism in the network. This scenario can be investigated by using a nontransferable utility coalitional game model. We show that there exists a joint action to make the core nonempty. A general method with exponential computational complexity to get such a joint action is discussed. Then, we relate the core of this game to a competitive equilibrium of an exchange economy setting under special situations. As a result, several available efficient centralized or distributed algorithms in economics can be employed to compute a member in the core. In a nutshell, this paper constitutes the design of new coalition based dynamics that could be used in future CR networks. Index Terms—Cognitive radio networks, cooperative diversity transmission, coalitional game, core, exchange economy, competitive equilibrium. I.
Distributed algorithms via gradient descent for fisher markets.
 In Proc. 12th ACM Conference on Electronic Commerce,
, 2011
"... ABSTRACT Designing distributed algorithms that converge quickly to an equilibrium is one of the foremost research goals in algorithmic game theory, and convex programs have played a crucial role in the design of algorithms for Fisher markets. In this paper we shed new light on both aspects for Fish ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
ABSTRACT Designing distributed algorithms that converge quickly to an equilibrium is one of the foremost research goals in algorithmic game theory, and convex programs have played a crucial role in the design of algorithms for Fisher markets. In this paper we shed new light on both aspects for Fisher markets with linear and spending constraint utilities. We show fast convergence of the Proportional Response dynamics recently introduced by Wu and Zhang [WZ07]. The convergence is obtained from a new perspective: we show that the Proportional Response dynamics is equivalent to a gradient descent algorithm (with respect to a Bregman divergence instead of euclidean distance) on a convex program that captures the equilibria for linear utilities. We further show that the convex program program easily extends to the case of spending constraint utilities, thus resolving an open question raised by
New Convex Programs and Distributed Algorithms for Fisher Markets with Linear and Spending Constraint Utilities
"... In this paper we shed new light on convex programs and distributed algorithms for Fisher markets with linear and spending constraint utilities. • We give a new convex program for the linear utilities case of Fisher markets. This program easily extends to the case of spending constraint utilities as ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
In this paper we shed new light on convex programs and distributed algorithms for Fisher markets with linear and spending constraint utilities. • We give a new convex program for the linear utilities case of Fisher markets. This program easily extends to the case of spending constraint utilities as well, thus resolving an open question raised by [Vaz10]. • We show that the gradient descent algorithm with respect to a Bregman divergence converges with rate O(1/t) under a condition that is weaker than having Lipschitz continuous gradient (which is the usual assumption in the optimization literature for obtaining the same rate). • We show that the Proportional Response dynamics recently introduced by Zhang [Zha09] is equivalent to a gradient descent algorithm for solving the new convex program. This insight also gives us better convergence rates, and helps us generalize it to spending constraint utilities. 1
Isoelastic agents and wealth updates in machine learning markets. ICML
, 2012
"... Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alphamixtures, with a particular form of mixing component relating to each agent’s wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts. 1.
Tatonnement Beyond Gross Substitutes? Gradient Descent to the Rescue
, 2013
"... Tatonnement is a simple and natural rule for updating prices in Exchange (ArrowDebreu) markets. In this paper we define a class of markets for which tatonnement is equivalent to gradient descent. This is the class of markets for which there is a convex potential function whose gradient is always eq ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Tatonnement is a simple and natural rule for updating prices in Exchange (ArrowDebreu) markets. In this paper we define a class of markets for which tatonnement is equivalent to gradient descent. This is the class of markets for which there is a convex potential function whose gradient is always equal to the negative of the excess demand and we call it Convex Potential Function (CPF) markets. We show the following results. • CPF markets contain the class of Eisenberg Gale (EG) markets, defined previously by Jain and Vazirani. • The subclass of CPF markets for which the demand is a differentiable function contains exactly those markets whose demand function has a symmetric negative semidefinite Jacobian. • We define a family of continuous versions of tatonnement based on gradient descent using a Bregman divergence. As we show, all processes in this family converge to an equilibrium for any CPF market. This is analogous to the classic result for markets satisfying the Weak Gross Substitutes property. • A discrete version of tatonnement converges toward the equilibrium for the following markets of complementary goods; its convergence rate for these settings is analyzed using a common potential function. – Fisher markets in which all buyers have Leontief utilities. The tatonnement process reduces the distance to the equilibrium, as measured by the potential function, to an ɛ fraction of its initial value in O(1/ɛ) rounds of price updates. – Fisher markets in which all buyers have complementary CES utilities. Here, the distance to the
Advertising Space Exchange in a Network using Market Equilibrium Algorithms
"... We present a prototype of an online advertisement space exchange platform that enables its participants to advertise on each others ’ websites and simulates a virtual exchange economy. Our main contribution is a system design that effectively and practically realizes the exchange based on a competit ..."
Abstract
 Add to MetaCart
(Show Context)
We present a prototype of an online advertisement space exchange platform that enables its participants to advertise on each others ’ websites and simulates a virtual exchange economy. Our main contribution is a system design that effectively and practically realizes the exchange based on a competitive equilibrium computed from the elicited preferences of the advertisers. The current prototype is used by 741 bloggers registered in various communities including Academia, Cuisine, Life and Parenting. The platform circulated roughly 2, 000 advertisements at any given time serving nearly 80, 000 impressions per day. The current paper discusses the implementation of the prototype and its performance in practice. We also present observations about the exchange market dynamics, the structure of the underlying network and its effects on the distribution of prices, wealth and income.
CS787: Advanced Algorithms Final Project
"... We introduce the concept of Market Equilibria related to game theory. In the market, there exists sellers which sell divisible goods and buyers who have a desire to purchase some set of goods. Each buyer places a value on each of the goods in his list that relates to the importance of purchasing tha ..."
Abstract
 Add to MetaCart
(Show Context)
We introduce the concept of Market Equilibria related to game theory. In the market, there exists sellers which sell divisible goods and buyers who have a desire to purchase some set of goods. Each buyer places a value on each of the goods in his list that relates to the importance of purchasing that specific good. At market equilibrium, no party (seller or buyer) has incentive to deviate from