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Correction to “An Efficient Game Form for MultiRate Multicast Service Provisioning”
"... THIS note corrects an error in our paper, “An Efficient ..."
1 Correction to “An Efficient Game Form for Unicast
"... Abstract—A correction to the specification of the mechanism proposed in [1] is given. Index Terms — Budget balance, game form/mechanism, individual rationality, Nash implementation, Unicast service provisioning. Due to an error, the mechanism presented in [1] has a tax function which is not differen ..."
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Abstract—A correction to the specification of the mechanism proposed in [1] is given. Index Terms — Budget balance, game form/mechanism, individual rationality, Nash implementation, Unicast service provisioning. Due to an error, the mechanism presented in [1] has a tax function which is not differentiable with respect to the allocations. We need a tax function which is differentiable with respect to the allocations so that we can have Nash implementation. We correct this error as follows. We consider the problem formulated in [1]. We use the same notation as in [1]. Specification of the game form/mechanism: Message space: The message space is the same as that of the mechanism presented in [1]. A message of user i ∈ N (N denotes the set of users) is of the form mi = (xi, p li 1 i, p li 2 i, · · · , p li R i  i), where xi denotes the (nonnegative) bandwidth user i requests at all the links of his route, and p li k i ≥ 0 denotes the price user i is willing to pay per unit of bandwidth at link ljk of his route Ri. Outcome function: For any m ∈ M, the outcome function is defined as follows: f(m) = (x1, x2, · · · , xn, t1, t2, · · · , tn) ti = ∑ t l i, l∈Ri where tl i is the tax paid by user i for using link l. The form of tl i is the same as the tax function defined in [1] excluding the term that is of the form described by relation (23) in [1]. For example, if Gl > 3, (Gl denotes the set of users using link l) the tax function in Eq. (13) of [1] now becomes, where t l i = P l −ixi + (p l i − P l −i − ζ l +) 2 − 2P l ( l −i pi − P l)
Tight Bounds on the Redundancy of Huffman Codes
 Proc. of IEEE ITW
, 2006
"... Consider a discrete finite source with N symbols, and with the probability distribution p: = (u1, u2,..., uN). It is wellknown that the Huffman encoding algorithm [1] provides an optimal prefix code for this source. A Dary Huffman ..."
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Cited by 6 (1 self)
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Consider a discrete finite source with N symbols, and with the probability distribution p: = (u1, u2,..., uN). It is wellknown that the Huffman encoding algorithm [1] provides an optimal prefix code for this source. A Dary Huffman
Volume 31, Issue 3 Games on Social Networks: On a Problem Posed by Goyal
"... Within the context of games on networks S. Goyal (Goyal (2007), pg. 39) posed the following problem. Under any arbitrary but fixed topology, does there exist at least one pure Nash equilibrium that exhibits a positive relation between the cardinality of a player's set of neighbors and its utili ..."
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Within the context of games on networks S. Goyal (Goyal (2007), pg. 39) posed the following problem. Under any arbitrary but fixed topology, does there exist at least one pure Nash equilibrium that exhibits a positive relation between the cardinality of a player's set of neighbors and its utility payoff? In this paper we present a class of games/topologies in which pure Nash equilibria with the above property do not exist.
Abstract
, 706
"... In this paper we consider the class of antiuniform Huffman codes and derive tight lower and upper bounds on the average length, entropy, and redundancy of such codes in terms of the alphabet size of the source. The Fibonacci distributions are introduced which play a fundamental role in AUH codes. I ..."
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In this paper we consider the class of antiuniform Huffman codes and derive tight lower and upper bounds on the average length, entropy, and redundancy of such codes in terms of the alphabet size of the source. The Fibonacci distributions are introduced which play a fundamental role in AUH codes. It is shown that such distributions maximize the average length and the entropy of the code for a given alphabet size. Another previously known bound on the entropy for given average length follows immediately from our results. 1
An efficient game form for unicast service provisioning
, 2011
"... We consider the decentralized bandwidth/rate allocation problem in unicast service provisioning with strategic users. We present a mechanism/game form which possesses the following properties when the users’ utilities are concave: (1) It implements in Nash equilibria the solution of the correspondin ..."
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Cited by 11 (7 self)
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We consider the decentralized bandwidth/rate allocation problem in unicast service provisioning with strategic users. We present a mechanism/game form which possesses the following properties when the users’ utilities are concave: (1) It implements in Nash equilibria the solution of the corresponding centralized rate allocation problem in unicast service provisioning. (2) It is individually rational. (3) It is budgetbalanced at all Nash equilibria of the game induced by the mechanism/game form as well as off equilibrium. When the users’ utilities are quasiconcave the mechanism possesses properties (2) and (3) stated above. Moreover, every Nash equilibrium of the game induced by the proposed mechanism results in a Walrasian equilibrium.
Power Allocation and Spectrum Sharing in MultiUser, MultiChannel Systems with Strategic Users 1
"... We consider the decentralized power allocation and spectrum sharing problem in multiuser, multichannel systems with strategic users. We present a mechanism/game form that has the following desirable features. (1) It is individually rational. (2) It is budget balanced at every Nash equilibrium of th ..."
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Cited by 6 (3 self)
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We consider the decentralized power allocation and spectrum sharing problem in multiuser, multichannel systems with strategic users. We present a mechanism/game form that has the following desirable features. (1) It is individually rational. (2) It is budget balanced at every Nash equilibrium of the game induced by the game form as well as off equilibrium. (3) The allocation corresponding to every Nash equilibrium (NE) of the game induced by the mechanism is a Lindahl allocation, that is, a weakly Pareto optimal allocation. Our proposed game form/mechanism achieves all the above desirable properties without any assumption about, concavity, differentiability, monotonicity, or quasilinearity of the users’ utility functions.
An Efficient Game Form for Unicast Service
"... Abstract—We consider the decentralized bandwidth/rate allocation problem in unicast service provisioning with strategic users. We present a mechanism/game form which possesses the following properties when the users ’ utilities are concave: 1) It implements in Nash equilibria the solution of the co ..."
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Abstract—We consider the decentralized bandwidth/rate allocation problem in unicast service provisioning with strategic users. We present a mechanism/game form which possesses the following properties when the users ’ utilities are concave: 1) It implements in Nash equilibria the solution of the corresponding centralized rate allocation problem in unicast service provisioning. 2) It is individually rational. 3) It is budgetbalanced at all Nash equilibria of the game induced by the mechanism/game form as well as off equilibrium. When the users ’ utilities are quasiconcave the mechanism possesses properties 2) and 3) stated above. Moreover, every Nash equilibrium of the game induced by the proposed mechanism results in a Walrasian equilibrium. Index Terms—Budget balance, game form/mechanism, individual rationality, Nash implementation, Unicast service provisioning.
An Efficient Game Form for Multirate Multicast Service Provisioning
"... We consider the decentralized bandwidth/rate allocation problem in multirate multicast service provisioning with strategic users. We demonstrate that such a situation is the combination of a market problem and a public good problem. We present a mechanism/game form which possesses the following pro ..."
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Cited by 3 (2 self)
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We consider the decentralized bandwidth/rate allocation problem in multirate multicast service provisioning with strategic users. We demonstrate that such a situation is the combination of a market problem and a public good problem. We present a mechanism/game form which possesses the following properties when the users ’ utilities are concave: (1) It implements in Nash equilibria the solution of the corresponding centralized rate allocation problem in multirate multicast service provisioning. (2) It is individually rational. (3) It is budgetbalanced at all Nash equilibria of the game induced by the mechanism/game form as well as off equilibrium.
Games on Social Networks: On a Problem Posed by
, 2011
"... Within the context of games on networks S. Goyal (Goyal (2007), pg. 39) posed the following problem. Under any arbitrary but fixed topology, does there exist at least one pure Nash equilibrium that exhibits a positive relation between the cardinality of a player’s set of neighbors and its utility pa ..."
Abstract
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Within the context of games on networks S. Goyal (Goyal (2007), pg. 39) posed the following problem. Under any arbitrary but fixed topology, does there exist at least one pure Nash equilibrium that exhibits a positive relation between the cardinality of a player’s set of neighbors and its utility payoff? In this paper we present a class of topologies in which pure Nash equilibria with the above property do not exist. 1 IntroductionMotivation Games on social networks is a rapidly developing discipline the importance of which has been extensively discussed in recent publications Goyal (2007), Jackson (2008) and VegaRedondo (2007). One of the goals of this discipline is the development of a framework within which the effect of the structure of relationships on individual
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