P. Dubey, "Inefficiency of nash equilibria," Math. Oper. Res., vol. 11, pp. 1--8, Feb. 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....model becomes a game; remarkably, we will show that the Nash equilibria of this game lead to allocations at which total utility is no worse than 3 4 the aggregate system utility. The fact that Nash equilibria of a game may not achieve full efficiency has been well known in the economics literature [9]. Recent research efforts have focused on quantifying this loss for specific game environments; the resulting degree of efficiency loss is known as the price of anarchy [10] Most of the results on price of anarchy have focused on routing [11] and traffic networks [12, 13] as well as a special ....

P. Dubey, "Inefficiency of Nash equilibria," Mathematics of Operations Research, vol. 11, pp. 1--8, 1986.

....finally disappears as the number of classes increases. These situations look quite paradoxical and surprising, although we know the existence of the prisoners dilemma, and although it has been already shown that Nash equilibria, even with smooth payoff functions, are generally Pareto inefficient [5]. II. Numerical Results on Asymmetric Models In order to give some insight into the problem, we present here a part of the numerical results we obtained for simple asymmetrical models. b b f f 12 21 1 2 1 1 2 node 1 node 2 Fig. 1. The system model examined in Section II. We examine ....

P. Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research 11, 1, pp.1-8, 1986.

....Nash Equilibrium Point (NEP) if, for all i I, the following holds: j(f) min ji(f, fi , fi, fi , f) fi F i The importance of an NEP is that it is a point at which no user has an incentive to deviate. However, one problem with an NEP is that it is not necessarily very efficient [5]. In fact, Korillis, Lazar, and Orda [15] give numerical examples with natural cost functions where the difference between the total cost at the system wide optimum point and that at the NEP could be more than 20 percent. In our analysis, we consider a family of type B cost functions in [21] For ....

P. Dubey, "Inefficiency of Nash equilibria", Mathematics of Operations Research, Vol. 11, pp. 1-8, 1986

....the problem is that, in general, the problem cannot be formulated as a convex programming problem. Thus, the KKT condition cannot be used for the sufficient condition of the optimal solution. In most of works on utility and pricing for power control, only Nash equilibria, which are inefficient [5], have been obtained. 0 7803 7476 2 02 17.00 (c) 2002 IEEE. Utility based algorithms without pricing are considered in [6] 7] Oh and Wasserman [6] consider an uplink power and spreading gain control problem for the non real time services. They use an instantaneous throughput for each mobile ....

P. Dubey, "Inefficiency of Nash equilibria," Mathematics of Operations Research, vol. 11, pp. 1--8, 1986.

....number of classes increases unlimitedly. These situations look quite paradoxical and surprising to us, although we know the existence of the prisoners dilemma and although it has been already shown that Nash equilibria of games even with smooth payoff functions are generally Pareto inefficient [5]. 2 The Model and Assumptions We consider a system with m nodes (host computers or processors) connected with a communication means. The jobs that arrive at each node i, i = 1; 2; Delta Delta Delta ; m, are classified into n types k, k = 1; 2; Delta Delta Delta ; n. Consequently, we have mn ....

P. Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research 11, 1, pp.1-8, 1986. 21

....2F i J i ( f 1 ; Delta Delta Delta ; f i Gamma1 ; f i ; f i 1 ; Delta Delta Delta ; f I ) The importance of an NEP is that it is a point at which no user has an incentive to deviate. However, one problem with an NEP is that it is not necessarily very efficient [4]. In fact, Korillis, Lazar, and Orda [12] give numerical examples with natural cost functions where the difference between the total cost at the system wide optimum point and that at the NEP could be more than 20 percent. 9 In our analysis, we consider a family of type B cost functions in [18] ....

P. Dubey, "Inefficiency of Nash equilibria", Mathematics of Operations Research, Vol. 11, pp. 1-8, 1986

....[7] 8] and virtual path bandwidth allocation [9] in modern networking. These studies mainly investigate the structure of the Nash equilibria and provide valuable insight into the nature of networking under decentralized and noncooperative control. Nash equilibria are generically inefficient [10] and exhibit suboptimal network performance. This deficiency can be overcome with the intervention of a network agent, namely the network designer or manager, that architects the network so that the resulting equilibria are efficient according to some systemwide criterion. In essence, the ....

....: 1) all users do at least as well, i.e. for all , and 2) at least one user does strictly better, i.e. there is a user for which . Clearly, Pareto efficiency is a desirable property for the operating point of the network. Noncooperative equilibria, however, are generically Pareto inefficient [10]. Let us now explain that maximally efficient strategies of the manager drive the network to Pareto efficient operating points. Assume that is the operating point induced by a maximally efficient strategy of the manager. To see that is Pareto efficient, assume that there exists another strategy ....

P. Dubey, "Inefficiency of Nash equilibria," Math. Oper. Res., vol. 11, pp. 1--8, Feb. 1986.

....[HSIA91, MAZ91, ZHA92, ALT93, ORD93, KOR93, ALT94] routing [ECO91, ORD93] and pricing [COC93] in modern networking. These studies mainly investigate the structure of the network operating points, i.e. the Nash equilibria of the respective games. Such equilibria are inherently inefficient [DUB86] and, in general, exhibit suboptimal network performance. The goal of this paper is to demonstrate that, while users make noncooperative decisions, there is still room for improving network performance. Improvements can be achieved both during the provisioning phase, i.e. when the network ....

Pradeep Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research, vol. 11, pp. 1--8, February 1986.

....ORD93] and virtual path bandwidth allocation [LAZ95] in modern networking. These studies mainly investigate the structure of the Nash equilibria and provide valuable insight into the nature of networking under decentralized and noncooperative control. Nash equilibria are inherently inefficient [DUB86] and exhibit, in general, suboptimal network performance. This deficiency can be overcome with the intervention of a network agent, namely the network designer or manager, that architects the network so that the resulting equilibria are efficient according to some systemwide criterion. In ....

Pradeep Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research, vol. 11, pp. 1--8, February 1986.

....[7] 8] and virtual path bandwidth allocation [9] in modern networking. These studies mainly investigate the structure of the Nash equilibria and provide valuable insight into the nature of networking under decentralized and noncooperative control. Nash equilibria are generically inefficient [10] and ex This work was supported by the Office of Naval Research under Contract # N00014 90 J 1289. This paper was presented in part at the IEEE INFOCOM 96, San Francisco, CA, March 1996. Y. A. Korilis is with Bell Laboratories, Lucent Technologies, Holmdel, NJ 07733 USA. This work was carried ....

....) for all i 2 I 0 , and (ii) at least one user does strictly better, i.e. there is a user j 2 I 0 for which J j ( f) J j (f ) Clearly, Pareto efficiency is a desirable property for the operating point of the network. Noncooperative equilibria, however, are generically Pareto inefficient [10]. Let us now explain that maximally efficient strategies of the manager drive the network to Pareto efficient operating points. Assume that f = f 0 ; N 0 (f 0 ) is the operating point induced by a maximally efficient strategy f 0 of the manager. To see that f is Pareto efficient, assume ....

P. Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research, vol. 11, pp. 1--8, February 1986. KORILIS, LAZAR, AND ORDA: ACHIEVING NETWORK OPTIMA USING STACKELBERG ROUTING STRATEGIES 13

....routing [6, 7] and virtual path bandwidth allocation [8] in modern networking. These studies mainly investigate the structure of the Nash equilibria and provide valuable insight into the nature of networking under decentralized and noncooperative control. Nash equilibria are inherently inefficient [9] and exhibit, in general, suboptimal network performance. This deficiency can be overcome with the intervention of a network agent, namely the network designer or manager, that architects the network so that the resulting equilibria are efficient according to some systemwide criterion. In essence, ....

P. Dubey, "Inefficiency of Nash Equilibria," Math. of OR, vol. 11, pp. 1--8, February 1986.

....of flow control [3] 7] routing [8] 10] virtual path bandwidth allocation [11] and pricing [12] in modern networking. These studies mainly investigate the structure of the network operating points, i.e. the Nash equilibria of the respective games. Such equilibria are inherently inefficient [13] and, in general, exhibit suboptimal network performance. The goal of this paper is to demonstrate that, while users make noncooperative decisions, there is still room for improving network performance. Improvements can be achieved both during the provisioning phase, i.e. when This paper was ....

P. Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research, vol. 11, pp. 1--8, February 1986.

....game depends on the form of the joint strategy space R. As an Why is Flow Control Hard: Optimality, Fairness, Partial and Delayed Information 51 example, if R = 0 and, for all k 2 P; 0 k is the unit simplex in IR N k , then the set of Nash equilibria is nonempty and, generically, 16 finite [DUB86]. A more general class of games is studied in [ROSE65] the class of concave games on a convex and compact joint strategy space R. A K person game is called concave, if for every player k 2 P its utility function OE k is concave in the player s strategy fl k . A characterization of the set of ....

.... (OE 1 ; OE K ) fl 1 ; fl K ) OE i fl j # i;j : If fl 2 IR K is Pareto efficient, then jG( fl)j = 0: 16 For the purposes of this presentation, suffice it to say that generically means for almost all games ; a rigorous definition of the term can be found in [DUB86]. Why is Flow Control Hard: Optimality, Fairness, Partial and Delayed Information 52 A.3 The Nash Bargaining Scheme In this section we discuss the concept of an arbitration scheme in a K person cooperative game and in particular the Nash bargaining scheme, due to John Nash [NAS50] This ....

Pradeep Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research, vol. 11, pp. 1--8, February 1986.

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P. Dubey, "Inefficiency of nash equilibria," Math. Oper. Res., vol. 11, pp. 1--8, Feb. 1986.

No context found.

P. Dubey, "Inefficiency of nash equilibria," Mathematics of Operations Research, vol. 11, pp. 1--8, 1986.

No context found.

P. Dubey, "Inefficiency of Nash Equilibria," Mathematics of Operations Research vol 11, pp. 1-8, 1986

No context found.

P. Dubey, "Inefficiency of Nash equilibria," Mathemat. Oper. Res., vol. 11, pp. 1--8, 1986.

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P. Dubey, "Inefficiency of Nash equilibria," Math. Oper. Res., vol. 11, pp. 1--8, 1986.

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Dubey, P. (1986): "Inefficiency of Nash Equilibria," Mathematics of Operations Research, 11, pp. 1-8.

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