Pareto-optimal Nash equilibrium in capacity allocation game for self-managed networks

Abstract

In this paper we introduce a capacity allocation game which models the problem of maximizing network utility from the perspective of distributed noncooperative agents. Motivated by the idea of self-managed networks, in the developed framework decision-making entities are associated with individual transmission links, deciding on the way they split capacity among concurrent flows. An efficient decentralized algorithm is given for computing strongly Pareto-optimal strategies, constituting a pure Nash equilibrium. Subsequently, we discuss the properties of the introduced game related to the Price of Anarchy and Price of Stability. The paper is concluded with an experimental study.

Approximation of Isomorphic Infinite Two-Person Non-Cooperative Games by Variously Sampling the Players’ Payoff Functions and Reshaping Payoff Matrices into Bimatrix Game

“…be the r -th player's pure strategy, corresponding to its pure strategy in initial infinite game (3) with components in (15), whose indices are included into set (16). Hence, the first , has many solutions in forms of utility or equity equilibrium -Nash equilibrium, strong Nash equilibrium [7], [23], [31], [32], Pareto equilibrium [2], [6], [33], [34], Mertens-stable equilibrium [35], trembling hand perfect equilibrium [36], perfect Bayesian equilibrium [9], [37], [38], Markov perfect equilibrium [39], [40] and many others.…”

“…Notwithstanding exclusive importance of (26) and (27) for the game approximation acceptance, ESS (24) This is a definition of the most primitive consistency for the approximate solution of game (3). It could be strengthened in (27) and (34) with the part of   1 S  , which would make the cardinality of every player's ESS and their densities be non-decreasing within minimal neighbourhood of the sampling steps.…”

Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

“…Sometimes a two-sided noncooperative game is the most appropriate model for removing uncertainties in technical problems [6], [7]. For instance, this is for preventing a denial of service, when a server (reservoir) runs out of resources while a number of queries (demands) is not less than the rejection number [8], [9].…”

“…However, NE-solutions render a lot of the refined or modified principles of optimality, allowing to smooth differences in utility and equity [2], [10], [11]. Mainly, they are principles of Pareto equilibrium [2], [6], [8], [10], [13], [14], Mertens-stable equilibrium [15], trembling hand perfect equilibrium [16], proper equilibrium [17], [18], correlated equilibrium [19], sequential equilibrium [20], [21], quasi-perfect equilibrium [18], [22], [23], perfect Bayesian equilibrium [18], [20], [24], [25], quantal response equilibrium [26], [27], self-confirming equilibrium [28], [29], strong Nash equilibrium [30], [31], Markov perfect equilibrium [32], [33]. The question is only to find NEsolutions as fast as possible.…”

“…ON COMPACT ACTION SPACES Finding NE-solutions in even the finite noncooperative game is a computational difficulty [8], [34], [35]. Locally, solving dyadic games with three players takes some technique of visualization of the cube of situations in pure strategies [6], [10], whereupon dyadic games with four players and more are solved purely in analytics, requiring more computational resources [10], [36].…”