Cognitive Radio Simultaneous Spectrum Access/ One-shot Game Modelling

The aim of this work is to asses simultaneous spectrum access situations that may occur in Cognitive Radio (CR) environments. The approach is that of one shot, noncooperative games describing CR interactions. Open spectrum access scenarios are modelled based on continuous and discrete reformulations of the Cournot game theoretical model. CR interaction situations are described by Nash and Pareto equilibria. Also, the heterogeneity of players is captured by the new concept of joint Nash-Pareto equilibrium, allowing CRs to be biased toward different types of equilibrium. Numerical simulations reveal equilibrium situations that may be reached in simultaneous access scenarios of two and three users.Comment: 6 double-column pages, 8 figures, CSNDSP 2012. arXiv admin note: substantial text overlap with arXiv:1207.3365, arXiv:1209.5387, arXiv:1209.501

Beyond Nash Equilibrium in Open Spectrum Sharing: Lorenz Equilibrium in Discrete Games

A new game theoretical solution concept for open spectrum sharing in cognitive radio (CR) environments is presented, the Lorenz equilibrium (LE). Both Nash and Pareto solution concepts have limitations when applied to real world problems. Nash equilibrium (NE) rarely ensures maximal payoff and it is frequently Pareto inefficient. The Pareto set is usually a large set of solutions, often too hard to process. The Lorenz equilibrium is a subset of Pareto efficient solutions that are equitable for all players and ensures a higher payoff than the Nash equilibrium. LE induces a selection criterion of NE, when several are present in a game (e.g. many-player discrete games) and when fairness is an issue. Besides being an effective NE selection criterion, the LE is an interesting game theoretical situation per se, useful for CR interaction analysis.Comment: 5 pages, 4 figure