Game Theory for Networks. Third International ICST Conference, GameNets 2012, Vancouver, BC, Canada, May 24-26, 2012, Revised Selected Papers

Research Article

A Game Theoretic Optimization of the Multi-channel ALOHA Protocol

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  • @INPROCEEDINGS{10.1007/978-3-642-35582-0_6,
        author={Kobi Cohen and Amir Leshem and Ephraim Zehavi},
        title={A Game Theoretic Optimization of the Multi-channel ALOHA Protocol},
        proceedings={Game Theory for Networks. Third International ICST Conference, GameNets 2012, Vancouver, BC, Canada, May 24-26, 2012, Revised Selected Papers},
        proceedings_a={GAMENETS},
        year={2012},
        month={12},
        keywords={Collision channels multi-channel ALOHA Nash equilibrium point best response potential games},
        doi={10.1007/978-3-642-35582-0_6}
    }
    
  • Kobi Cohen
    Amir Leshem
    Ephraim Zehavi
    Year: 2012
    A Game Theoretic Optimization of the Multi-channel ALOHA Protocol
    GAMENETS
    Springer
    DOI: 10.1007/978-3-642-35582-0_6
Kobi Cohen1,*, Amir Leshem1, Ephraim Zehavi1
  • 1: Bar-Ilan University
*Contact email: kobi.cohen10@gmail.com

Abstract

In this paper we consider the problem of distributed throughput maximization of networks with multi-channel ALOHA medium access protocol. In the multi-channel ALOHA protocol, each user tries to randomly access a channel using a probability vector defining the access probability to the various channels. First, we characterize the Nash Equilibrium Points (NEPs) of the network when users solve the unconstrained rate maximization. We show that in this case, for any NEP, each user’s probability vector is a standard unit vector (i.e., each user tries to access a single channel with probability one and does not try to access other channels). Specifically, when the number of users, , is equal to the number of channels there are ! NEPs. However, when the number of users is much larger than the number of channels, most of the users get a zero utility (due to collisions). To overcome this problem we propose to limit each user’s total access probability and solve the problem under a total probability constraint. We characterize the NEPs when user rates are subject to a total transmission probability constraint. We propose a simple best-response algorithm that solves the constrained rate maximization, where each user updates its strategy using its local channel state information (CSI) and by monitoring the channel utilization. We prove that the constrained rate maximization can be formulated as an exact potential game. This implies that convergence of the proposed algorithm is guaranteed. Finally, we provide numerical examples to demonstrate the algorithm’s performance.