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Fairness of Equilibrium in Proportional Sharing Mechanisms with Bid Costs | IEEE Conference Publication | IEEE Xplore

Fairness of Equilibrium in Proportional Sharing Mechanisms with Bid Costs


Abstract:

This paper considers the proportional sharing mechanism [4] from the lens of fairness. Deviating from prior work we consider the net utility to users by incorporating a w...Show More

Abstract:

This paper considers the proportional sharing mechanism [4] from the lens of fairness. Deviating from prior work we consider the net utility to users by incorporating a weighted cost of bidding, one example being the use of power, incurred at user-dependent costs, to competitively bid for throughput in wireless systems. In this context, we analyze the price of anarchy of the equilibrium when the social welfare is measured both by a fair-sharing utility measure, as well as the sum of utility measures. In the context of power bids by users, we consider both continuous and discrete bids. The analysis shows the PoA can be zero and even for a uniform linear utility function when using the sum-total measure, but with distinct costs of bids, is asymptotically zero with increasing number of users indicating that a number of users/clients were starved of resources. This illustrates that accounting for the cost of bids can substantially change the structure of the equilibrium as compared to uniform costs. We also investigate the number of such starved users experimentally. In order to determine equilibrium, we show convex program formulations as well as present approximation methods to determine (1+\epsilon) -approximate equilibrium via an efficient algorithm. We also design methods to compute the optimum solution. Optimization of the social utility in the general case, where multiple resources can be chosen by users, is shown to be NP-hard. Experimental results illustrate the asymptotic behavior of the PoA and of the number of users that are starved of resources when users (competition) increases.
Date of Conference: 24-27 September 2024
Date Added to IEEE Xplore: 04 November 2024
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Conference Location: Urbana, IL, USA

References

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