We study the resource allocation game in which price anticipating players compete for multiple divisible resources. In the scheme, each player submits a bid to a resource and receives a share of the resource according to the proportion of his bid to the total bids. Unlike the previous study (e.g. [5]), we consider the case when the players have budget constraints, i.e. each player's total bids is fixed. We show that there always exists a Nash equilibrium when the players' utility functions are strongly competitive. We study the efficiency and fairness at the Nash equilibrium. We show the tight efficiency bound of Θ(1/√m) for the m player balanced game. For the special cases when there is only one resource or when there are two players with linear utility functions, the efficiency is 3/4. We extend the classical notion of envy-freeness to measure fairness. We show that despite a possibly large utility gap, any Nash equilibrium is 0.828-approximately envy-free in this game. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Zhang, L. (2005). The efficiency and fairness of a fixed budget resource allocation game. In Lecture Notes in Computer Science (Vol. 3580, pp. 485–496). Springer Verlag. https://doi.org/10.1007/11523468_40
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