An efficient and almost budget balanced cost sharing method
For a convex technology C we characterize cost sharing games where the Nash equilibrium demands maximize total surplus. Budget balance is possible if and only if C is polynomial of degree n-1 or less. For general C, the residual* cost shares are balanced if at least one demand is null, a characteristic property. If the cost function is totally monotone, a null demand receives cash and total payments may exceed actual cost. The ratio of excess payment to efficient surplus is at most . For power cost functions, C(a)=ap, p>1, the ratio of budget imbalance to efficient surplus vanishes as . For analytic cost functions, the ratio converges to zero exponentially along a given sequence of users. All asymptotic properties are lost if the cost function is not smooth.
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