E. Engel, R. Fisher, A. Galetovic (2001). Least Present Value of Revenue Auctions and Highway Franchising, Journal of Political Economy, vol. 109, 993-1020.

In this paper we show that fixed-term contracts, which are commonly
used to franchise highways, do not allocate demand risk optimally.
We characterize the optimal risk-sharing contract and show that it can
be implemented with a fairly straightforward mechanism—a least-present-value-of-revenue auction. Instead of bidding on tolls (or franchise
lengths), as in the case of fixed-term franchises, in an LPVR auction
the bidding variable is the present value of toll revenues. The lowest
bid wins and the franchise ends when that amount has been collected.
We also show that the welfare gains that can be attained by replacing
fixed-term auctions with LPVR auctions are substantial.

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