Abstract
Government agencies are increasingly using economic incentives to encourage landowners to adopt conservation practices. Auctions enable agencies to identify land conservation practices with low opportunity costs. At the same time, landowners’ opportunity costs contain useful information for government agencies to rank conservation priorities. This paper introduces a new reverse auction mechanism that performs well both from the cost effectiveness and cost-revelation perspectives and compares three multi-award reverse auction mechanisms. The first mechanism is called the Uniform Price Reverse (UPR) auction, where each winning bidder is paid the lowest rejected bid. The second mechanism is called the First Price Reverse (FPR) auction, where winning bidders are paid their submitted bids. The third, novel, mechanism is called the Generalized Second Price Reverse (GSPR) auction, where each winning bidder is paid the bid that is immediately higher. Theoretically, I derive the equilibrium bidding strategy for each auction mechanism and show that a symmetric equilibrium strategy may not exist under the GSPR auction. Empirically, lab experiment results show that UPR and GSPR auctions lead to a higher efficiency level compared to FPR, while UPR auction yields the lowest auctioneer surplus and is the least cost effective. As a result, GSPR maintains good incentive properties similar to UPR and presents potential large cost-saving opportunities to the auctioneer.
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Notes
In the context of conservation auctions, a higher surplus for the auctioneer means more money for the government and less for the landowners from a single auction. Overall, when the government faces a limited budget, a high surplus for the auctioneer implies a higher level of realized environmental benefits when more acres are enrolled.
The “click-through rate” measures the number of clicks advertisers receive on their advertisements per number of impressions. It reflects the potential benefits and is similar to the heterogeneous environmental quality in conservation auctions.
I also assume a random tie breaking rule in case there are multiple bids at the same price.
The equilibrium bids are lower than 20 experimental dollars based on the induced cost range in theory. Experimental data suggest that only high cost individuals occasionally bid over 20 experimental dollars. The $30 upper limit is set to rule out extremely unlikely scenarios where all bidders submit unusually high bids, which could break our budget. Only a tiny fraction of the bids (0.63%) are at $30 experimental dollars.
Note that the existence of Nash equilibrium depends on the specific experimental parameters and the equilibrium outcome is less likely to be observed when N and M are large. Therefore, our parameters are chosen so that the equilibrium bidding strategy does not exist to offer more generalizable comparison among the three reverse auction mechanisms based on experimental performance.
In addition, I run a simple OLS regression using the bid as the independent variable and the cost and period as the explanatory variable. Our results show that the coefficient associated with the period is 0.0081 with a standard error of 0.0050 (\(p=0.11\)) based on the FPR subsample; the coefficient associated with the period is 0.0005 with a standard error of 0.0055 (\(p=0.93\)) based on the GSPR subsample, implying GSPR auction is less likely to lead to opportunities to game the system over time relative to the FPR auction.
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Appendices
Appendix
A: Equilibrium Strategy in GSPR
Following Gomes and Sweeney (2014), the bidder i’s (with a private cost c) expected payment in equilibrium is denoted by E(p(c)), by the Revelation Principle, the E(p(c)) has to satisfy
According to the Integral-form Envelop Theorem (Milgrom and Segal 2002), equation (22) implies that,
where \(E(p(\hat{c}))=0\) as the highest cost bidder expects to receive zero payment with a zero probability of winning the auction. According to the definition of GSPR,
Based on equations (23) and (24)
where
Differentiating w.r.t. c on both sides,
Differentiating equation (26),
Combining equations (27) and (28),
Rewrite the above equation,
Therefore, we have
where
Specifically, when \(N=5\), \(M=2\), equation (31) implies
or
which can be further simplified to
Rewrite the above equation as
Non-existence of Symmetric Equilibrium Take the first order derivative with respect to c,
When \(s(c)>0\) and \(c\in [5,20]\), according to equation (37), we can show that \(s^{\prime }<0\), which violates the requirement that \(s^{\prime }(c)\) must be strictly increasing for an efficient equilibrium, and a symmetric equilibrium does not exist in our case (Caragiannis et al. 2011; Gomes and Sweeney 2014).
B: Additional Regression Results and Figures
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Liu, P. Balancing Cost Effectiveness and Incentive Properties in Conservation Auctions: Experimental Evidence from Three Multi-award Reverse Auction Mechanisms. Environ Resource Econ 78, 417–451 (2021). https://doi.org/10.1007/s10640-021-00538-0
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DOI: https://doi.org/10.1007/s10640-021-00538-0
Keywords
- Conservation programs
- Environmental market
- Procurement auction
- Generalized second price reverse auction
- Experimental economics