A second eminent conclusion is that the size of discounts during the random phase mattered more to prices than the frequency or number of bids. For instance, one bid lowering the price significantly was better than multiple bidders lowering the price by just a few cents, or just enough to get ahead on the rankings. This appears to indicate that high-frequency bidding attributed to bots does not contribute to awarding at the lowest prices. Measures such as the ones taken by the State of São Paulo that may require a minimum reduction over the bidder’s previous bid might be productive to counter high-frequency bidding when combined with other adaptive measures, such as extending the length of the random phase.

We estimate that the federal government could save 1.1% or R$ 210 million per year if the random phase was extended to its maximum every time a price reduction in the last three minutes is bigger than the 90th percentile. Again, this shows the impact of the length of the random phase on prices, which is too great to be left as random.

The number of bidders had a material impact on prices and more bidders contributed to drive prices down, albeit with a non-linear relationship. In this vein, we recommend maxing out the length of the random phase whenever there are 15 bidders or more in the auction. That tactic can produce substantial 2.6% savings or R$ 500 million based on 2018 spending.

As a benchmark, we also include here the potential savings effect of a policy, not related to auction design: demand aggregation. The quantity purchased in an auction can have an impact on prices, as buying in bulk can lower prices compared to small purchases. In another study (World Bank, 2017), we estimated that the federal government can save 8% with bulk buying of high volume, low complexity items. That amount corresponds to about R$ 4 billion based on 2018 spending value. Thus, good planning that allows for leveraging the demand of the federal government as a whole when buying high-volume items should certainly be part of a strategy to achieve lower prices in public procurement.

Table 5. below summarizes the main conclusions and corresponding policy recommendations.

Table 5. Summary of policy options and estimated savings potential

|**Variable**|**Policy option**|**Potential**<br>**savings **|**Yearly savings**<br>**(2018 baseline)**|
|---|---|---|---|
|**Length of random**|Increase average length by 450 seconds|**2.8%**|**R$ 540 million**|
|**phase**|Increase minimum length by 450 seconds|**0.6%**|**R$ 116 million**|
|**Number of bidders**|Maximum time for random phase if 15+<br>bidders|**2.6%**|**R$ 500 million**|
||Maximum time for random phase if|||
|**Size of discount**|discount in last three minutes bigger than<br>90th percentile|**1.1%**|**R$ 210 million**|
|**Buying in bulk**|Aggregating all purchases into larger<br>tenders which are below 361 units per<br>tender|**8%**|**R$ 4 billion**<br>(*not only e‐reverse<br>auctions)|

While this research delivered a range of policy‐relevant and robust results, it merely represents the first steps towards better understanding competitive behavior in online auctions and devising ways to better tap into the potential of healthy competition. As a logical next step, further research could validate 19