## 6 Considerations on a Proposed Auction for Brazilian 6G
### Proxy Phase  
With the conclusion of the _clock_ phase, in which prices are adjusted until there is balance between supply and demand (or by auctioneer's decision), the auctioneer identifies the combination of bids that results in the greatest allocative efficiency. As illustrated in Table 13, this combination guarantees the maximum possible efficiency because it is able to sell all available goods. The prices shown in columns \(P\{A\}\), \(P\{B\}\), and \(P\{C\}\) reflect the values found in the initial round, except for item \(\{\text{A}\}\), which only clears the market when \(P\{A\}=12.50\). The previous allocation at \(P\{A\}=11\) still exists, since, when maximizing their _payoff_, Player 3 demands in some round the bundle \(\{4A\times 11,2C\times 3\}=50\). This bundle does not trigger _market clearing_ in market \(\{\text{A}\}\), causing prices to continue to rise iteratively until \(P\{A\}=12.50\). The auctioneer opts for the allocation at \(P\{A\}=11\), submitted in a previous round by Player 3, which is preferable in the auctioneer's view to the bundle \(\{4A\times 12.50\}=50\) because it implies greater dispersion of the available licenses. Then, these are defined as the minimum price for submitting bids requesting specific blocks and allocation preferences. It should be noted that bidders are not required to offer these prices in this round because if there are no distortions in the _price discovery_, the _proxy_ round does not alter the allocations even if no bidder submits any bids. In our example, there is a distortion caused by the activity rule in the second round, as shown in Table 11.  
Bidders now enter a more strategic moment in the auction. Previously, they were competing for generic blocks; now they have the opportunity to define preferences for specific spectrum licenses. The _proxy_ phase introduces a closed-bid mechanism to allow efficient allocation. During this phase, the bidders learn the specifics of the licenses up for auction. Instead of generic 5 MHz blocks, participants learn that Block C comprises two paired licenses: (708-713 MHz) and (713-718 MHz). This differentiation allows bidders to reveal more granular preferences--especially for incumbent operators who wish to acquire spectrum adjacent to their holdings. Bids in this phase are placed in closed envelopes and must respect minimum prices established during the clock phase. Bidders may submit additional bids to maximize their synergy. This approach prevents bidders from overpaying, while also allowing efficient price discovery. To ensure the bids reflect true valuations, Vickrey pricing is used to determine the winners and payments. In cases where combinatorial constraints arise, the _Nearest Core Vickrey Price_ (NCVP) may be used. This guarantees incentives for bidders to submit their true valuations (\(v_{i}\)) for their respective blocks or combinations, keeping the spirit of the Vickrey auction pricing and both eliminating the winner's curse and incentivizing straightforward bidding. Table 14 shows the bids that each bidder placed in their closed envelopes for blocks {A}, {B}, and {C}. Q_A, Q_B, and Q_C represent the number of licenses each bidder wins for each block. The minimum prices needed to enable preferred spectrum delivery are represented in the last column for each bidder. Player 2, aware that they cannot suffer the curse of the winner due to Vickrey pricing under NCVP, bids USD 7 for three C licenses, securing preferred delivery due to their highest closed envelope bid and the fact that they were the only bidder when Market C cleared under the activity rule. This same bidder is also rewarded with the preferred delivery for Market B for having placed the highest closed envelope bid and for being the only bidder during market B clearing (Table 12). Finally, for Item {A}, Player 1 prevails, noting that the critical price for this license was set at 11 (Table 13).