<latexit sha1_base64="k9lIOCe/L4yz1skhX58h85/dsQY=">AB7HicbVBNS8NAEJ3Ur1q/qh69LBbBiyWRgj0WvHisYNpCG8pmu2XbjZhd1Iob/BiwdFvPqDvPlv3LY5aOuDgcd7M8zMCxMpDLrut1PY2t7Z3Svulw4Oj45PyqdnLROnmnGfxTLWnZAaLoXiPgqUvJNoTqNQ8nY4uV/47SnXRsTqCWcJDyI6UmIoGEUr+VNyQ5J+ueJW3SXIJvFyUoEczX75qzeIWRpxhUxSY7qem2CQUY2CST4v9VLDE8omdMS7lioacRNky2Pn5MoqAzKMtS2FZKn+nshoZMwsCm1nRHFs1r2F+J/XTXFYDzKhkhS5YqtFw1QSjMniczIQmjOUM0so08LeStiYasrQ5lOyIXjrL2+S1m3Vq1Vrj7VKo57HUYQLuIRr8OAOGvATfCBgYBneIU3RzkvzrvzsWotOPnMOfyB8/kDx9WN/A=</latexit> Cr Credible, Truthful, and Two-Ro Round (Optimal) Auctions via Cr Cryptogr graphic Co Commitments Matheus V. X. Ferreira, S. Matthew Weinberg • Model: There is 𝑜 bidders with private independent values drawn from 𝐸 . • Quasilinear utility v − p • Myerson Auction is Truthful and Optimal BUT not credible . Auctioneer Alice Bob Bid $80 Bid $79 Fake Bid Pay $79
<latexit sha1_base64="IoKSeAZIBn0IRp7n+Xj4aSRn2qA=">AB83icbVDLSgNBEOyNrxhfUY9eBoMQcKuBPQYyMVjBPOAZAmzk0kyZB7LzGwgLPkNLx4U8erPePNvnCR70MSChqKqm+6uKObMWN/9nJb2zu7e/n9wsHh0fFJ8fSsZVSiCW0SxZXuRNhQziRtWmY57cSaYhFx2o4m9YXfnlJtmJPdhbTUOCRZENGsHVSr6EYLY8vUH6ul8s+RV/CbRJgoyUIEOjX/zqDRJBJWcGxMN/BjG6ZYW0Y4nRd6iaExJhM8ol1HJRbUhOny5jm6csoADZV2JS1aqr8nUiyMmYnIdQpsx2bdW4j/ed3EDu/DlMk4sVS1aJhwpFVaBEAGjBNieUzRzDRzN2KyBhrTKyLqeBCNZf3iSt20pQrVQfq6VaLYsjDxdwCWUI4A5q8ANaAKBGJ7hFd68xHvx3r2PVWvOy2bO4Q+8zx/VQZDl</latexit> <latexit sha1_base64="qcf9l1Cw8U8Fx60bWIuSOGHS7tg=">AB7XicbVBNSwMxEJ2tX7V+VT16CRahgpRdKeix4MVjBfsB7VKyabaNzSZLki2Upf/BiwdFvPp/vPlvzLZ70NYHA4/3ZpiZF8ScaeO6305hY3Nre6e4W9rbPzg8Kh+ftLVMFKEtIrlU3QBrypmgLcMp91YURwFnHaCyV3md6ZUaSbFo5nF1I/wSLCQEWys1K5Or5C6HJQrbs1dAK0TLycVyNEclL/6Q0mSiApDONa657mx8VOsDCOczkv9RNMYkwke0Z6lAkdU+ni2jm6sMoQhVLZEgYt1N8TKY60nkWB7YywGetVLxP/83qJCW/9lIk4MVSQ5aIw4chIlL2OhkxRYvjMEkwUs7ciMsYKE2MDKtkQvNWX10n7ubVa/WHeqXRyOMowhmcQxU8uIEG3EMTWkDgCZ7hFd4c6bw4787HsrXg5DOn8AfO5w8JI5A</latexit> Credible Auctions [Akbarpour, Li 20’] • The auctioneer publicly `` promises ’’ to implement an auction format. • Safe deviation. A deviation of the promise auction is safe if for all bidders, the outcome of the auction is always consistent with some realization of the auction. • Credible Auction. No safe deviation yields more revenue than the promised auction. • Impossibility [Akbarpour, Li 20’] . The ascending price auction is the ONLY auction that is Revenue Optimal, Strategyproof, Credible, BUT it requires unbounded rounds ! • Main Result: Assuming cryptographic commitments there is a two-round auction that is Revenue Optimal, Strategyproof and Credible. Commit ( v, r ) 𝑠 : random seed Auctioneer ( v, r )
Deferred Revelation Auction Commit bids ⟹ Broadcast bids ⟹ Reveal bids ⟹ Implement Myerson Auction • Caveat : There is no cost to submit fake bids. • AND there is no cost for aborting fake bidders. • Solution : any bidder that aborts loses deposit 𝑔(𝑜, 𝐸) to the WINNER! Fake Bidders 𝑤 … 80 99 77 78 79 81 82 1 2 98 … Conceal Reveal
<latexit sha1_base64="P8VRmDP7iUNaRIg9yOJ3jpfh82s=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkYI8FLx5bsB/QhrLZTtq1m03Y3Qgl9Bd48aCIV3+SN/+N2zYHbX0w8Hhvhpl5QSK4Nq7RS2tnd294r7pYPDo+OT8ulZR8epYthmsYhVL6AaBZfYNtwI7CUKaRQI7AbTu4XfUKleSwfzCxBP6JjyUPOqLFSyx2WK27VXYJsEi8nFcjRHJa/BqOYpRFKwTVu+5ifEzqgxnAuelQaoxoWxKx9i3VNItZ8tD52TK6uMSBgrW9KQpfp7IqOR1rMosJ0RNRO97i3E/7x+asK6n3GZpAYlWy0KU0FMTBZfkxFXyIyYWUKZ4vZWwiZUWZsNiUbgrf+8ibp3FS9WrXWqlUa9TyOIlzAJVyDB7fQgHtoQhsYIDzDK7w5j86L8+58rFoLTj5zDn/gfP4AeF2MsQ=</latexit> <latexit sha1_base64="ps/y4QD2IWJs1mntzOm3gMT80U=">AB7XicbVA9SwNBEJ2LXzF+RS1tFoNgFe4kYMqAjWUEkwjJEeY2m2TN3u6xuyeEI/BxkIRW/+Pnf/GTXKFJj4YeLw3w8y8KBHcWN/9gobm1vbO8Xd0t7+weFR+fikbVSqKWtRJZR+iNAwSVrW4Fe0g0wzgSrBNbuZ+54lpw5W8t9OEhTGOJB9yitZJ7R6KZIz9csWv+guQdRLkpAI5mv3yV2+gaBozalAY7qBn9gwQ205FWxW6qWGJUgnOGJdRyXGzITZ4toZuXDKgAyVdiUtWai/JzKMjZnGkeuM0Y7NqjcX/O6qR3Ww4zLJLVM0uWiYSqIVWT+OhlwzagVU0eQau5uJXSMGql1AZVcCMHqy+ukfVUNatXaXa3SqOdxFOEMzuESAriGBtxCE1pA4RGe4RXePOW9eO/ex7K14OUzp/AH3ucPisWPFQ=</latexit> <latexit sha1_base64="pMEkpDpuKgdJTmh0nWthEscVe70=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkYI8FLx5bsB/QhrLZTtq1m03Y3Qgl9Bd48aCIV3+SN/+N2zYHbX0w8Hhvhpl5QSK4Nq7RS2tnd294r7pYPDo+OT8ulZR8epYthmsYhVL6AaBZfYNtwI7CUKaRQI7AbTu4XfUKleSwfzCxBP6JjyUPOqLFSyxuWK27VXYJsEi8nFcjRHJa/BqOYpRFKwTVu+5ifEzqgxnAuelQaoxoWxKx9i3VNItZ8tD52TK6uMSBgrW9KQpfp7IqOR1rMosJ0RNRO97i3E/7x+asK6n3GZpAYlWy0KU0FMTBZfkxFXyIyYWUKZ4vZWwiZUWZsNiUbgrf+8ibp3FS9WrXWqlUa9TyOIlzAJVyDB7fQgHtoQhsYIDzDK7w5j86L8+58rFoLTj5zDn/gfP4AeGMsg=</latexit> How big should be the penalties? Regular • MHR Distributions: MHR • Credible when fines are at least Myerson reserve. ⍺ - Strongly Regular • Regular Distributions: • Not credible. • There is distributions where the optimal auction has revenue 1. • YET , the auctioneer can extract ∞ revenue. • For ⍺ -Strongly Regular: • Credible with a single bidder and ε-Credible with multiple bidders. ε-Credible Credible Not Credible α 1 0 MHR Regular
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