Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Related Work


Preliminaries
3.1 TFMs: Desirable Properties
3.2 Groves’ Redistribution Mechanism (RM)


IDEAL-TFRM: Impossibility of Achieving Strictly Positive Redistribution Index


Transaction Fee Redistribution Mechanism (TFRM)


R-TFRM: A TFRM Robust to Miner Manipulation
6.1 R-TFRM: Analyzing Impact of Miner Manipulation on Rebate and Miner Revenue


R2-TFRM: Robust and Rational TFRM


Conclusion and References Related Work Related Work Related Work Preliminaries
3.1 TFMs: Desirable Properties
3.2 Groves’ Redistribution Mechanism (RM) Preliminaries Preliminaries 3.1 TFMs: Desirable Properties 3.1 TFMs: Desirable Properties 3.2 Groves’ Redistribution Mechanism (RM) 3.2 Groves’ Redistribution Mechanism (RM) IDEAL-TFRM: Impossibility of Achieving Strictly Positive Redistribution Index IDEAL-TFRM: Impossibility of Achieving Strictly Positive Redistribution Index IDEAL-TFRM: Impossibility of Achieving Strictly Positive Redistribution Index Transaction Fee Redistribution Mechanism (TFRM) Transaction Fee Redistribution Mechanism (TFRM) Transaction Fee Redistribution Mechanism (TFRM) R-TFRM: A TFRM Robust to Miner Manipulation
6.1 R-TFRM: Analyzing Impact of Miner Manipulation on Rebate and Miner Revenue R-TFRM: A TFRM Robust to Miner Manipulation R-TFRM: A TFRM Robust to Miner Manipulation 6.1 R-TFRM: Analyzing Impact of Miner Manipulation on Rebate and Miner Revenue 6.1 R-TFRM: Analyzing Impact of Miner Manipulation on Rebate and Miner Revenue R2-TFRM: Robust and Rational TFRM R2-TFRM: Robust and Rational TFRM R2-TFRM: Robust and Rational TFRM Conclusion and References Conclusion and References Conclusion and References A. Proofs for Results from Section 4 and 5 A. Proofs for Results from Section 4 and 5 B. Proofs for Results from Section 6 B. Proofs for Results from Section 6 C. Proofs for Results from Section 7 C. Proofs for Results from Section 7 A PROOFS FOR RESULTS FROM SECTION 4 AND 5 A.1 Proof of Theorem 2 Theorem (Ideal-TFRM Impossibility). If𝑟 ★ is an anonymous rebate function that satisfies Theorem 1, no Ideal-TFRM can guarantee a non-zero redistribution index (RI) in the worst case. If𝑟 ★ is an anonymous rebate function that satisfies Theorem 1, no Ideal-TFRM can guarantee a non-zero redistribution index (RI) in the worst case. A.2 Proof of Theorem 3 B PROOFS FOR RESULTS FROM SECTION 6 B.1 Proof of Claim 1 B.2 Proof of Claim 2 B.3 Proof of Claim 3 B.4 Proof of Claim 4 B.5 Proof of Theorem 4 Theorem*. For any𝑛 and 𝑘 such that𝑛 ≥ 𝑘+2, the R-TFRMmechanism is unique. The fraction redistributed to the top-k users in the worst-case is given by:* B.6 Proof of Theorem 5 C PROOFS FOR RESULTS FROM SECTION 7 C.1 Proof of Theorem 6 C.2 Proof of Theorem 7 Proof. Similar to Theorem 5, the fraction of redistribution remains constant. For every true user (not fake), the 𝛼𝑘/𝑛 fraction of the payment is returned back as the rebate in expectation. Authors:
(1) Sankarshan Damle, IIIT, Hyderabad, Hyderbad, India (sankarshan.damle@research.iiit.ac.in);
(2) Manisha Padala, IISc, Bangalore, Bangalore, India (manishap@iisc.ac.in);
(3) Sujit Gujar, IIIT, Hyderabad, Hyderbad, India (sujit.gujar@iiit.ac.in). Authors: Authors: (1) Sankarshan Damle, IIIT, Hyderabad, Hyderbad, India (sankarshan.damle@research.iiit.ac.in); (2) Manisha Padala, IISc, Bangalore, Bangalore, India (manishap@iisc.ac.in); (3) Sujit Gujar, IIIT, Hyderabad, Hyderbad, India (sujit.gujar@iiit.ac.in). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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Mathematical Proofs for Truthful Rebate Mechanisms (TFRM)

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