Trustworthy Reputation Games and Applications to Proof-of-Reputation Blockchains

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Abstract
Reputation systems play an essential role in the Internet era, as they enable people to decide whom to trust, by collecting and aggregating data about users' behavior. Recently, several works proposed the use of reputation for the design and scalability improvement of decentralized (blockchain) ledgers; however, such systems are prone to manipulation and to our knowledge no game-theoretic treatment exists that can support their economic robustness. In this work we put forth a new model for the design of what we call, {\em trustworthy reputation systems}. Concretely, we describe a class of games, which we term {\em trustworthy reputation games}, that enable a set of users to report a function of their beliefs about the trustworthiness of each server in a set -- i.e., their estimate of the probability that this server will behave according to its specified strategy -- in a way that satisfies the following properties: 1. It is $(\epsilon$-)best response for any rational user in the game to play a prescribed (truthful) strategy according to their true belief. 2. Assuming that the users' beliefs are not too far from the {\em true} trustworthiness of the servers, playing the above ($\epsilon-$)Nash equilibrium allows anyone who observes the users' strategies to estimate the relative trustworthiness of any two servers. Our utilities and decoding function build on a connection between the well known PageRank algorithm and the problem of trustworthiness discovery, which can be of independent interest. Finally, we show how the above games are motivated by and can be leveraged in proof-of-reputation (PoR) blockchains.

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