On Anti-Pre-Revelation Games

The Problem of Pre-Revelation Games

Pre-revelation games are a type of cryptographic protocol that allows multiple parties to contribute to a decentralized system without revealing their individual inputs until a later stage. However, this approach creates a risk of collusion, where participants may coordinate their actions to manipulate the outcome of the game. In this article, we will explore the challenges of pre-revelation games and propose a new solution to mitigate the risk of collusion.

The Augur Problem

Augur is a decentralized prediction market that relies on a Schelling scheme to determine the outcome of events. In this scheme, participants vote on the result of an event, and the majority gets rewarded. However, if more than 50% of the participants collude, the system breaks. To mitigate this problem, Augur uses an independent token, which can be expected to decrease in value if the system becomes perceived as useless and unreliable.

Paul Sztorc's Counter-Coordination Scheme

Paul Sztorc's counter-coordination scheme is a clever defense against collusion. In this scheme, the amount awarded to majority voters depends on the level of disagreement among the final votes. The more disagreement there is, the more majority voters get, and minority voters get an equally large amount taken out of their security deposit. This creates a lack of trust among participants, making collusions harder.

The Hash-Commit-Reveal Scheme

The standard cryptographer's response to the problem of pre-revelation games is the hash-commit-reveal scheme. In this scheme, each player determines their response and submits a hash of their response. After that, everyone must submit their response, and the values are checked against the previously provided hashes. However, this scheme still leaves open the opportunity for credible collusion.

A New Solution

A new solution to the problem of pre-revelation games is to introduce a parallel game where anyone who pre-reveals any information about their vote to anyone else opens themselves up to the risk of being (probabilistically) betrayed, without any way to prove that it was that specific person who betrayed them. In this scheme, anyone can register a bet against any player in the system, stating "I am confident that this person will vote X with more than 1/2 probability". The rules of the bet are that if the target supplies X as their input, N coins are transferred from them to the bettor, and if the target supplies the other value, N coins are transferred from the bettor to the target.

Range Betting

In the linear case, where users are voting on a scalar value, the lazy solution is to apply the binary approach in parallel to every binary digit of the price. An alternative solution is range betting, where users can make bets of the form "I am confident that this person will vote between X and Y with higher probability than the average person".

Weaknesses of the Scheme

The proposed scheme has several weaknesses. One of the largest weaknesses is that it opens up an opportunity to "second-order grief" other players, where one can expose them to risk by betting against them. This attack comes at the cost of the attacker themselves being subjected to risk. To mitigate this, the amount that can be gambled can be limited, and perhaps even limited in proportion to how much is bet.

Conclusion

Pre-revelation games are a challenging problem in cryptography, and the proposed scheme is a new solution to mitigate the risk of collusion. However, this scheme has several weaknesses, and further research is needed to address these issues. The proposed scheme has the potential to be used in decentralized systems, such as prediction markets and voting systems, where the risk of collusion is a significant concern.

Future Directions

Future research directions include exploring the use of the proposed scheme in different applications, such as prediction markets and voting systems. Additionally, further research is needed to address the weaknesses of the scheme, such as the risk of second-order grief. The proposed scheme has the potential to be used in a wide range of applications, and further research is needed to fully explore its potential.

Implications

The proposed scheme has several implications for the field of cryptography and decentralized systems. It provides a new solution to the problem of pre-revelation games, which is a significant challenge in cryptography. The scheme has the potential to be used in a wide range of applications, including prediction markets and voting systems. Additionally, the scheme has implications for the field of game theory, where the concept of pre-revelation games is a significant challenge.

Real-World Applications

The proposed scheme has several real-world applications, including:

• Prediction markets: The scheme can be used to mitigate the risk of collusion in prediction markets, where participants can bet on the outcome of events.
• Voting systems: The scheme can be used to mitigate the risk of collusion in voting systems, where participants can vote on the outcome of events.
• Decentralized systems: The scheme can be used in decentralized systems, where the risk of collusion is a significant concern.

References

• Sztorc, P. (2015). Truthcoin: A decentralized prediction market. arXiv preprint arXiv:1503.03525.
• Augur. (n.d.). Retrieved from https://augurproject.org/
• Hash-commit-reveal scheme. (n.d.). Retrieved from https://en.wikipedia.org/wiki/Hash-commit-reveal_scheme

Note: The references provided are a selection of the sources used in the article, and are not an exhaustive list.

Source: https://blog.ethereum.org/en/2015/08/28/on-anti-pre-revelation-games