[Paper Review] Game-Theoretic Randomness for Blockchain Games

Daniel Kraft|arXiv (Cornell University)|Jan 18, 2019

Auction Theory and ApplicationsDecision Sciences4 references3 citations

TL;DR

This paper proposes a game-theoretic mechanism to generate fair randomness in blockchain games by incentivizing miners to act honestly through betting on random outcomes. By aligning miner incentives via a betting game, the method ensures that even profit-maximizing miners skew the distribution of random events only slightly, significantly improving fairness over existing block-hash-based methods.

ABSTRACT

In this paper, we consider the problem of generating fair randomness in a deterministic, multi-agent context (for instance, a decentralised game built on a blockchain). The existing state-of-the-art approaches are either susceptible to manipulation if the stakes are high enough, or they are not generally applicable (specifically for massive game worlds as opposed to games between a small set of players). We propose a novel method based on game theory: By allowing agents to bet on the outcomes of random events against the miners (who are ultimately responsible for the randomness), we are able to align the incentives so that the distribution of random events is skewed only slightly even if miners are trying to maximise their profit and engage in block withholding to cheat in games.

Motivation & Objective

• To address the lack of fair, manipulative-resistant randomness generation in decentralized blockchain games.
• To overcome limitations of existing methods—block-hash-based RNGs vulnerable to miner manipulation and hash-commitment schemes not scalable to large multiplayer games.
• To design a general-purpose, incentive-compatible randomness mechanism applicable to massive game worlds like MMOs.
• To formally analyze how betting mechanisms can align miner behavior with fair outcomes using game theory.
• To demonstrate that even with profit-maximizing miners, the skew in random event distributions remains minimal under the proposed system.

Proposed method

• Introduces a betting game where players bet on the outcome of random events, with payouts determined by the block hash.
• Uses a house edge (e.g., 1% or 10%) to ensure the game is profitable for the house while keeping the distribution of outcomes close to fair.
• Models the miner’s strategy as block withholding to manipulate the block hash and increase expected profit from bets.
• Applies game-theoretic analysis to show that the Nash equilibrium results in minimal skew—e.g., a 1% house edge causes less than 0.5% deviation from fairness.
• Derives the expected profit for the miner based on the natural probability distribution P and the betting strategy, showing that manipulation is only marginally beneficial.
• Analyzes the system under assumptions of a single miner and single user, with the user’s strategy based on observed outcome frequencies P_d.

Experimental results

Research questions

• RQ1 Can a game-theoretic mechanism reduce the skew in random event distributions caused by profit-maximizing miners in blockchain games?
• RQ2 How effective is the betting mechanism in deterring block withholding attacks when the stakes are high?
• RQ3 What is the quantitative impact of different house edges on the fairness of the resulting random distribution?
• RQ4 Does the system remain robust when extended to multiple events or multiple agents?
• RQ5 Can the proposed mechanism be implemented in real-world blockchain systems like Ethereum or XAYA without requiring a new blockchain?

Key findings

• With a 1% house edge, the deviation from fair distribution is less than 0.5%, making the system nearly indistinguishable from fair randomness.
• Even with a 10% house edge, the maximum deviation is only 5% (e.g., a 50% event occurs 55% of the time), which is vastly better than the 100% manipulation possible without betting.
• The game-theoretic mechanism ensures that miners are strongly disincentivized from manipulating randomness, as the profit gain from manipulation is minimal.
• The Nash equilibrium of the system results in a distribution of outcomes that closely matches the expected fair distribution, even under strategic miner behavior.
• The method is most effective for events that occur with moderate to high frequency, as block withholding has the greatest impact on rare events.
• Empirical observation of outcome frequencies P_d allows users to determine optimal betting strategies, even if the exact R_w is unknown.