Arbitrable stochastic games: three variations of the heads-or-tails game for bitcoin

Key Points

• The aim is to introduce arbitrable stochastic games and explore fair pricing methods using different criteria.
• Introduced a novel reward criterion for defining fair play prices in stochastic games.
• Illustrated concepts through three variations of the coin-toss game using chips.
• Provided proofs using Doob’s theorem focusing on supermartingales and developed practical algorithms.
• Established a new framework for understanding fair pricing in non-competitive stochastic games.
• Validated the variations of the coin-toss game as examples of arbitrable stochastic games.
• Demonstrated enhanced understanding of the Bitcoin protocol through these concepts.

Abstract