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

We introduce the concept of arbitrable stochastic games, which appears to be new. To do so, we consider a reward criterion different from the standard gamma-weighted criterion. This allows us to define the fair price to play a non-competitive stochastic game. We then illustrate the concept through three variations of the classical coin-toss game with chips, providing proofs via Doob’s theorem for supermartingales and practical algorithms. These examples deepen our understanding of the Bitcoin protocol.