Rewarding Miners: Bankruptcy games and Pooling Strategies

Speaker : Marianna Belotti
SU&CNAM&Caisse des Dépôts
Date: 18/12/2019
Time: 2:00 pm - 3:00 pm
Location: Paris-Rennes Room (EIT Digital)


In the Bitcoin system, mining is the procedure through which miners can gain money on regular basis by finding solutions to a mathematical crypto puzzle (full solution) which validates bitcoin transactions. In order to reduce the uncertainty of the remuneration over time, miners cooperate and form pools. Each pool receives a reward which has to be split among pool’s participants. The focus of this paper is to understand which is best method for a mining pool to redistribute the reward among cooperating miners using proper game theoretical models.
There exist, in the literature and in practice, several reward functions which allocate bitcoins inside pools such as: (i) the proportional rule, (ii) the pay-per-share rule and (iii) an incentive compatible rule ensuring that miners report full solutions to the pool immediately and not with a delay. However, this last rule encourages a harmful intra-pool behaviour (i.e. pool hopping) in bankruptcy situations (where the gained reward results insufficient to remunerate pool miners) that causes a loss in terms of pool’s computational power.
By reinterpreting the allocating rules as outcomes of bankruptcy games (i.e., a type of cooperative games) we construct two new reward functions (i.e., the PPS-CEA and the PPS-CEL) and investigate their properties. The PPS-CEL rules results having a good inter-pool behavior discouraging pool hopping however, concerning the intra-pool behavior it does not behave as well as the incentive compatible rule.
We provide then a suitable modification of the PPS-CEL that discourages pool hopping in bankruptcy situations while guaranteeing the incentive compatible property.