Distributed Participation to Threshold Signature Analyzed via Game Theory

We investigate the performance of a distributed threshold signature scheme, where at least t out of n signers must participate to authenticate a message. We model this scheme as a participation game, where individual signers choose whether to submit their contribution to the (t, n) signature with a certain probability and incur a cost in doing so. We discuss the resulting Nash equilibria of the game and specifically investigate the symmetric mixed-strategy Nash equilibrium, which corresponds to a stable operating point of distributed decisions made individually by the agents. Finally, we show how tweaking the information revealed to the signers may improve the efficiency of this resulting equilibrium. This study highlights a fundamental trade-off between system-wide efficiency and individual resource consumption. Our proposed mechanism thus provides a practical method for steering a decentralized system towards a more globally efficient outcome without resorting to an impractical and unfair centralized control structure.