A game theoretic framework for distributed computing with dynamic set of agents

We consider a distributed computing setting wherein a central entity seeks power from computational providers by offering a certain reward in return. The computational providers are classified into long-term stakeholders that invest a constant amount of power over time and players that can strategize on their computational investment. In this paper, we model and analyze a stochastic game in such a distributed computing setting, wherein players arrive and depart over time. While our model is formulated with a focus on volunteer computing, it equally applies to certain other distributed computing applications such as mining in blockchain. We prove that, in Markov perfect equilibrium, only players with cost parameters in a relatively low range which collectively satisfy a certain constraint in a given state, invest. We infer that players need not have knowledge about the system state and other players’ parameters, if the total power that is being received by the central entity is communicated to the players as part of the system’s protocol. If players are homogeneous and the system consists of a reasonably large number of players, we observe that the total power received by the central entity is proportional to the offered reward and does not vary significantly despite the players’ arrivals and departures, thus resulting in a robust and reliable system. We then study by way of simulations and mean field approximation, how the players’ utilities are influenced by their arrival and departure rates as well as the system parameters such as the reward’s amount and dispensing rate. We observe that the players’ expected utilities are maximized when their arrival and departure rates are such that the average number of players present in the system is typically between 1 and 2, since this leads to the system being in the condition of least competition with high probability. Further, their expected utilities increase almost linearly with the offered reward and converge to a constant value with respect to its dispensing rate. We conclude by studying a Stackelberg game, where the central entity decides the amount of reward to offer, and the computational providers decide how much power to invest based on the offered reward.