Game-theoretic model of a volunteer computer GRID

In the paper we propose a simple game-theoretic model of a Desktop Grid for volunteer computing. Task replication reduces the risk of accepting wrong answers due to sabotage. Saboteur's attack by intruding multiple computing nodes brings him some profit in case a wrong answer is accepted, while the server suffers some penalty in this case. Nodes are assigned some reputation as a monotone function of the number of produced correct (or not exposed) answers. We obtain the optimal mixed strategies and show that the average gain of the players depends only on the server's penalty, nodes' reputation, and the size of the subgrid of nodes with the same reputation. Also we estimate the server's cost per an answer. Numerical examples show that the average cost of the server is not more than that in the case when the number of intruders is known.