Strategies for repeated games with subsystem takeovers implementable by deterministic and self-stabilising automata

Systems of selfish-computers are subject to transient faults due to temporal malfunctions; just as the society is subjected to human mistakes. Game theory uses punishment for deterring improper behaviour. Due to faults, selfish-computers may punish well-behaved ones. This is one of the key motivations for forgiveness that follows any effective and credible punishment. Therefore, unplanned punishments must provably cease in order to avoid infinite cycles of unsynchronised behaviour of 'tit for tat'. We investigate another aspect of these systems. We consider the possibility of subsystem takeover. The takeover may lead to joint deviations coordinated by an arbitrary selfish-computer that controls an unknown group of subordinate computers. We present strategies that deter the coordinator from deviating in infinitely repeated games. We construct deterministic automata that implement these strategies with optimal complexity. Moreover, we prove that all unplanned punishments eventually cease by showing that the automata can recover from transient faults.