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

Abstract

Systems of selfish-computers, such as the Internet, are subject to transient faults due to hardware/software temporal malfunctions; just as the society is subjected to human mistakes due to a moment of weakness. Game theory uses punishment for deterring improper behavior. 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 be proven to have ceased in order to avoid infinite cycles of unsynchronized behavior of "tit for tat".We investigate another aspect of selfish-computer systems. We consider the possibility of subsystem takeover, say, by the use of hostile malware. 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 (and its subordinates) from deviating in infinitely repeated games. We construct deterministic and finite 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.