Reaching Distributed Equilibrium with Limited ID Space
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We examine the relation between the size of the id space and the number of rational agents in a network under which equilibrium in distributed algorithms is possible. When the number of agents in the network is not a-priori known, a single agent may duplicate to gain an advantage, pretending to be more than one agent. However, when the id space is limited, each duplication involves a risk of being caught. By comparing the risk against the advantage, given an id space of size L, we provide a method of calculating the minimal threshold t, the required number of agents in the network, such that the algorithm is in equilibrium. That is, it is the minimal value of t such that if agents a-priori know that n ≥ t then the algorithm is in equilibrium. We demonstrate this method by applying it to two problems, Leader Election and Knowledge Sharing, as well as providing a constant-time approximation t ≈L/5 of the minimal threshold for Leader Election.
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