Reaching Distributed Equilibrium with Limited ID Space.

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, but the id space is limited, a single agent may duplicate to gain an advantage but each duplication involves a risk of being caught. Given an id space of size L, we provide a method of calculating the threshold, the minimal value t such that agents know that (n ge t), such that the algorithm is in equilibrium. We apply the method to Leader Election and Knowledge Sharing, and provide a constant-time approximation (t approx frac{L}{5}) of the threshold for Leader Election.