Following [4] we extend and generalize the game-theoretic model of distributed computing, identifying different utility functions that encompass different potential preferences of players in a distributed system. A good distributed algorithm in the game-theoretic context is one that prohibits the agents (processors with interests) from deviating from the protocol; any deviation would result in the agent losing, i.e., reducing its utility at the end of the algorithm. We distinguish between different utility functions in the context of distributed algorithms, e.g., utilities based on communication preference, solution preference, and output preference. Given these preferences we construct two basic building blocks for game theoretic distributed algorithms, a wake-up building block resilient to any preference and in particular to the communication preference (to which previous wake-up solutions were not resilient), and a knowledge sharing building block that is resilient to any and in particular to solution and output preferences. Using the building blocks we present several new algorithms for consensus, and renaming as well as a modular presentation of the leader election algorithm of [4].

The question of what global information must distributed rational agents a-priori know about the network in order for equilibrium to be possible is researched here. Until now, distributed algorithms with rational agents have assumed that n, the size of the network, is a-priori known to the participants. We investigate the above question, considering different distributed computing problems and showing how much each agent must a-priori know about n in order for distributed algorithms to be equilibria. The main tool considered throughout the paper is the advantage an agent may gain by duplication-pretending to be more than one agent.We start by proving that when no bound on n is given equilibrium for Coloring and Knowledge Sharing is impossible. We provide new algorithms for both problems when n is a-priori known to all agents, thus showing that there are algorithms in which the only way for an agent to gain an advantage is duplication. We further show that for each distributed problem there is an a-priori known range, an upper and a lower bound on n, such that if the actual n is guaranteed to lay in that range, equilibrium is possible. By providing equilibria for a specific range, and impossibility results for any larger range, we prove the tight range necessary for equilibrium in: Leader Election, Knowledge Sharing, Coloring, Partition and Orientation. Regular submissionEligible for best student paper award.

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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