Equilibria of Games in Networks for Local Tasks
Distributed tasks such as constructing a maximal independent set (MIS) in a network, or properly coloring the nodes or the edges of a network with reasonably few colors, are known to admit efficient distributed randomized algorithms. Those algorithms essentially proceed according to some simple generic rules, by letting each node choosing a temptative value at random, and checking whether this choice is consistent with the choices of the nodes in its vicinity. If this is the case, then the node outputs the chosen value, else it repeats the same process. Although such algorithms are, with high probability, running in a polylogarithmic number of rounds, they are not robust against actions performed by rational but selfish nodes. Indeed, such nodes may prefer specific individual outputs over others, e.g., because the formers suit better with some individual constraints. For instance, a node may prefer not being placed in a MIS as it is not willing to serve as a relay node. Similarly, a node may prefer not being assigned some radio frequencies (i.e., colors) as these frequencies would interfere with other devices running at that node. In this paper, we show that the probability distribution governing the choices of the output values in the generic algorithm can be tuned such that no nodes will rationally deviate from this distribution. More formally, and more generally, we prove that the large class of so-called LCL tasks, including MIS and coloring, admit simple "Luby's style" algorithms where the probability distribution governing the individual choices of the output values forms a Nash equilibrium. In fact, we establish the existence of a stronger form of equilibria, called symmetric trembling-hand perfect equilibria for those games.
Local distributed computing
Locally checkable labelings
Theory of computation~Distributed algorithms
Theory of computation~Algorithmic game theory
Theory of computation~Network games
6:1-6:16
Regular Paper
Simon
Collet
Simon Collet
CNRS and University Paris Diderot, France
Funded by the European Research Council (ERC) under the H2020 research and innovation program (grant No 648032).
Pierre
Fraigniaud
Pierre Fraigniaud
CNRS and University Paris Diderot, France
Additional supports from the ANR project DESCARTES, and from the Inria project GANG.
Paolo
Penna
Paolo Penna
ETH Zurich, Switzerland
10.4230/LIPIcs.OPODIS.2018.6
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Simon Collet, Pierre Fraigniaud, and Paolo Penna
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