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**Published in:** LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Is there an equilibrium for distributed consensus when all agents except one collude to steer the decision value towards their preference? If an equilibrium exists, then an n-1 size coalition cannot do better by deviating from the algorithm, even if it prefers a different decision value. We show that an equilibrium exists under this condition only if the number of agents in the network is odd and the decision is binary (among two possible input values). That is, in this framework we provide a separation between binary and multi-valued consensus. Moreover, the input and output distribution must be uniform, regardless of the communication model (synchronous or asynchronous). Furthermore, we define a new problem - Resilient Input Sharing (RIS), and use it to find an iff condition for the (n-1)-resilient equilibrium for deterministic binary consensus, essentially showing that an equilibrium for deterministic consensus is equivalent to each agent learning all the other inputs in some strong sense. Finally, we note that (n-2)-resilient equilibrium for binary consensus is possible for any n. The case of (n-2)-resilient equilibrium for multi-valued consensus is left open.

Itay Harel, Amit Jacob-Fanani, Moshe Sulamy, and Yehuda Afek. Consensus in Equilibrium: Can One Against All Decide Fairly?. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{harel_et_al:LIPIcs.OPODIS.2019.20, author = {Harel, Itay and Jacob-Fanani, Amit and Sulamy, Moshe and Afek, Yehuda}, title = {{Consensus in Equilibrium: Can One Against All Decide Fairly?}}, booktitle = {23rd International Conference on Principles of Distributed Systems (OPODIS 2019)}, pages = {20:1--20:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-133-7}, ISSN = {1868-8969}, year = {2020}, volume = {153}, editor = {Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.20}, URN = {urn:nbn:de:0030-drops-118065}, doi = {10.4230/LIPIcs.OPODIS.2019.20}, annote = {Keywords: distributed computing, game theory, rational agents, consensus} }

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**Published in:** LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

What can be computed by a network of n randomized finite state machines communicating under the stone age model (Emek & Wattenhofer, PODC 2013)? The inherent linear upper bound on the total space of the network implies that its global computational power is not larger than that of a randomized linear space Turing machine, but is this tight? We answer this question affirmatively for bounded degree networks by introducing a stone age algorithm (operating under the most restrictive form of the model) that given a designated I/O node, constructs a tour in the network that enables the simulation of the Turing machine's tape. To construct the tour with high probability, we first show how to 2-hop color the network concurrently with building a spanning tree.

Yehuda Afek, Yuval Emek, and Noa Kolikant. The Synergy of Finite State Machines. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{afek_et_al:LIPIcs.OPODIS.2018.22, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{The Synergy of Finite State Machines}}, booktitle = {22nd International Conference on Principles of Distributed Systems (OPODIS 2018)}, pages = {22:1--22:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-098-9}, ISSN = {1868-8969}, year = {2019}, volume = {125}, editor = {Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.22}, URN = {urn:nbn:de:0030-drops-100825}, doi = {10.4230/LIPIcs.OPODIS.2018.22}, annote = {Keywords: finite state machines, stone-age model, beeping communication scheme, distributed network computability} }

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**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

This paper studies a variant of the leader election problem under the stone age model (Emek and Wattenhofer, PODC 2013) that considers a network of n randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the beeping model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as k-leader selection, in which a leader should be selected out of at most k initial candidates. Our main contribution is an algorithm that solves k-leader selection for bounded k in the aforementioned stone age model. On (general topology) graphs of diameter D, this algorithm runs in O~(D) time and succeeds with high probability. The assumption that k is bounded turns out to be unavoidable: we prove that if k = omega (1), then no algorithm in this model can solve k-leader selection with a (positive) constant probability.

Yehuda Afek, Yuval Emek, and Noa Kolikant. Selecting a Leader in a Network of Finite State Machines. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{afek_et_al:LIPIcs.DISC.2018.4, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{Selecting a Leader in a Network of Finite State Machines}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {4:1--4:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.4}, URN = {urn:nbn:de:0030-drops-97933}, doi = {10.4230/LIPIcs.DISC.2018.4}, annote = {Keywords: stone age model, beeping communication scheme, leader election, k-leader selection, randomized finite state machines, asynchronous scheduler} }

Document

**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Until now, distributed algorithms for rational agents have assumed a-priori knowledge of n, the size of the network. This assumption is challenged here by proving how much a-priori knowledge is necessary for equilibrium in different distributed computing problems. Duplication - pretending to be more than one agent - is the main tool used by agents to deviate and increase their utility when not enough knowledge about n is given.
We begin by proving that when no information on n is given, equilibrium is impossible for both Coloring and Knowledge Sharing. We then provide new algorithms for both problems when n is a-priori known to all agents. However, what if agents have partial knowledge about n? We provide tight upper and lower bounds that must be a-priori known on n for equilibrium to be possible in Leader Election, Knowledge Sharing, Coloring, Partition and Orientation.

Yehuda Afek, Shaked Rafaeli, and Moshe Sulamy. The Role of A-priori Information in Networks of Rational Agents. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{afek_et_al:LIPIcs.DISC.2018.5, author = {Afek, Yehuda and Rafaeli, Shaked and Sulamy, Moshe}, title = {{The Role of A-priori Information in Networks of Rational Agents}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {5:1--5:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.5}, URN = {urn:nbn:de:0030-drops-97945}, doi = {10.4230/LIPIcs.DISC.2018.5}, annote = {Keywords: rational agents, distributed game theory, coloring, knowledge sharing} }

Document

**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

The consensus hierarchy classifies shared an object according to its consensus number, which is the maximum number of processes that can solve consensus wait-free using the object. The question of whether this hierarchy is precise enough to fully characterize the synchronization power of deterministic shared objects was open until 2016, when Afek et al. showed that there is an infinite hierarchy of deterministic objects, each weaker than the next, which is strictly between i and i+1-processors consensus, for i >= 2. For i=1, the question whether there exist a deterministic object whose power is strictly between read-write and 2-processors consensus, remained open.
We resolve the question positively by exhibiting an infinite hierarchy of simple deterministic objects which are equivalent to set-consensus tasks, and thus are stronger than read-write registers, but they cannot implement consensus for two processes. Still our paper leaves a gap with open questions.

Eli Daian, Giuliano Losa, Yehuda Afek, and Eli Gafni. A Wealth of Sub-Consensus Deterministic Objects. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{daian_et_al:LIPIcs.DISC.2018.17, author = {Daian, Eli and Losa, Giuliano and Afek, Yehuda and Gafni, Eli}, title = {{A Wealth of Sub-Consensus Deterministic Objects}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {17:1--17:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.17}, URN = {urn:nbn:de:0030-drops-98061}, doi = {10.4230/LIPIcs.DISC.2018.17}, annote = {Keywords: shared memory, distributed algorithms, wait-free, set consensus} }

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Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

What can be computed by a network of n randomized finite state machines communicating under the stone age model (a generalization of the beeping model’s communication scheme)? The inherent linear upper bound on the total space of the network implies that its global computational power is not larger than that of a randomized linear space Turing machine, but is this tight? The reported reseach answers this question affirmatively for bounded degree networks by introducing a stone age algorithm (operating under the most restrictive form of the model) that given a designated I/O node, constructs a tour in the network that enables the simulation of the Turing machine’s tape. To construct the tour, it is first shown how to 2-hop color the network concurrently with building a spanning tree with high probability.

Yehuda Afek, Yuval Emek, and Noa Kolikant. Brief Announcement: The Synergy of Finite State Machines. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 42:1-42:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{afek_et_al:LIPIcs.DISC.2017.42, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{Brief Announcement: The Synergy of Finite State Machines}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {42:1--42:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.42}, URN = {urn:nbn:de:0030-drops-80072}, doi = {10.4230/LIPIcs.DISC.2017.42}, annote = {Keywords: beeping communication, finite state machine, stone age model, distributed network complexity} }