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An Algebraic Approach for Computing Equilibria of a Subclass of Finite Normal Form Games [article]

Samaresh Chatterji, Ratnik Gandhi
<span title="2010-05-30">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We define "rational payoff irrational equilibria games" to be the games with all rational payoffs and all irrational equilibria.  ...  In this paper, we consider the problem of computing Nash equilibria of a subclass of generic finite normal form games.  ...  A finite normal form game with its all payoff values rational numbers its all Nash equilibria irrational numbers is called an rational payoff irrational equilibria(RPIE) game.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.5507v1">arXiv:1005.5507v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dvujcjdn2ngszjmxqosp77xbmy">fatcat:dvujcjdn2ngszjmxqosp77xbmy</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1005.5507/1005.5507.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/49/82/4982147befcd429803e20e6e5756f5a9757ce292.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.5507v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Some Algebraic Properties of a Subclass of Finite Normal Form Games [article]

Samaresh Chatterji, Ratnik Gandhi
<span title="2010-01-27">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the problem of computing all Nash equilibria of a subclass of finite normal form games.  ...  With algebraic characterization of the games, we present a method for computing all its Nash equilibria.  ...  Our convention is to write totally mixed real-irrational Nash equilibria as irrational Nash equilibria.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1001.4887v1">arXiv:1001.4887v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lbp3i2jy3jarbafpnwebpk4sda">fatcat:lbp3i2jy3jarbafpnwebpk4sda</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1001.4887/1001.4887.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a7/36/a7365f9a19dacc094f761cae2559bf42d7a5f426.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1001.4887v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Special Issue on Algorithmic Game Theory

Giuseppe Persiano
<span title="2013-12-29">2013</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qj6jzeossfhihfshwf7nb7lbcq" style="color: black;">Theory of Computing Systems</a> </i> &nbsp;
The paper Complexity of Ration and Irrational Nash Equilibria shows that is hard to decide whether a game has a rational equilibrium. I would like to thank the authors that contributed to this issue.  ...  and studies their equilibria and dynamics. The main result is a proof of existence of equilibrium for agents that do not overbid.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-013-9525-5">doi:10.1007/s00224-013-9525-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/73bvlzb6yvg47on4uuaxd2cc2e">fatcat:73bvlzb6yvg47on4uuaxd2cc2e</a> </span>
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The Complexity of Decision Problems about Nash Equilibria in Win-Lose Games [chapter]

Vittorio Bilò, Marios Mavronicolas
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
[2], (ix) A Nash equilibrium in which the total utility of players is at most a given number?, (x) A rational Nash equilibrium (i.e., one with all probabilities rational)? [1] .  ...  In this work, we settle the complexity of the natural decision problems about Nash equilibria previously considered in [2,3] (or introduced here) for win-lose games, i.e., games in which all utilities  ...  Choosing the gadget game as a three-player win-lose game with a single irrational Nash equilibrium implies that deciding the existence of a rational Nash equilibrium is N P-hard for three-player win-lose  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-33996-7_4">doi:10.1007/978-3-642-33996-7_4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nyx7bqqzr5gwxanubs2qvp3u34">fatcat:nyx7bqqzr5gwxanubs2qvp3u34</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810132150/http://annualreport.dmf.unisalento.it/2012/maths/bilo/sagt.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/89/28/89282ed3699b4d3f2bb16fa324bac81f7f330197.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-33996-7_4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the Computational Complexity of Decision Problems about Multi-Player Nash Equilibria [article]

Marie Louisa Tølbøll Berthelsen, Kristoffer Arnsfelt Hansen
<span title="2020-01-15">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that deciding if a game has an irrational valued Nash equilibrium is ∃R-hard, answering a question of Bilò and Mavronicolas, and address also the computational complexity of deciding if a game  ...  We study the computational complexity of decision problems about Nash equilibria in m-player games.  ...  ∃PARETOOPTIMALSNE and ∃STRONGSNE are ∃R-complete, even for 3-player games. We now turn to irrational and rational valued symmetric Nash equilibria.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.05196v1">arXiv:2001.05196v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sx77zgx66fcklhwlfyzdafdmyi">fatcat:sx77zgx66fcklhwlfyzdafdmyi</a> </span>
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Solution Concepts in A-Loss Recall Games: Existence and Computational Complexity [article]

Jiri Cermak and Branislav Bosansky and Michal Pechoucek
<span title="2017-05-24">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
numbers for rational input, and (3) NP-hardness of problems related to finding maxmin strategies and existence of a NE strategy.  ...  We derive novel properties of A-loss recall games, including (1) a sufficient and necessary condition for the existence of NE in A-loss recall games, (2) example where both NE and maxmin require irrational  ...  This research was supported by the Czech Science Foundation (grant no. 15-23235S) and by the Grant Agency of the Czech Technical University in Prague, grant No. SGS16/235/OHK3/3T/13.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1608.01500v3">arXiv:1608.01500v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cvlabrc27bfo3eyav2juj6bdta">fatcat:cvlabrc27bfo3eyav2juj6bdta</a> </span>
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Equilibria, fixed points, and complexity classes

Mihalis Yannakakis
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x3ibtg2oifh47c73tgo66gjrw4" style="color: black;">Computer Science Review</a> </i> &nbsp;
Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing  ...  There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP.  ...  Irrational equilibria, nonlinear functions, and the class FIXP Games with three or more players are quite different than two-player games in several respects: Nash equilibria are generally irrational;  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cosrev.2009.03.004">doi:10.1016/j.cosrev.2009.03.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lhr6iqyodfgond7vjrochf44la">fatcat:lhr6iqyodfgond7vjrochf44la</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809103344/http://economics.yale.edu/sites/default/files/files/Workshops-Seminars/MicroTheory/yannakakis-111129.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d8/c7/d8c7aecf6cac6f3b068956d57a901a80e2974d91.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cosrev.2009.03.004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Equilibria, Fixed Points, and Complexity Classes [article]

Mihalis Yannakakis
<span title="2008-02-20">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing  ...  There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP.  ...  Irrational Equilibria, Nonlinear Functions, and the Class FIXP Games with 3 or more players are quite different from 2-player games: Nash equilibria are generally irrational; knowing the support of an  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0802.2831v1">arXiv:0802.2831v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nxsafbsw5jbo7khx47qwdmzotu">fatcat:nxsafbsw5jbo7khx47qwdmzotu</a> </span>
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Does Nash Envy Immunity [article]

Ching-Hua Yu
<span title="2017-03-09">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The most popular stability notion in games should be Nash equilibrium under the rationality of players who maximize their own payoff individually.  ...  Together with Nash equilibrium and another stability notion called immunity, we show how these separate notions are related to each other, whether they exist in games, and whether and when a strategy profile  ...  Acknowledgement The author would like to thank Ruta Metha for valuable comments and discussion.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1703.03262v1">arXiv:1703.03262v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ynyeszfi6fcnbmhntspkjgqgyu">fatcat:ynyeszfi6fcnbmhntspkjgqgyu</a> </span>
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Rationality and Bounded Rationality

Robert J. Aumann
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gjdubbzq4zd3bgbmuwnb2p7neq" style="color: black;">Games and Economic Behavior</a> </i> &nbsp;
a Nash equilibrium; insects and even flowers can and do arrive at Nash equilibria, perhaps more reliably than human beings.  ...  an expression of bounded rationality, -equilibria, and related topics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/game.1997.0585">doi:10.1006/game.1997.0585</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sjuwsrdgujhljdwscw2t4mtnye">fatcat:sjuwsrdgujhljdwscw2t4mtnye</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809231601/http://www.eecs.harvard.edu/~parkes/cs286r/spring06/papers/aumann_rat97.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ca/f5/caf57b61d496ec83a508bf6400e11492cb533e31.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/game.1997.0585"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Rationality and Bounded Rationality [chapter]

Robert J. Aumann
<span title="">1997</span> <i title="Springer Berlin Heidelberg"> Cooperation: Game-Theoretic Approaches </i> &nbsp;
a Nash equilibrium; insects and even flowers can and do arrive at Nash equilibria, perhaps more reliably than human beings.  ...  an expression of bounded rationality, -equilibria, and related topics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-60454-6_15">doi:10.1007/978-3-642-60454-6_15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bbxswf3qmvdqxodq3td6dc47ye">fatcat:bbxswf3qmvdqxodq3td6dc47ye</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809231601/http://www.eecs.harvard.edu/~parkes/cs286r/spring06/papers/aumann_rat97.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ca/f5/caf57b61d496ec83a508bf6400e11492cb533e31.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-60454-6_15"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Emergence of scale-free characteristics in socio-ecological systems with bounded rationality

Dharshana Kasthurirathna, Mahendra Piraveenan
<span title="2015-06-11">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tnqhc2x2aneavcd3gx5h7mswhm" style="color: black;">Scientific Reports</a> </i> &nbsp;
We argue that system rationality could be measured by the average Kullback--Leibler divergence between Nash and Quantal Response Equilibria, and that the convergence towards Nash equilibria on average  ...  Since the calculation of Nash equilibrium assumes perfect rationality of all players, we use  ...  Acknowledgements We express our thanks to Mike Harre, Mikhail Prokopenko and Sanjay Chawla for many fruitful discussions, and Yamuna Subramaniam for aiding with some programming tasks.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1038/srep10448">doi:10.1038/srep10448</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26065713">pmid:26065713</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4464151/">pmcid:PMC4464151</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aormvovtljchtl6kwz4lanb7bm">fatcat:aormvovtljchtl6kwz4lanb7bm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190224083411/http://pdfs.semanticscholar.org/558a/6fcca3eabf7300b4368973fd4ee7bf86cd2a.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/55/8a/558a6fcca3eabf7300b4368973fd4ee7bf86cd2a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1038/srep10448"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4464151" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Cryptographic Implications for Artificially Mediated Games [article]

Thomas Kellam Meyer
<span title="2009-12-30">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Chiefly, there exist a branch of non-cooperative games which have a correlated equilibrium as their solution. These equilibria tend to be superior to the conventional Nash equilibria.  ...  Yet, if these equilibria are in the best interest of players, it would be rational to construct a machine, or protocol, to calculate them.  ...  The set of Nash equilibria, , Ξ also defines a convex polytope. However, this set is of a much more complex and restricted nature, since it consists entirely of n-tuples which are fixed points.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1001.0054v1">arXiv:1001.0054v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kzmm6pgnljdbnkmsbxvi7ixuai">fatcat:kzmm6pgnljdbnkmsbxvi7ixuai</a> </span>
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Distributed computing meets game theory

Ittai Abraham, Lorenzo Alvisi, Joseph Y. Halpern
<span title="2011-06-10">2011</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vl3iv5wfbneltjzmeof4n5xqca" style="color: black;">ACM SIGACT News</a> </i> &nbsp;
Perhaps the best-known and most widely-used solution concept is Nash equilibrium (NE).  ...  There are various solution concepts in game theory-predictions regarding the outcome of a game with rational players.  ...  Acknowledgments: The work of Alvisi was supported in part by NSF grants CSR-0905625 and CNS-0509338.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1998037.1998055">doi:10.1145/1998037.1998055</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fgyitkqwezbgzamipb6djwihyy">fatcat:fgyitkqwezbgzamipb6djwihyy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180329083259/http://www.cs.utexas.edu:80/~lorenzo/papers/Abraham11Distributed.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/30/ce/30ce1ee5c7ee93773922de25b260274ae9595170.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1998037.1998055"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Distributed computing column 42

Idit Keidar
<span title="2011-06-10">2011</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vl3iv5wfbneltjzmeof4n5xqca" style="color: black;">ACM SIGACT News</a> </i> &nbsp;
It features a review of recent work that provides both flavors of robustness by Ittai Abraham, Lorenzo Alvisi, and Joe Halpern.  ...  Game theory and fault tolerance offer two different flavors of robustness to distributed systems -the former is robust against participants attempting to maximize their own utilities, whereas the latter  ...  Acknowledgments: The work of Alvisi was supported in part by NSF grants CSR-0905625 and CNS-0509338.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1998037.1998054">doi:10.1145/1998037.1998054</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sopmxjzo5rcjdadi6z74nyzaq4">fatcat:sopmxjzo5rcjdadi6z74nyzaq4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20161220005733/http://webee.technion.ac.il/~idish/sigactNews/DC-col42-Jun11.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/00/a0/00a012d30f5165c31f13fd2aa853968e0dddcd8c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1998037.1998054"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>
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