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Selection Equilibria of Higher-Order Games [chapter]

Jules Hedges, Paulo Oliva, Evguenia Shprits, Viktor Winschel, Philipp Zahn
2016 Lecture Notes in Computer Science  
In this paper we introduce a new solution concept for such higher-order games, which we call selection equilibrium. The original notion proposed in [4] is now called quantifier equilibrium.  ...  In previous work [2,4] a novel way of modelling games was introduced where players and their goals are more naturally described by a special class of higher-order functions called quantifiers.  ...  The selection equilibria of the higher-order representation of this game are exactly the coordinated strategies.  ... 
doi:10.1007/978-3-319-51676-9_9 fatcat:kxxoucibore3jp4roomgcvubxu

Higher-Order Game Theory [article]

Jules Hedges, Paulo Oliva, Evguenia Sprits, Viktor Winschel, Philipp Zahn
2015 arXiv   pre-print
In this paper we introduce a representation of games where players' goals are modeled based on so-called higher-order functions.  ...  We show that in higher-order functions formal descriptions of players may still exist where utility functions do not using a classical example, a variant of Keynes' beauty contest.  ...  Definition 3.1 (Higher-Order Games ).  ... 
arXiv:1506.01002v2 fatcat:jwi3w264hvaylm5vrqwme7mpmq

Notes on "refinements and higher order beliefs"

Atsushi Kajii, Stephen Morris
2019 Japanese Economic Review  
Acknowledgements Kajii acknowledges financial support from the Grant-in-aid for scientific research (S)18H05217 and (A)16H0202 as well as Nomura Foundation Research Grant for the Frontier of Research into  ...  The abstract of our 1997 survey paper on "Refinements and Higher Order Beliefs" reads: This paper presents a simple framework that allows us to survey and relate some different strands of the game theory  ...  It followed Fudenberg and Tirole (1991) , chapter 14, in providing a unified treatment of refinements and a literature on higher-order beliefs rather than proposing a particular solution concept.  ... 
doi:10.1007/s42973-019-00007-w fatcat:dio3kyf6o5hdtlbtrvknwqrmte

Evolutionary Dynamics of the Transitions across the Nash equilibria of a Tacit Coordination Game

Jasmina Arifovic
2001 European Journal of Economic and Social Systems  
Monomorphic equilibria of the game are neutrally stable.  ...  We investigate evolutionary adaptation in a repeated coordination game with strategic uncertainty. The game is characterized by multiplicity of stationary and cyclical Nash equilibria.  ...  I gratefully acknowledge financial support from the Social Sciences and Humanities Research Council of Canada.  ... 
doi:10.1051/ejess:2001100 fatcat:jxiukxxkhbcynoeku2wkt32nsi

A Relevant Equilibrium in Open Spectrum Sharing: Lorenz Equilibrium in Discrete Games [chapter]

Ligia C. Cremene, Dumitru Dumitrescu
2014 Lecture Notes in Computer Science  
LE induces a selection criterion of NE, when several are present in a game (e.g. many-player discrete games) and when fairness is an issue.  ...  The Lorenz equilibrium is a subset of Pareto efficient solutions that are equitable for all players and ensures a higher payoff than the Nash equilibrium.  ...  Where multiple equilibria exist (in discrete games, for instance), the need for equilibrium selection arises.  ... 
doi:10.1007/978-3-319-10353-2_31 fatcat:3s4gthgsajhc7j43gf753gcwnq

A Higher-order Framework for Decision Problems and Games [article]

Jules Hedges, Paulo Oliva, Evguenia Winschel, Viktor Winschel, Philipp Zahn
2014 arXiv   pre-print
We introduce a suitable generalisation of Nash equilibrium for games in terms of quantifiers and selection functions.  ...  We introduce a new unified framework for modelling both decision problems and finite games based on quantifiers and selection functions.  ...  In our version of the Battle of the Sexes game the set of generalised Nash equilibria and the set selection equilibria are in fact identical.  ... 
arXiv:1409.7411v1 fatcat:yxjcxmymbzh2vpbouwavnjfzyy

Beyond Nash Equilibrium in Open Spectrum Sharing: Lorenz Equilibrium in Discrete Games [article]

Ligia Cremene, D. Dumitrescu
2013 arXiv   pre-print
LE induces a selection criterion of NE, when several are present in a game (e.g. many-player discrete games) and when fairness is an issue.  ...  The Lorenz equilibrium is a subset of Pareto efficient solutions that are equitable for all players and ensures a higher payoff than the Nash equilibrium.  ...  Where multiple equilibria exist (in discrete games, for instance), the need for equilibrium selection arises.  ... 
arXiv:1304.1658v1 fatcat:4miyysy3vnckpkyrsohohtvieq

Evolutionary games in the multiverse

C. S. Gokhale, A. Traulsen
2010 Proceedings of the National Academy of Sciences of the United States of America  
For any number of players d with any number of strategies n, there can be at most (d-1)^(n-1) isolated internal equilibria.  ...  Some of these games may in fact take place between a number of individuals and not just between two. Here, we address one-shot games with multiple players.  ...  C.S.G. and A.T. acknowledge support by the Emmy-Noether program of the Deutsche Forschungsgemeinschaft and the DAAD (Project 0813008).  ... 
doi:10.1073/pnas.0912214107 pmid:20212124 pmcid:PMC2851774 fatcat:gdjqlsmrfvefdb2bazqz6mke4u

Cooperation against all predictions

Friedel Bolle, Jörg Spiller
2021 Economic Inquiry  
In four rather diverse examples of four-player Stag Hunt games, three prominent concepts of equilibrium selection favor E0.  ...  Also for k < n, the selected equilibria clearly differ from experimental behavior. We interpret our observations by suggesting the concept Behavioral Equilibrium Selection.  ...  Therefore, except for the Global Games selection for the asymmetric games, we need considerable amounts of altruism in order to prevent equilibrium E0 to be selected.  ... 
doi:10.1111/ecin.12976 fatcat:7lb6bbpupbegxl3tyi5qmxnuby

Equilibrium Finding in Normal-Form Games via Greedy Regret Minimization

Hugh Zhang, Adam Lerer, Noam Brown
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
by several orders of magnitude.  ...  We extend the classic regret minimization framework for approximating equilibria in normal-form games by greedily weighing iterates based on regrets observed at runtime.  ...  We also find that greedy weights tends to learn equilibria with higher social welfare than vanilla regret minimization methods in general-sum games.  ... 
doi:10.1609/aaai.v36i9.21181 fatcat:wndttj5l2jcjzdsrrkdad2qz5i

Competition for Order Flow as a Coordination Game

Frank Heinemann, Jutta Donges
2001 Social Science Research Network  
Competition for order flow can be characterized as a coordination game with multiple equilibria.  ...  By introducing private information, we prove existence of a unique equilibrium with market consolidation.  ...  However, Morris and Shin (2000) have shown that for a quite general class of symmetric coordination games with binary choices equilibria approach a single strategy profile that does not depend on higher  ... 
doi:10.2139/ssrn.276198 fatcat:o7wyvufknfeqfptmaiywq3beaa

On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

Sunanda Roy, Tarun Sabarwal
2007 Economic Theory  
(In particular, in n-player games of strategic substitutes with real-valued action spaces, symmetric equilibria increase with the parameter.)  ...  Indeed, for a given parameter value, a pair of distinct equilibria are never comparable.  ...  Indeed, for this class of games, symmetric equilibria are unique (as shown in the previous sub-section), and therefore (the unique) selection of symmetric equilibria is (weakly) increasing in t.  ... 
doi:10.1007/s00199-007-0285-9 fatcat:tpbhweutbbasvfpwmrv4cgm54q

RAT selection games in HetNets

Ehsan Aryafar, Alireza Keshavarz-Haddad, Michael Wang, Mung Chiang
2013 2013 Proceedings IEEE INFOCOM  
equilibria of these games.  ...  Our results reveal that: (i) Singleclass RAT selection games converge to Nash equilibria, while an improvement path can be repeated infinitely with a mixture of classes.  ...  Thus, only a very small number of states form the equilibria in these games.  ... 
doi:10.1109/infcom.2013.6566889 dblp:conf/infocom/AryafarKWC13 fatcat:jowdb7ttq5cw5ci2lqwkjfe35q

Coordination in the Presence of Asset Markets

Shimon Kogan, Anthony M. Kwasnica, Roberto A. Weber
2008 Social Science Research Network  
Markets lead to significantly lower efficiency across treatments, even when they produce no distortion of incentives in the game. Market prices forecast game outcomes.  ...  Across two experiments, we vary the payoffs from the market relative to the game, the degree of interdependence in the game, and whether traders' asset payoffs are dependent on outcomes in their own or  ...  equilibria involving input choices greater than 1 can be ruled out, but that for higher order statistics (1<j<n) the set of equilibria are unchanged.  ... 
doi:10.2139/ssrn.1108039 fatcat:yn4jayalzzbi5h2ojoc4aql6t4

Coordination in the Presence of Asset Markets

Shimon Kogan, Anthony M. Kwasnica, Roberto A. Weber
2008 Social Science Research Network  
Markets lead to significantly lower efficiency across treatments, even when they produce no distortion of incentives in the game. Market prices forecast game outcomes.  ...  Across two experiments, we vary the payoffs from the market relative to the game, the degree of interdependence in the game, and whether traders' asset payoffs are dependent on outcomes in their own or  ...  equilibria involving input choices greater than 1 can be ruled out, but that for higher order statistics (1<j<n) the set of equilibria are unchanged.  ... 
doi:10.2139/ssrn.1102309 fatcat:bfb324inkvchtmn2sc6m4yfvvi
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