scholarly journals Computing an Extensive-Form Correlated Equilibrium in Polynomial Time

2008 ◽  
pp. 506-513 ◽  
Author(s):  
Wan Huang ◽  
Bernhard von Stengel
Keyword(s):  
Polynomial Time ◽  
Correlated Equilibrium ◽  
Extensive Form

scholarly journals Quasi-Perfect Stackelberg Equilibrium

2019 ◽  
Vol 33 ◽  
pp. 2117-2124 ◽  
Author(s):  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Christian Kroer ◽  
Nicola Gatti ◽  
Tuomas Sandholm
Keyword(s):  
Broad Class ◽  
Stackelberg Equilibrium ◽  
Correlated Equilibrium ◽  
Equilibrium Concept ◽  
Extensive Form ◽  
Tree Form ◽  
Axiomatic Definition ◽  
Security Games ◽  
Definition Of ◽  
Perfect Equilibria

Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasiperfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings—that is, settings where a leader can commit to a strategy—which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes.

scholarly journals Polynomial-time computation of exact correlated equilibrium in compact games

2015 ◽  
Vol 91 ◽  
pp. 347-359 ◽  
Author(s):  
Albert Xin Jiang ◽  
Kevin Leyton-Brown
Keyword(s):  
Polynomial Time ◽  
Correlated Equilibrium

scholarly journals Extensive-Form Correlated Equilibrium: Definition and Computational Complexity

2008 ◽  
Vol 33 (4) ◽  
pp. 1002-1022 ◽  
Author(s):  
Bernhard von Stengel ◽  
Françoise Forges
Keyword(s):  
Computational Complexity ◽  
Correlated Equilibrium ◽  
Extensive Form

Can quantum entanglement implement classical correlated equilibria?

2014 ◽  
Vol 14 (5&6) ◽  
pp. 493-516
Author(s):  
Alan Deckelbaum
Keyword(s):  
Quantum State ◽  
Complete Information ◽  
Impossibility Result ◽  
Correlated Equilibrium ◽  
Extensive Form ◽  
Initial State ◽  
Equilibrium Distributions ◽  
Pure Quantum State ◽  
Correlated Equilibria ◽  
Classical Game

We ask whether players of a classical game can partition a pure quantum state to implement classical correlated equilibrium distributions. The main contribution of this work is an impossibility result: we provide an example of a classical correlated equilibrium that cannot be securely implemented without useful information leaking outside the system. We study the model where players of a classical complete information game initially share an entangled pure quantum state. Players may perform arbitrary local operations on their subsystems, but no direct communication (either quantum or classical) is allowed. We explain why, for the purpose of implementing classical correlated equilibria, it is desirable to restrict the initial state to be pure and to restrict communication. In this framework, we define the concept of pure quantum correlated equilibrium (PQCE) and show that in a normal form game, any outcome distribution implementable by a PQCE can also be implemented by a classical correlated equilibrium (CE), but that the converse is false. We extend our analysis to extensive form games, and compare the power of PQCE to extensive form classical correlated equilibria (EFCE) and immediate-revelation extensive form correlated equilibria (IR-EFCE).

Game Theory

2016 ◽  
Author(s):  
Cristina Bicchieri ◽  
Giacomo Sillari
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Evolutionary Game Theory ◽  
Repeated Games ◽  
Evolutionary Game ◽  
Complete Information ◽  
Decision Makers ◽  
Correlated Equilibrium ◽  
Extensive Form

Game theory aims to understand situations in which decision-makers interact strategically. Chess is an example, as are firms competing for business, politicians competing for votes, animals fighting over prey, bidders competing in auctions, threats and punishments in long-term relationships, and so on. In such situations, the outcome depends on what the parties do jointly. Decision-makers may be people, organizations, animals, or even genes. In this chapter, the authors review fundamental notions of game theory and their application to philosophy of science. In particular, Section 1 looks at games of complete information through normal and extensive form representations, introduce the notion of Nash equilibrium and its refinements. Section 2 touches on epistemic foundations and correlated equilibrium, and Section 3 examines repeated games and their importance for the analysis of altruism and cooperation. Section 4 deals with evolutionary game theory.

scholarly journals Coarse Correlation in Extensive-Form Games

2020 ◽  
Vol 34 (02) ◽  
pp. 1934-1941
Author(s):  
Gabriele Farina ◽  
Tommaso Bianchi ◽  
Tuomas Sandholm
Keyword(s):  
Normal Form ◽  
Saddle Points ◽  
Solution Concept ◽  
Correlated Equilibrium ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Rational Agents ◽  
Correlation Models ◽  
Correlated Equilibria ◽  
Special Case

Coarse correlation models strategic interactions of rational agents complemented by a correlation device which is a mediator that can recommend behavior but not enforce it. Despite being a classical concept in the theory of normal-form games since 1978, not much is known about the merits of coarse correlation in extensive-form settings. In this paper, we consider two instantiations of the idea of coarse correlation in extensive-form games: normal-form coarse-correlated equilibrium (NFCCE), already defined in the literature, and extensive-form coarse-correlated equilibrium (EFCCE), a new solution concept that we introduce. We show that EFCCEs are a subset of NFCCEs and a superset of the related extensive-form correlated equilibria. We also show that, in n-player extensive-form games, social-welfare-maximizing EFCCEs and NFCCEs are bilinear saddle points, and give new efficient algorithms for the special case of two-player games with no chance moves. Experimentally, our proposed algorithm for NFCCE is two to four orders of magnitude faster than the prior state of the art.

scholarly journals Decentralized No-regret Learning Algorithms for Extensive-form Correlated Equilibria (Extended Abstract)

2021 ◽  
Author(s):  
Andrea Celli ◽  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Nicola Gatti
Keyword(s):  
Normal Form ◽  
Private Information ◽  
Imperfect Information ◽  
Research Question ◽  
Correlated Equilibrium ◽  
Extensive Form ◽  
Learning Dynamics ◽  
Extensive Form Games ◽  
Normal Form Games ◽  
Correlated Equilibria

The existence of uncoupled no-regret learning dynamics converging to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normal-form game, the empirical frequency of play converges to a normal-form correlated equilibrium. Extensive-form games generalize normal-form games by modeling both sequential and simultaneous moves, as well as imperfect information. Because of the sequential nature and the presence of private information, correlation in extensive-form games possesses significantly different properties than in normal-form games. The extensive-form correlated equilibrium (EFCE) is the natural extensive-form counterpart to the classical notion of correlated equilibrium in normal-form games. Compared to the latter, the constraints that define the set of EFCEs are significantly more complex, as the correlation device ({\em a.k.a.} mediator) must take into account the evolution of beliefs of each player as they make observations throughout the game. Due to this additional complexity, the existence of uncoupled learning dynamics leading to an EFCE has remained a challenging open research question for a long time. In this article, we settle that question by giving the first uncoupled no-regret dynamics which provably converge to the set of EFCEs in n-player general-sum extensive-form games with perfect recall. We show that each iterate can be computed in time polynomial in the size of the game tree, and that, when all players play repeatedly according to our learning dynamics, the empirical frequency of play after T game repetitions is guaranteed to be a O(T^-1/2)-approximate EFCE with high probability, and an EFCE almost surely in the limit.

Are Individuals in Rorschach Nonpatient Samples Truly Psychologically Healthy?

2015 ◽  
Vol 36 (2) ◽  
pp. 112-155 ◽  
Author(s):  
Anna Maria Rosso ◽  
Andrea Camoirano ◽  
Gabriele Schiaffino
Keyword(s):  
Psychological Treatment ◽  
Coping Styles ◽  
Anxiety And Depression ◽  
Future Research ◽  
Extensive Form ◽  
Community Needs ◽  
Rorschach Comprehensive System ◽  
Form Quality ◽  
And Coping ◽  
Rorschach Variables

Abstract. The aim of this study was to collect a Rorschach Comprehensive System (RCS) adult nonpatient sample from Italy using more stringent exclusion criteria and controlling for psychopathology, taking into account the methodological suggestions of Ritzler and Sciara (2008) . The authors hypothesized that: (a) adult nonpatient samples are not truly psychologically healthy, in that a high number of psychopathological symptoms are experienced by participants, particularly anxiety and depression, although they have never been in psychological treatment; (b) significant differences emerge between healthy and nonhealthy groups on Rorschach variables, particularly on CS psychopathological indexes; (c) RCS psychopathological indexes are significantly correlated in the expected direction with scores on psychopathological scales. The results confirmed the hypotheses, indicating the need to collect psychologically healthy samples in addition to normative and nonpatient samples. Because differences were found in the comparison between Exner’s sample (2007) and the healthy group in this study regarding form quality and coping styles, the authors suggest that future research should investigate the construct validity of ambitent style and culturally specific influences on form quality. Moreover, the Rorschach scientific community needs to have more extensive form quality tables, enriched with objects that are currently not included.

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