A Bayesian Theory of Games. Iterative Conjectures and Determination of Equilibrium
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SummaryThis book introduces a new game theoretic equilibrium concept: Bayesian equilibrium by iterative conjectures (BEIC). The new equilibrium concept achieves consistencies in results among different types of games that current games theory at times fails to. BEIC requires players to make predictions on the strategies of other players starting from first order uninformative predictive distribution functions (or conjectures) and keep updating with Bayesian statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. In a BEIC, conjectures are consistent with the equilibrium or equilibriums they supported and so rationality is achieved for actions, strategies and beliefs and (statistical) decision rule. Given its ability to typically select only a unique equilibrium in games, the BEIC approach is capable of analyzing a larger set of games than current games theory, including games with noisy inaccurate observations and games with multiple sided incomplete information games.Key Features• Provides a unified and consistent analysis of many categories of games. • Its solution algorithm is iterative and has good computation properties.• Can analyze more types of games than current existing games theory.• The equilibrium concept and solution algorithm are based on Bayesian statistical decision theory. • In the new equilibrium, rationality is achieved for action, strategy, belief (both prior and posterior) and decision rule. • Beliefs are the results of optimization exercises of players.• Uses first order uninformative conjectures and reaction functions to derive higher and higher orders of conjectures until a convergence of conjectures is achieved. • Has great application value for it could solve many types of games and could model beliefs.The AuthorJimmy Teng currently teaches at the School of Economics of the University of Nottingham (Malaysia Campus). He is the author of many articles and two books. He received his economics PhD from the University of Toronto. He also earned a PhD in political Science and a MS in statistics from Duke University. He previously held research and teaching positions in Academia Sinica, National Taiwan University and Nanyang Technological UniversityReadershipGames theorists, decision theorists, economists, mathematicians, statisticians, operational researchers, social scientists, management researchers, public policy researchers, computer scientistsContentsSequential games with incomplete information and noisy inaccurate observationAn inflationary game exampleBayesian iterative conjectures algorithm as a Bayes decision ruleSequential games with perfect and imperfect informationBayesian iterative conjectures algorithm, subgame perfect equilibrium and perfect Bayesian equilibriumSolving sequential games of incomplete and perfect informationMultiple sided incomplete information sequential games with perfect informationSimultaneous gamesComplete information simultaneous gamesBEIC and refinements of Nash equilibriumSimultaneous games with incomplete inform
Transcript of A Bayesian Theory of Games. Iterative Conjectures and Determination of Equilibrium
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Chartridge Books Oxford
New Book Information
A Bayesian Theory of Games. Iterative Conjectures and Determination of Equilibrium
Dr Jimmy Teng, University of Nottingham (Malaysia Campus)
Summary
A Bayesian Theory of Games introduces a new game theoretic equilibrium concept: Bayesian equilibrium by iterative conjectures (BEIC). The new equilibrium concept achieves consistencies in results among different types of games that current games theory at times fails to. BEIC requires players to make predictions on the strategies of other players starting from first order uninformative predictive distribution functions (or conjectures) and keep updating with Bayesian statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. In a BEIC, conjectures are consistent with the equilibrium or equilibriums they supported and so rationality is achieved for actions, strategies and beliefs and (statistical) decision rule. Given its ability to typically select only a unique equilibrium in games, the BEIC approach is capable of analyzing a larger set of games than current games theory, including games with noisy inaccurate observations and games with multiple sided incomplete information games.
Key Features
Provides a unified and consistent analysis of many categories of games.
Its solution algorithm is iterative and has good computation properties.
Can analyze more types of games than current existing games theory.
The equilibrium concept and solution algorithm are based on Bayesian statistical decision theory.
In the new equilibrium, rationality is achieved for action, strategy, belief (both prior and posterior) and decision rule.
Beliefs are the results of optimization exercises of players.
Uses first order uninformative conjectures and reaction functions to derive higher and higher orders of conjectures until a convergence of conjectures is achieved.
Has great application value for it could solve many types of games and could model beliefs.
The Author Jimmy Teng currently teaches at the School of Economics of the University of Nottingham (Malaysia Campus). He is the author of many articles and two books. He received his economics PhD from the University of Toronto. He also earned a PhD in political Science and a MS in statistics from Duke University. He previously held research and teaching positions in Academia Sinica, National Taiwan University and Nanyang Technological University
Readership Games theorists, decision theorists, economists, mathematicians, statisticians, operational researchers, social scientists, management researchers, public policy researchers, computer scientists
Contents Sequential games with incomplete information and noisy inaccurate observation An inflationary game example Bayesian iterative conjectures algorithm as a Bayes decision rule Sequential games with perfect and imperfect information Bayesian iterative conjectures algorithm, subgame perfect equilibrium and perfect Bayesian equilibrium Solving sequential games of incomplete and perfect information Multiple sided incomplete information sequential games with perfect information
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Simultaneous games Complete information simultaneous games BEIC and refinements of Nash equilibrium Simultaneous games with incomplete inform Publication: September 2013 Pages: c150 Size: 234 x 156 mm Paperback: ISBN 9781909287761 30.00/$45.00/35.00/$49.00 Australian/$48.00 Canadian Ebook: Digital PDF: ISBN 9781909287778 18.00/$28.00/21.00/Australian $29.00/$28.00 Canadian EPUB: ISBN 9781909287785 18.00/$28.00/21.00/Australian $29.00/$28.00 Canadian MOBI: ISBN 9781909287792 18.00/$28.00/21.00/Australian $29.00/$28.00 Canadian Territorial rights: worldwide Availability status: NYP Readership: university and professional BIC2 code(s): PBUD, PB BISAC code(s): MAT011000, MAT000000
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