Prudent Rationalizability in Generalized Extensive-form Games with Unawareness PDF Download
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Author: Aviad Heifetz
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Languages : en
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We define a cautious version of extensive-form rationalizability for generalized extensive- form games with unawareness that we call prudent rationalizability. It is an extensive-form analogue of iterated admissibility. In each round of the procedure, for each tree and each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. We demonstrate the applicability of prudent rationalizability. In games of disclosure of verifiable information, we show that prudent rationalizability yields unraveling under full awareness but unraveling might fail under unawareness. We compare prudent rationalizability to extensive-form rationalizability. We show that prudent rationalizability may not refine extensive-form rationalizability strategies but conjecture that the paths induced by prudent rationalizable strategy profiles (weakly) refine the set of paths induced by extensive-form rationalizable strategies.
Author: Aviad Heifetz
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ISBN:
Category :
Languages : en
Pages :
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Book Description
We define a cautious version of extensive-form rationalizability for generalized extensive- form games with unawareness that we call prudent rationalizability. It is an extensive-form analogue of iterated admissibility. In each round of the procedure, for each tree and each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. We demonstrate the applicability of prudent rationalizability. In games of disclosure of verifiable information, we show that prudent rationalizability yields unraveling under full awareness but unraveling might fail under unawareness. We compare prudent rationalizability to extensive-form rationalizability. We show that prudent rationalizability may not refine extensive-form rationalizability strategies but conjecture that the paths induced by prudent rationalizable strategy profiles (weakly) refine the set of paths induced by extensive-form rationalizable strategies.
Author: Aviad Heifetz
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We define an extensive-form analogue of iterated admissibility, called Prudent Rationalizability (PR). In each round of the procedure, for each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. Somewhat surprisingly, prudent rationalizable strategies may not refine the set of Extensive-Form Rationalizable (EFR) strategies (Pearce 1984). However, we prove that the paths induced by PR strategy-profiles (weakly) refine the set of paths induced by EFR strategies. PR applies also to generalized extensive-form games which model mutual unawareness of actions (Heifetz, Meier and Schipper, 2011a). We demonstrate the applicability of PR in the analysis of verifiable communication, and show that it yields the same, full information unraveling prediction as does the unique sequential equilibrium singled out by Milgrom and Roberts (1986); yet, we also show that under unawareness full unraveling might fail. -- Prudent rationalizability ; caution ; extensive-form rationalizability ; extensive-form games ; unawareness, verifiable communication
Author: Aviad Heifetz
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence. We define also a new variant of this solution concept, prudent rationalizability, which refines the set of outcomes induced by extensive-form rationalizable strategies. We apply prudent rationalizability to the analysis of verifiable communication with unawareness. Finally, we define the normal form of a generalized extensive-form game, and characterize in it extensive-form rationalizability by iterative conditional dominance.
Author: Martin Meier
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Heifetz, Meier and Schipper (2013) introduced generalized extensive-form games that allow for asymmetric unawareness. Here, we study the normal form of a generalized extensiveform game. The generalized normal-form game associated to a generalized extensive-form game with unawareness may consist of a collection of normal-form games. We use it to characterize extensive-form rationalizability (resp. prudent rationalizability) in generalized extensive-form games by iterative conditional strict (resp. weak) dominance in the associated generalized normal-form. We also show that the analogue to iterated admissibility for generalized normal-form games is not independent of the extensive-form structure. This is because under unawareness, a player's information set not only determines which nodes he considers possible but also of which game tree(s) he is aware of.
Author: Simon P. Anderson
Publisher: Elsevier
ISBN: 0444636951
Category : Business & Economics
Languages : en
Pages : 820
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Book Description
Handbook of Media Economics provides valuable information on a unique field that has its own theories, evidence, and policies. Understanding the media is important for society, and while new technologies are altering the media, they are also affecting our understanding of their economics. Chapters span the large scope of media economics, simultaneously offering in-depth analysis of particular topics, including the economics of why media are important, how media work (including financing sources, institutional settings, and regulation), what determines media content (including media bias), and the effects of new technologies. The volumes provide a powerful introduction for those interested in starting research in media economics. - Helps academic and non-academic economists understand recent rapid changes in theoretical and empirical advances, in structural empirical methods, and in the media industry's connection with the democratic process - Presents the only detailed summary of media economics that emphasizes political economy, merger policy, and competition policy - Pays special attention to the economic influences of the Internet, including developments in social media, user-generated content, and advertising, as well as the Internet's effects on newspapers, radio, and television
Author: Simon P. Anderson
Publisher: Elsevier
ISBN: 0444627243
Category : Business & Economics
Languages : en
Pages : 563
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Book Description
Handbook of Media Economics provides valuable information on a unique field that has its own theories, evidence, and policies. Understanding the media is important for society, and while new technologies are altering the media, they are also affecting our understanding of their economics. The book spans the large scope of media economics, simultaneously offering in-depth analysis of particular topics, including the economics of why media are important, how media work (including financing sources, institutional settings, and regulation), what determines media content (including media bias), and the effects of new technologies. The book provides a powerful introduction for those interested in starting research in media economics. - Helps academic and non-academic economists understand recent rapid changes in theoretical and empirical advances, in structural empirical methods, and in the media industry's connection with the democratic process - Presents the only detailed summary of media economics that emphasizes political economy, merger policy, and competition policy - Pays special attention to the economic influences of the Internet, including developments in social media, user-generated content, and advertising, as well as the Internet's effects on newspapers, radio, and television
Author: Burkhard C. Schipper
Publisher:
ISBN:
Category :
Languages : en
Pages : 52
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Book Description
Equilibrium notions for games with unawareness in the literature cannot be interpreted as steady-states of a learning process because players may discover novel actions during play. In this sense, many games with unawareness are "self-destroying" as a player's representation of the game may change after playing it once. We define discovery processes where at each state there is an extensive-form game with unawareness that together with the players' play determines the transition to possibly another extensive-form game with unawareness in which players are now aware of actions that they have discovered. A discovery process is rationalizable if players play extensive-form rationalizable strategies in each game with unawareness. We show that for any game with unawareness there is a rationalizable discovery process that leads to a self-confirming game that possesses a self-confirming equilibrium in extensive-form rationalizable strategies. This notion of equilibrium can be interpreted as steady-state of both a discovery and learning process.
Author: Andrés Perea
Publisher: Springer Science & Business Media
ISBN: 9780792375401
Category : Business & Economics
Languages : en
Pages : 256
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Book Description
This book is concerned with situations in which several persons reach decisions independently and the final consequence depends, potentially, upon each of the decisions taken. Such situations may be described formally by an extensive form game: a mathematical object which specifies the order in which decisions are to be taken, the information available to the decision makers at each point in time, and the consequence that results for each possible combination of decisions. A necessary requirement for rational behavior in such games is that each decision maker should reach a decision that is optimal, given his preferences over his own decisions. This requirement is far from sufficient, however, since every decision maker should in addition base his preferences upon the conjecture that his opponents will act optimally as well. It is this principle that distinguishes noncooperative game theory from one-person decision theory. The main purpose of Rationality in Extensive Form Games is to discuss different formalizations of this principle in extensive form games, such as backward induction, Nash equilibrium, forward induction and rationalizability, under the assumption that the decision makers' preferences are given by subjective expected utility functions. The various formalizations, or rationality criteria, are illustrated by examples, and the relationships among the different criteria are explored.
Author: Yossi Feinberg
Publisher:
ISBN:
Category : Fantasy gamers
Languages : en
Pages : 51
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Book Description
We provide a tool to model and solve strategic situations where players' perceptions are limited, in the sense that they may only be aware of, or model, some of the aspects of the strategic situations at hand, as well as situations where players realize that other players' perceptions may be limited. We define normal, repeated, incomplete information, and dynamic (extensive) form games with unawareness using a unified methodology. A game with unawareness is defined as a collection of standard games (of the corresponding form). The collection specifies how each player views the game, how she views the other players' perceptions of the game and so on. The modeler's description of perceptions, the players' description of other players' reasoning, etc. are shown to have consistent representations. We extend solution concepts such as rationalizability and Nash equilibrium to these games and study their properties. It is shown that while unawareness in normal form games can be mapped to incomplete information games, the extended Nash equilibrium solution is not mapped to a known solution concept in the equivalent incomplete information games, implying that games with unawareness generate novel types of behavior.
Author: Pierpaolo Battigalli
Publisher:
ISBN:
Category : Economics, Mathematical
Languages : en
Pages : 80
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