Search results for 'backward induction' (try it on Scholar)

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  1.  86
    Alexandru Baltag, Sonja Smets & Jonathan Alexander Zvesper (2009). Keep 'Hoping' for Rationality: A Solution to the Backward Induction Paradox. Synthese 169 (2):301 - 333.
    We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation (...)
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  2.  20
    Wlodek Rabinowicz (1998). Grappling With the Centipede: Defence of Backward Induction for BI-Terminating Games. Economics and Philosophy 14 (1):95.
    According to a standard objection to the use of backward induction in extensive-form games with perfect information, backward induction can only work if the players are confident that each player is resiliently rational - disposed to act rationally at each possible node that the game can reach, even at the nodes that will certainly never be reached in actual play - and also confident that these beliefs in the players’ future resilient rationality are robust, i.e. that (...)
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  3.  20
    Thorsten Clausing (2003). Doxastic Conditions for Backward Induction. Theory and Decision 54 (4):315-336.
    The problem of finding sufficient doxastic conditions for backward induction in games of perfect information is analyzed in a syntactic framework with subjunctive conditionals. This allows to describe the structure of the game by a logical formula and consequently to treat beliefs about this structure in the same way as beliefs about rationality. A backward induction and a non-Nash equilibrium result based on higher level belief in rationality and the structure of the game are derived.
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  4.  20
    Steven J. Brams & D. Marc Kilgour (1998). Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem. [REVIEW] Theory and Decision 45 (3):263-289.
    A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on (1) the evenness/oddness of the number of rounds (the parity problem) and (2) uncertainty about the endpoint of the game (the uncertainty problem). Since there is no (...)
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  5.  24
    Christian W. Bach & Conrad Heilmann (2011). Agent Connectedness and Backward Induction. International Game Theory Review 13 (2):195-208.
    We conceive of a player in dynamic games as a set of agents, which are assigned the distinct tasks of reasoning and node-specific choices. The notion of agent connectedness measuring the sequential stability of a player over time is then modeled in an extended type-based epistemic framework. Moreover, we provide an epistemic foundation for backward induction in terms of agent connectedness. Besides, it is argued that the epistemic independence assumption underlying backward induction is stronger than usually (...)
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  6.  33
    Magnus Jiborn & Wlodek Rabinowicz (2003). Reconsidering the Foole's Rejoinder: Backward Induction in Indefinitely Iterated Prisoner's Dilemmas. Synthese 136 (2):135 - 157.
    According to the so-called “Folk Theorem” for repeated games, stable cooperative relations can be sustained in a Prisoner’s Dilemma if the game is repeated an indefinite number of times. This result depends on the possibility of applying strategies that are based on reciprocity, i.e., strategies that reward cooperation with subsequent cooperation and punish defectionwith subsequent defection. If future interactions are sufficiently important, i.e., if the discount rate is relatively small, each agent may be motivated to cooperate by fear of retaliation (...)
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  7.  27
    John W. Carroll (2000). The Backward Induction Argument. Theory and Decision 48 (1):61-84.
    The backward induction argument purports to show that rational and suitably informed players will defect throughout a finite sequence of prisoner's dilemmas. It is supposed to be a useful argument for predicting how rational players will behave in a variety of interesting decision situations. Here, I lay out a set of assumptions defining a class of finite sequences of prisoner's dilemmas. Given these assumptions, I suggest how it might appear that backward induction succeeds and why it (...)
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  8.  13
    Antonio Quesada (2002). Belief System Foundations of Backward Induction. Theory and Decision 53 (4):393-403.
    Two justifications of backward induction (BI) in generic perfect information games are formulated using Bonanno's (1992; Theory and Decision 33, 153) belief systems. The first justification concerns the BI strategy profile and is based on selecting a set of rational belief systems from which players have to choose their belief functions. The second justification concerns the BI path of play and is based on a sequential deletion of nodes that are inconsistent with the choice of rational belief functions.
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  9.  14
    Joe Mintoff (1999). Decision-Making and the Backward Induction Argument. Pacific Philosophical Quarterly 80 (1):64–77.
    The traditional form of the backward induction argument, which concludes that two initially rational agents would always defect, relies on the assumption that they believe they will be rational in later rounds. Philip Pettit and Robert Sugden have argued, however, that this assumption is unjustified. The purpose of this paper is to reconstruct the argument without using this assumption. The formulation offered concludes that two initially rational agents would decide to always defect, and relies only on the weaker (...)
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  10.  29
    Ken Binmore (1997). Rationality and Backward Induction. Journal of Economic Methodology 4 (1):23-41.
    This paper uses the Centipede Game to criticize formal arguments that have recently been offered for and against backward induction as a rationality principle. It is argued that the crucial issues concerning the interpretation of counterfactuals depend on contextual questions that are abstracted away in current formalisms. I have a text, it always is the same, And always has been, Since I learnt the game. Chaucer, The Pardoner's Tale.
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  11.  20
    Jordan Howard Sobel (1993). Backward-Induction Arguments: A Paradox Regained. Philosophy of Science 60 (1):114-133.
    According to a familiar argument, iterated prisoner's dilemmas of known finite lengths resolve for ideally rational and well-informed players: They would defect in the last round, anticipate this in the next to last round and so defect in it, and so on. But would they anticipate defections even if they had been cooperating? Not necessarily, say recent critics. These critics "lose" the backward-induction paradox by imposing indicative interpretations on rationality and information conditions. To regain it I propose subjunctive (...)
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  12.  24
    Giacomo Bonanno (2001). Branching Time, Perfect Information Games and Backward Induction. Games and Economic Behavior 36 (1):57-73.
    The logical foundations of game-theoretic solution concepts have so far been explored within the con¯nes of epistemic logic. In this paper we turn to a di®erent branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. The branching time framework is extended by adding agents and by de¯ning the notion of prediction. A syntactic characterization of backward induction in terms of the property of internal consistency (...)
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  13.  13
    Cristina Bicchieri (1988). Backward Induction Without Common Knowledge. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:329 - 343.
    A large class of games is that of non-cooperative, extensive form games of perfect information. When the length of these games is finite, the method used to reach a solution is that of a backward induction. Working from the terminal nodes, dominated strategies are successively deleted and what remains is a unique equilibrium. Game theorists have generally assumed that the informational requirement needed to solve these games is that the players have common knowledge of rationality. This assumption, however, (...)
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  14.  33
    Ken Binmore (2011). Interpreting Knowledge in the Backward Induction Problem. Episteme 8 (3):248-261.
    Robert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.
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  15.  4
    Wlodek Rabinowicz, Backward Induction in Games: An Attempt at Logical Reconstruction.
    Backward induction has been the standard method of solving finite extensive-form games with perfect information, notwithstanding the fact that this procedure leads to counter-intuitive results in various games. However, beginning in the late eighties, the method of backward induction became an object of criticism. It is claimed that the assumptions needed for its defence are quite implausible, if not incoherent. It is therefore natural to ask for the justification of backward induction: Can one show (...)
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  16.  22
    Michael Bacharach (1992). Backward Induction and Beliefs About Oneself. Synthese 91 (3):247-284.
    According to decision theory, the rational initial action in a sequential decision-problem may be found by backward induction or folding back. But the reasoning which underwrites this claim appeals to the agent's beliefs about what she will later believe, about what she will later believe she will still later believe, and so forth. There are limits to the depth of people's beliefs. Do these limits pose a threat to the standard theory of rational sequential choice? It is argued, (...)
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  17.  3
    Pierre Livet (1998). Jeux évolutionnaires et paradoxe de l'induction rétrograde (backward induction). Philosophiques 25 (2):181-201.
    La théorie des jeux évolutionnaires s'oppose à la théorie des jeux classique en ce qu 'elle élimine les raisonnements des joueurs. Peut-elle dépasser les apories de la théorie classique ? Mais en reconsidérant le raisonnement classique d'induction rétrograde, en y introduisant des possibilités de révision, on évite son aspect paradoxal. L'intérêt de la théorie des jeux évolutionnaires est donc surtout de simuler l'évolution d'interactions dans des populations.Evolutionary game theory does not take into account reasoning players, in contrast with classical (...)
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  18.  9
    Christian W. Bach & Conrad Heilmann, Agent Connectedness and Backward Induction.
    We analyze the sequential structure of dynamic games with perfect information. A three-stage account is proposed, that species setup, reasoning and play stages. Accordingly, we define a player as a set of agents corresponding to these three stages. The notion of agent connectedness is introduced into a type-based epistemic model. Agent connectedness measures the extent to which agents' choices are sequentially stable. Thus describing dynamic games allows to more fully understand strategic interaction over time. In particular, we provide suffcient conditions (...)
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  19. John Kemp & Bruce Philp (1996). Epitaph for a Legless Centipede? A Paradox of Backward Induction. Manchester Metropolitan University.
     
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  20.  44
    Robert Stalnaker (1998). Belief Revision in Games: Forward and Backward Induction. Mathematical Social Sciences 36 (1):31 - 56.
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  21.  47
    Philip Pettit & Robert Sugden (1989). The Backward Induction Paradox. Journal of Philosophy 86 (4):169-182.
  22.  5
    L. Bovens (1997). The Backward Induction Argument for the Finite Iterated Prisoner's Dilemma and the Surprise Exam Paradox. Analysis 57 (3):179-186.
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  23. Luc Bovens (1997). The Backward Induction Argument for the Finite Iterated Prisoner’s Dilemma and the Surprise Exam Paradox. Analysis 57 (3):179–186.
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  24.  12
    Harald Wiese (2012). Backward Induction in Indian Animal Tales. International Journal of Hindu Studies 16 (1):93-103.
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  25.  12
    Christina Bicchieri (1989). Counterfactuals and Backward Induction. Philosophica 44.
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  26.  16
    Martin Hollis (1991). Penny Pinching and Backward Induction. Journal of Philosophy 88 (9):473-488.
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  27.  1
    Alexandru Baltag, Sonja Smets & Jonathan Alexander Zvesper (2009). Keep ‘Hoping’ for Rationality: A Solution to the Backward Induction Paradox. Synthese 169 (2):301-333.
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  28.  8
    Roy Sorensen (1999). Infinite "Backward" Induction Arguments. Pacific Philosophical Quarterly 80 (3):278–283.
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  29.  1
    Cristina Bicchieri (1992). Knowledge-Dependent Games: Backward Induction. In Cristina Bicchieri, Dalla Chiara & Maria Luisa (eds.), Knowledge, Belief, and Strategic Interaction. Cambridge University Press 327--343.
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  30. Magnus Jiborn & Wlodek Rabinowicz (2004). Reconsidering the Foole's Rejoinder: Backward Induction in Indefinitely Iterated Prisoner's Dilemmas. Synthese 136 (2):135-157.
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  31.  87
    John Broome & Wlodek Rabinowicz (1999). Backwards Induction in the Centipede Game. Analysis 59 (264):237–242.
    The standard backward-induction reasoning in a game like the centipede assumes that the players maintain a common belief in rationality throughout the game. But that is a dubious assumption. Suppose the first player X didn't terminate the game in the first round; what would the second player Y think then? Since the backwards-induction argument says X should terminate the game, and it is supposed to be a sound argument, Y might be entitled to doubt X's rationality. Alternatively, (...)
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  32.  41
    Andrew M. Colman (2003). Cooperation, Psychological Game Theory, and Limitations of Rationality in Social Interaction. Behavioral and Brain Sciences 26 (2):139-153.
    Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality but also common (...)
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  33.  42
    Boudewijn de Bruin (2008). Common Knowledge of Rationality in Extensive Games. Notre Dame Journal of Formal Logic 49 (3):261-280.
    We develop a logical system that captures two different interpretations of what extensive games model, and we apply this to a long-standing debate in game theory between those who defend the claim that common knowledge of rationality leads to backward induction or subgame perfect (Nash) equilibria and those who reject this claim. We show that a defense of the claim à la Aumann (1995) rests on a conception of extensive game playing as a one-shot event in combination with (...)
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  34.  35
    Max Albert & Hannes Rusch, Indirect Reciprocity, Golden Opportunities for Defection, and Inclusive Reputation. MAGKS Discussion Paper Series in Economics.
    In evolutionary models of indirect reciprocity, reputation mechanisms can stabilize cooperation even in severe cooperation problems like the prisoner’s dilemma. Under certain circumstances, conditionally cooperative strategies, which cooperate iff their partner has a good reputation, cannot be invaded by any other strategy that conditions behavior only on own and partner reputation. The first point of this paper is to show that an evolutionary version of backward induction can lead to a breakdown of this kind of indirectly reciprocal cooperation. (...)
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  35.  42
    Wlodek Rabinowicz (2001). A Centipede for Intransitive Preferrers. Studia Logica 67 (2):167-178.
    In the standard money pump, an agent with cyclical preferences can avoid exploitation if he shows foresight and solves his sequential decision problem using backward induction (BI). This way out is foreclosed in a modified money pump, which has been presented in Rabinowicz (2000). There, BI will lead the agent to behave in a self-defeating way. The present paper describes another sequential decision problem of this kind, the Centipede for an Intransitive Preferrer, which in some respects is even (...)
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  36.  94
    Ken Levy (2009). The Solution to the Surprise Exam Paradox. Southern Journal of Philosophy 47 (2):131-158.
    The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...)
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  37.  48
    Wlodek Rabinowicz (1995). To Have One's Cake and Eat It, Too: Sequential Choice and Expected-Utility Violations. Journal of Philosophy 92 (11):586-620.
    An agent whose preferences violate the Independence Axiom or for some other reason are not representable by an expected utility function, can avoid 'dynamic inconsistency' either by foresight ('sophisticated choice') or by subsequent adjustment of preferences to the chosen plan of action ('resolute choice'). Contrary to McClennen and Machina, among others, it is argued these two seemingly conflicting approaches to 'dynamic rationality' need not be incompatible. 'Wise choice' reconciles foresight with a possibility of preference adjustment by rejecting the two assumptions (...)
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  38.  11
    Enrica Carbone & John D. Hey (2001). A Test of the Principle of Optimality. Theory and Decision 50 (3):263-281.
    This paper reports on an experimental test of the Principle of Optimality in dynamic decision problems. This Principle, which states that the decision-maker should always choose the optimal decision at each stage of the decision problem, conditional on behaving optimally thereafter, underlies many theories of optimal dynamic decision making, but is normally difficult to test empirically without knowledge of the decision-maker's preference function. In the experiment reported here we use a new (...)
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  39.  78
    José Luis Bermúdez (1999). Rationality and the Backwards Induction Argument. Analysis 59 (4):243–248.
    Many philosophers and game theorists have been struck by the thought that the backward induction argument (BIA) for the finite iterated pris- oner’s dilemma (FIPD) recommends a course of action which is grossly counter-intuitive and certainly contrary to the way in which people behave in real-life FIPD-situations (Luce and Raiffa 1957, Pettit and Sugden 1989, Bovens 1997).1 Yet the backwards induction argument puts itself forward as binding upon rational agents. What are we to conclude from this? Is (...)
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  40.  7
    Rudolf Schuessler (1989). The Gradual Decline of Cooperation: Endgame Effects in Evolutionary Game Theory. Theory and Decision 26 (2):133-155.
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  41.  19
    Wlodek Rabinowicz (2000). Preference Stability and Substitution of Indifferents: A Rejoinder to Seidenfeld. Theory and Decision 48 (4):311-318.
    Seidenfeld (Seidenfeld, T. [1988a], Decision theory without 'Independence' or without 'Ordering', Economics and Philosophy 4: 267-290) gave an argument for Independence based on a supposition that admissibility of a sequential option is preserved under substitution of indifferents at choice nodes (S). To avoid a natural complaint that (S) begs the question against a critic of Independence, he provided an independent proof of (S) in his (Seidenfeld, T. [1988b], Rejoinder [to Hammond and McClennen], Economics and Philosophy 4: 309-315). In reply to (...)
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  42.  12
    Bertrand R. Munier (1993). Are Game Theoretic Concepts Suitable Negotiation Support Tools? From Nash Equilibrium Refinements Toward a Cognitive Concept of Rationality. Theory and Decision 34 (3):235.
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  43. Oliver Schulte, Iterated Backward Inference: An Algorithm for Proper Rationalizability.
    An important approach to game theory is to examine the consequences of beliefs that agents may have about each other. This paper investigates respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A assigns probability 1 to the choice of a given that B chooses a or b. Respect for public preferences requires that if it is common belief that B prefers a (...)
     
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  44. Oliver Schulte, Respect for Public Preferences and Iterated Backward Inference.
    An important approach to game theory is to examine the consequences of beliefs that rational agents may have about each other. This paper considers respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A considers the choice of a “infinitely more likely” than the choice of B; equivalently, if A assigns probability 1 to the choice of a given that B chooses a (...)
     
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  45.  78
    Johan van Benthem, Rational Dynamics and Epistemic Logic in Games.
    Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes (...)
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  46.  26
    Johan van Benthem, Preference Logic, Conditionals and Solution Concepts in Games.
    Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference logic (cf. Hansson [10]) studies (...)
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  47.  46
    Sujata Ghosh, Ben Meijering & Rineke Verbrugge (2014). Strategic Reasoning: Building Cognitive Models From Logical Formulas. Journal of Logic, Language and Information 23 (1):1-29.
    This paper presents an attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. There have been extensive formal debates about the merits of the principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracking study, it has turned out that (...)
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  48.  29
    Joseph G. Johnson & Jerome R. Busemeyer (2001). Multiple-Stage Decision-Making: The Effect of Planning Horizon Length on Dynamic Consistency. Theory and Decision 51 (2/4):217-246.
    Many decisions involve multiple stages of choices and events, and these decisions can be represented graphically as decision trees. Optimal decision strategies for decision trees are commonly determined by a backward induction analysis that demands adherence to three fundamental consistency principles: dynamic, consequential, and strategic. Previous research found that decision-makers tend to exhibit violations of dynamic and strategic consistency at rates significantly higher than choice inconsistency across various levels of potential reward. The current research extends these findings under (...)
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  49.  11
    Thorsten Clausing (2004). Belief Revision in Games of Perfect Information. Economics and Philosophy 20 (1):89-115.
    A syntactic formalism for the modeling of belief revision in perfect information games is presented that allows to define the rationality of a player's choice of moves relative to the beliefs he holds as his respective decision nodes have been reached. In this setting, true common belief in the structure of the game and rationality held before the start of the game does not imply that backward induction will be played. To derive backward induction, a “forward (...)
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  50.  10
    Matt Jones & Jun Zhang (2003). Which is to Blame: Instrumental Rationality, or Common Knowledge? Behavioral and Brain Sciences 26 (2):166-167.
    Normative analysis in game-theoretic situations requires assumptions regarding players' expectations about their opponents. Although the assumptions entailed by the principle of common knowledge are often violated, available empirical evidence – including focal point selection and violations of backward induction – may still be explained by instrumentally rational agents operating under certain mental models of their opponents.
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