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

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  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.score: 240.0
    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. Magnus Jiborn & Wlodek Rabinowicz (2003). Reconsidering the Foole's Rejoinder: Backward Induction in Indefinitely Iterated Prisoner's Dilemmas. Synthese 136 (2):135 - 157.score: 240.0
    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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  3. Christian W. Bach & Conrad Heilmann (2011). Agent Connectedness and Backward Induction. International Game Theory Review 13 (2):195-208.score: 240.0
    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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  4. Wlodek Rabinowicz (1998). Grappling With the Centipede: Defence of Backward Induction for BI-Terminating Games. Economics and Philosophy 14 (01):95-.score: 240.0
    According to a standard objection to the use of backward induction in extensive-form games with perfect information, backward induction (BI) 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. (...)
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  5. 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.score: 240.0
    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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  6. John W. Carroll (2000). The Backward Induction Argument. Theory and Decision 48 (1):61-84.score: 240.0
    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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  7. Joe Mintoff (1999). Decision-Making and the Backward Induction Argument. Pacific Philosophical Quarterly 80 (1):64–77.score: 240.0
    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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  8. Thorsten Clausing (2003). Doxastic Conditions for Backward Induction. Theory and Decision 54 (4):315-336.score: 240.0
    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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  9. Antonio Quesada (2002). Belief System Foundations of Backward Induction. Theory and Decision 53 (4):393-403.score: 240.0
    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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  10. Ken Binmore (2011). Interpreting Knowledge in the Backward Induction Problem. Episteme 8 (3):248-261.score: 180.0
    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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  11. Jordan Howard Sobel (1993). Backward-Induction Arguments: A Paradox Regained. Philosophy of Science 60 (1):114-133.score: 180.0
    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. Michael Bacharach (1992). Backward Induction and Beliefs About Oneself. Synthese 91 (3):247 - 284.score: 180.0
    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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  13. Ken Binmore (1997). Rationality and Backward Induction. Journal of Economic Methodology 4 (1):23-41.score: 180.0
    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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  14. Cristina Bicchieri (1988). Backward Induction Without Common Knowledge. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:329 - 343.score: 180.0
    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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  15. Giacomo Bonanno (2001). Branching Time, Perfect Information Games and Backward Induction. Games and Economic Behavior 36 (1):57-73.score: 180.0
    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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  16. Wlodek Rabinowicz, Backward Induction in Games: An Attempt at Logical Reconstruction.score: 180.0
    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 (iterated prisoner's dilemma, centipede, chain store, etc.). However, beginning in the late eighties, the method of backward induction became an object of criticism. It is claimed (most notably, by Reny 1988, 1989, Binmore 1987, Bicchieri 1989, and Pettit & Sugden 1989) that the assumptions needed for its defence are (...)
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  17. Christian W. Bach & Conrad Heilmann, Agent Connectedness and Backward Induction.score: 174.0
    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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  18. John Broome & Wlodek Rabinowicz (1999). Backwards Induction in the Centipede Game. Analysis 59 (264):237–242.score: 160.0
    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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  19. Philip Pettit & Robert Sugden (1989). The Backward Induction Paradox. Journal of Philosophy 86 (4):169-182.score: 150.0
  20. Robert Stalnaker (1998). Belief Revision in Games: Forward and Backward Induction. Mathematical Social Sciences 36 (1):31 - 56.score: 150.0
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  21. Luc Bovens (1997). The Backward Induction Argument for the Finite Iterated Prisoner’s Dilemma and the Surprise Exam Paradox. Analysis 57 (3):179–186.score: 150.0
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  22. Roy Sorensen (1999). Infinite "Backward" Induction Arguments. Pacific Philosophical Quarterly 80 (3):278–283.score: 150.0
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  23. Martin Hollis (1991). Penny Pinching and Backward Induction. Journal of Philosophy 88 (9):473-488.score: 150.0
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  24. Christina Bicchieri (1989). Counterfactuals and Backward Induction. Philosophica 44.score: 150.0
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  25. Pierre Livet (1998). Jeux Évolutionnaires Et Paradoxe de l'Induction Rétrograde (Backward Induction). Philosophiques 25 (2):181-201.score: 150.0
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  26. 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.score: 150.0
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  27. Harald Wiese (2012). Backward Induction in Indian Animal Tales. International Journal of Hindu Studies 16 (1):93-103.score: 150.0
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  28. José Luis Bermúdez (1999). Rationality and the Backwards Induction Argument. Analysis 59 (4):243–248.score: 100.0
    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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  29. Boudewijn de Bruin (2008). Common Knowledge of Rationality in Extensive Games. Notre Dame Journal of Formal Logic 49 (3):261-280.score: 90.0
    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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  30. Andrew M. Colman (2003). Cooperation, Psychological Game Theory, and Limitations of Rationality in Social Interaction. Behavioral and Brain Sciences 26 (2):139-153.score: 90.0
    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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  31. Max Albert & Hannes Rusch, Indirect Reciprocity, Golden Opportunities for Defection, and Inclusive Reputation. MAGKS Discussion Paper Series in Economics.score: 90.0
    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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  32. Wlodek Rabinowicz (2001). A Centipede for Intransitive Preferrers. Studia Logica 67 (2):167-178.score: 90.0
    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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  33. Graham Priest (2000). The Logic of Backwards Inductions. Economics and Philosophy 16 (2):267-285.score: 60.0
    Backwards induction is an intriguing form of argument. It is used in a number of different contexts. One of these is the surprise exam paradox. Another is game theory. But its use is problematic, at least sometimes. The purpose of this paper is to determine what, exactly, backwards induction is, and hence to evaluate it. Let us start by rehearsing informally some of its problematic applications.
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  34. 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.score: 60.0
    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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  35. Gian Aldo Antonelli & Cristina Bicchieri, Backwards Forwards Induction.score: 60.0
    Gian Aldo Antonelli and Cristina Bicchieri. Backwards Forwards Induction.
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  36. Bertrand R. Munier & Jean-Louis Rulli�re (1993). Are Game Theoretic Concepts Suitable Negotiation Support Tools? From Nash Equilibrium Refinements Toward a Cognitive Concept of Rationality. Theory and Decision 34 (3):235-253.score: 60.0
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  37. Wlodek Rabinowicz (2000). Preference Stability and Substitution of Indifferents: A Rejoinder to Seidenfeld. Theory and Decision 48 (4):311-318.score: 60.0
    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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  38. Enrica Carbone & John D. Hey (2001). A Test of the Principle of Optimality. Theory and Decision 50 (3):263-281.score: 60.0
    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 experimental procedure to get round this difficulty, which also (...)
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  39. Oliver Schulte, Iterated Backward Inference: An Algorithm for Proper Rationalizability.score: 60.0
    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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  40. Oliver Schulte, Respect for Public Preferences and Iterated Backward Inference.score: 60.0
    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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  41. Rudolf Schuessler (1989). The Gradual Decline of Cooperation: Endgame Effects in Evolutionary Game Theory. Theory and Decision 26 (2):133-155.score: 60.0
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  42. Ken Binmore (2005). Economic Man – or Straw Man? Behavioral and Brain Sciences 28 (6):817-818.score: 30.0
    This commentary on the paper “Economic Man” in Cross-Cultural Perspective [20] is fiercely critical, but the criticism is not directed at the anthropological field work reported in the paper, which seems to me entirely admirable. The criticism is directed at the editorial rhetoric that accompanies the scientific reports of the experiments carried out in the fifteen small-scale societies studied. The rhetoric is markedly more subdued than in the book Foundations of Human Sociality [19] from which the current paper is extracted. (...)
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  43. Brian Skyrms (1998). Subjunctive Conditionals and Revealed Preference. Philosophy of Science 65 (4):545-574.score: 30.0
    Subjunctive conditionals are fundamental to rational decision both in single agent and multiple agent decision problems. They need explicit analysis only when they cause problems, as they do in recent discussions of rationality in extensive form games. This paper examines subjunctive conditionals in the theory of games using a strict revealed preference interpretation of utility. Two very different models of games are investigated, the classical model and the limits of reality model. In the classical model the logic of backward (...)
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  44. Yanis Varoufakis (1993). Modern and Postmodern Challenges to Game Theory. Erkenntnis 38 (3):371 - 404.score: 30.0
    Equilibrium game theory borrows from neoclassical economics its rationality concept which it immediately puts to work in order to produce the basic results it needs for building an elaborate narrative of social interaction. This paper focuses on some recent objections to game theory's use of rationality assumptions in general, and of backward induction and subgame perfection in particular, and interprets them in the light of the postmodern critique of the grand meta-narratives which social theorists often rely on for (...)
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  45. Cristina Bicchieri & Gian Aldo Antonelli (1995). Game-Theoretic Axioms for Local Rationality and Bounded Knowledge. Journal of Logic, Language and Information 4 (2):145-167.score: 30.0
    We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like rationality at a node and knowledge at a node. We distinguish between the game theorist's and the players' own theory of the game. The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...)
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  46. Horacio Arló-Costa & Cristina Bicchieri (2007). Knowing and Supposing in Games of Perfect Information. Studia Logica 86 (3):353 - 373.score: 30.0
    The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this (...)
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  47. Dov Samet, Counterfactuals in Wonderland.score: 30.0
    The literary source of the main ideas in Aumann's article "Backward Induction and Common Knowledge of Rationality" is exposed and analyzed. The primordial archetypal images that underlie both this literary source and Aumann's work are delineated and are used to explain the great emotive impact that this work had on the community of game theorists.
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  48. Ashton T. Sperry-Taylor (2011). Bounded Rationality in the Centipede Game. Episteme 8 (3):262-280.score: 30.0
    Normative game theory unsatisfactorily explains rational behavior. Real people do not behave as predicted, and what is prescribed as rational behavior is normally unattainable in real-life. The problem is that current normative analysis does not account for people's cognitive limitations – their bounded rationality. However, this paper develops an account of bounded rationality that explains the rationality of more realistic behavior. I focus on the Centipede Game, in which boundedly rational players explore and test others' immediate behavior, until they can (...)
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  49. Gian Aldo Antonelli & Cristina Bicchieri (1995). Game-Theoretic Axioms for Local Rationality and Bounded Knowledge. Journal of Logic, Language and Information 4 (2):145-167.score: 30.0
    We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...)
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  50. Johan Van Benthem (2011). Logic in a Social Setting. Episteme 8 (3):227-247.score: 30.0
    Taking Backward Induction as its running example, this paper explores avenues for a logic of information-driven social action. We use recent results on limit phenomena in knowledge updating and belief revision, procedural rationality, and a ‘Theory of Play’ analyzing how games are played by different agents.
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