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We formally assume that players in a game consider Nash Equilibrium (NE) the behavioral norm. In finite games of perfect information this leads to a refinement of NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of the "trimmed" game, obtained by restricting the original tree to its NE paths. Thus, it always exists but it need not be unique. Iterating the norm ensures uniqueness of outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide an alternative view of tenable threats in equilibrium analysis. [ABSTRACT FROM AUTHOR]

The analysis of dynamic games hinges on assumptions about players' actions and beliefs at information sets that are not expected to be reached during game play. Under the standard notion of sequential rationality, these assumptions cannot be tested on the basis of observed, on‐path behavior. This paper introduces a novel optimality criterion, structural rationality, which addresses this concern. In any dynamic game, structural rationality implies weak sequential rationality (Reny (1992)). If players are structurally rational, assumptions about on‐path and off‐path beliefs concerning off‐path actions can be tested via suitable "side bets." Structural rationality also provides a theoretical rationale for the use of a novel version of the strategy method (Selten (1967)) in experiments. [ABSTRACT FROM AUTHOR]

We extend the generic equivalence result of Blume and Zame (Econometrica 62:783–794, 1994) to a broader context of perfectly and sequentially rational strategic behavior (including equilibrium and nonequilibrium behavior) through a unifying solution concept of "mutually acceptable course of action" (MACA) proposed by Greenberg et al. (Econ Theory 40:91–112, 2009. https://doi.org/10.1007/s00199-008-0349-5). As a by-product, we show, in the affirmative, Dekel et al.'s (J Econ Theory 89:165–185, 1999) conjecture on the generic equivalence between the sequential and perfect versions of rationalizable self-confirming equilibrium. [ABSTRACT FROM AUTHOR]

Fixed points of the (most) refined best reply correspondence, introduced in Balkenborg et al. (2013), in the agent normal form of extensive form games with perfect recall have a remarkable property. They induce fixed points of the same correspondence in the agent normal form of every subgame. Furthermore, in a well-defined sense, fixed points of this correspondence refine even trembling hand perfect equilibria, while, on the other hand, reasonable equilibria that are not weak perfect Bayesian equilibria are fixed points of this correspondence. [ABSTRACT FROM AUTHOR]

Newman’s (1959, Operations Research, 7, 557–560) solution for a variant of poker with continuous hand spaces and an unlimited bet size is modified to incorporate sequential rationality.

Newman's (1959, Operations Research, 7, 557-560) solution for a variant of poker with continuous hand spaces and an unlimited bet size is modified to incorporate sequential rationality. [ABSTRACT FROM AUTHOR]

In mobile ad hoc networks, nodes have the inherent ability to move. Aside from conducting attacks to maximize their utility and cooperating with regular nodes to deceive them, malicious nodes get better payoffs with the ability to move. In this paper, we propose a game theoretic framework to analyze the strategy profiles for regular and malicious nodes. We model the situation as a dynamic Bayesian signaling game and analyze and present the underlining connection between nodes' best combination of actions and the cost and gain of the individual strategy. Regular nodes consistently update their beliefs based on the opponents' behavior, while malicious nodes evaluate their risk of being caught to decide when to flee. Some possible countermeasures for regular nodes that can impact malicious nodes' decisions are presented as well. An extensive analysis and simulation study shows that the proposed equilibrium strategy profile outperforms other pure or mixed strategies and proves the importance of restricting malicious nodes' advantages brought by the flee option. [ABSTRACT FROM AUTHOR]

Abstract: We use an agent''s strict preferences to define indifference and incompleteness relations that identify the sequences of trades that are rational to undertake. If an agent makes sequences of trades of options labeled indifferent, the agent will never be led to an inferior outcome, but trades of options where no preference judgments obtain can lead to diminished welfare. For one-shot choices, in contrast, there can be no behavioral distinction between indifference and incompleteness. Applications include: an isomorphism for incomplete preferences that indicates when weak and strict preferences contain interchangeable information, a characterization of the (possibly incomplete) preference relations consistent with a one-shot choice function, and an equivalent definition of incompleteness that relies on the philosophical theory of incommensurability. [Copyright &y& Elsevier]

In this paper we analyze dynamic strategic behavior by means of the idea of "stability." We develop a solution concept of "sequentially stable equilibrium (SSE)" that satisfies subgame consistency. All SSEs are characterized by the largest stable set that yields exactly all the backward induction outcomes. We also provide a refinement of the SSE. We compare the SSE and its refinement with some existing solution concepts in the literature [ABSTRACT FROM AUTHOR]

We show that an individual using a choice function is sequentially rational and the decisions he makes are independent of the order of implementation of the rationales if and only if he is rational with the union of the rationales as a base binary relation. When he makes his decisions following a choice correspondence, the sufficiency part of this claim still holds, the necessity part of it does not. [ABSTRACT FROM AUTHOR]

Based on the Selten [Mathematical Social Sciences 5 (1983) 269] and Oh [Three Essays on Equilibrium Selection in Games, PhD Thesis, (1995) Graduate College of The University of Iowa] symmetries, we introduce weak isomorphism of extensive games that, in contrast to the Peleg et al. [The canonical extensive form of a game form: Symmetries. In: Alkan, A., Aliprantis, C., Yannelis, N. (Eds.), Current Trends in Economics: Theory and Applications, Springer, (1999) pp. 367–387] isomorphism, is compatible with the traditional extensive representation of strategic games. While being sufficiently ‘weak’ to ignore the order of moves to some extent, weak isomorphism is ‘strong’ enough not to violate sequential rationality considerations as incorporated in the concept of sequential equilibrium. In addition, there is some generic equivalence between weak isomorphism and isomorphism of the agent normal form. [Copyright &y& Elsevier]

In an extensive form game, an assessment is said to satisfy the one-deviation property if for all possible payoffs at the terminal nodes the following holds: if a player at each of his information sets cannot improve upon his expected payoff by deviating unilaterally at this information set only, he cannot do so by deviating at any arbitrary collection of information sets. Hendon et al. (1996. Games Econom. Behav. 12, 274–282) have shown that pre-consistency of assessments implies the one-deviation property. In this note, it is shown that an appropriate weakening of pre-consistency, termed updating consistency, is both a sufficient and necessary condition for the one-deviation property. The result is extended to the context of rationalizability. [Copyright &y& Elsevier]

A weakening of Kreps and Wilson's (1982) notion of sequential rationality for extensive form games is presented. The motivation behind this weakening stems from the difficulty in justifying sequentially rational behavior in subgames reachable only through a violation of sequential rationality. Although the notion of weak sequential rationality developed here is based upon extensive form considerations, it. bears a close relation to Selten's (1975) normal form perfect equilibria. Also, a class of restrictions one might impose upon out of equilibrium beliefs is suggested. The weakest of these results from the assumption that deviators are expected utility maximizers. The strongest yields backward induction outcomes in generic games with perfect information. Lastly, it is argued, with the aid of an example having imperfect information, that sequential rationality is not the consequence of equilibrium play and the absence of incredible threats. [ABSTRACT FROM AUTHOR]