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  • 1
    Electronic Resource
    Electronic Resource
    Rationality and the definition of consistent pairs (1998)
    Springer
    International journal of game theory 27 (1998), S. 49-59 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Consistent pairs ; rationality ; lexicographic probability systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. A consistent pair specifies a set of “rational” strategies for both players such that a strategy is rational if and only if it is a best reply to a Bayesian belief that gives positive probability to every rational strategy of the opponent and probability zero otherwise. Although the idea underlying consistent pairs is quite intuitive, the original definition suffers from non-existence problems. In this article, we propose an alternative formalization of consistent pairs. According to our definition, a strategy is “rational” if and only if it is a best reply to some lexicographic probability system that satisfies certain consistency conditions. These conditions imply in particular that a player's probability system gives infinitely more weight to rational strategies than to other strategies. We show that modified consistent pairs exist for every game.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001820050057
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  • 2
    Electronic Resource
    Electronic Resource
    Rationality and the definition of consistent pairs (1998)
    Springer
    International journal of game theory 27 (1998), S. 49-59 
    Details
    ISSN: 1432-1270
    Keywords: Consistent pairs ; rationality ; lexicographic probability systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A consistent pair specifies a set of “rational” strategies for both players such that a strategy is rational if and only if it is a best reply to a Bayesian belief that gives positive probability to every rational strategy of the opponent and probability zero otherwise. Although the idea underlying consistent pairs is quite intuitive, the original definition suffers from non-existence problems. In this article, we propose an alternative formalization of consistent pairs. According to our definition, a strategy is “rational” if and only if it is a best reply to some lexicographic probability system that satisfies certain consistency conditions. These conditions imply in particular that a player's probability system gives infinitely more weight to rational strategies than to other strategies. We show that modified consistent pairs exist for every game.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01243194
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  • 3
    Electronic Resource
    Electronic Resource
    The survival value of assuming others to be rational (2000)
    Springer
    International journal of game theory 29 (2000), S. 147-163 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Evolutionary psychology ; rationality ; beliefs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. I study the evolution of rationality, using an indirect evolutionary approach, in which nature selects a decision-making procedure, and the procedure chooses actions in matching-games. The main result is that in order for (knowledge of) rationality to survive, it is necessary and sufficient that the rational procedure respects the attraction principle. That is, when a rational agent eliminates a strictly dominated action A, he should only increase the choice probability of the actions actually dominating A and not change the choice probability of other undominated actions. The attraction principle sharpens gametheoretic predictions. Attraction effects have been verified in psychological experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001820070001
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  • 4
    Electronic Resource
    Electronic Resource
    Approximated solutions in rational form for systems of differential equations (1999)
    Springer
    Numerical algorithms 21 (1999), S. 185-203 
    Details
    ISSN: 1572-9265
    Keywords: systems of differential equations ; analytic solutions ; matrix Padé approximation ; rationality ; minimum degrees ; uniqueness ; partial differential equations ; 41A21 ; 34A45 ; 35A35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we present a technique to study the existence of rational solutions for systems of differential equations — for an ordinary differential equation, in particular. The method is relatively straightforward; it is based on a rationality characterisation that involves matrix Padé approximants. It is important to note that, when the solution is rational, we use formal power series “without taking into account” their circle of convergence; at the end of this paper we justify this. We expound the theory for systems of linear first-order ordinary differential equations in the general case. However, the main ideas are applied in numerical resolution of partial differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019109429882
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  • 5
    Electronic Resource
    Electronic Resource
    Matrix Padé Approximation of rational functions (1997)
    Springer
    Numerical algorithms 15 (1997), S. 167-192 
    Details
    ISSN: 1572-9265
    Keywords: Matrix Padé Approximation ; rationality ; minimum degrees ; uniqueness ; 65 ; 41 ; 15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In many applications it is of major interest to decide whether a given formal power series with matrix-valued coefficients of arbitrary dimensions results from a matrix-valued rational function. As the main result of this paper we provide an answer to this question in terms of Matrix Padé Approximants of the given power series. Furthermore, given a matrix rational function, the “smallest” degrees of the matrix polynomials which represent it are not necessarily unique. Therefore we study a certain minimality-type, that is, minimum degrees. We aim to obtain all the minimum degrees for the polynomials which represent the function as equivalents. In addition, given that the rational representation of the function for the same pair of degrees need not be unique, we have obtained conditions to study the uniqueness of said representation. All the results obtained are presented graphically in tables setting out the above information. They lead to a number of properties concerning special structures, staired blocks, in the Padé Table.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019193820428
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  • 6
    Electronic Resource
    Electronic Resource
    An axiomatic analysis of the Nash equilibrium concept (1992)
    Springer
    Theory and decision 33 (1992), S. 177-189 
    Details
    ISSN: 1573-7187
    Keywords: Axioms ; cooperation ; game theory ; Nash equilibrium ; rationality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract The purpose of this paper is to analyze axiomatically the Nash equilibrium concept. The class of games under study is a (relatively large) subclass of n-person normal form games. Solutions are correspondences which associate to each game a non empty set of strategy vectors of this game. It is shown that if a solution satisfies the axioms Independence of irrelevant alternatives (IIA) and Individual rationality (IR), then all the strategy vectors in this solution are Nash equilibria. This result holds good also if IR is replaced by Strong individual monotonicity (SIM) or Weak principle of fair compromise (WPFC).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00134095
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  • 7
    Electronic Resource
    Electronic Resource
    Instrumental rationality and cognitive rationality (1989)
    Springer
    Theory and decision 27 (1989), S. 7-36 
    Details
    ISSN: 1573-7187
    Keywords: rationality ; information ; expectations ; beliefs ; dynamic games ; game equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract Beside instrumental rationality, concerned with consistency between available means and pursued objectives, cognitive rationality, concerned with consistency between current beliefs and detained information, is nowadays bursting in economic theory. For an individual decision, the two notions are expressed structurally in similar forms, but they heavily interact in the deliberation process, especially when the agent is searching relevant information on his environment and his own determiners. In a game framework, the players' representations are formalized in a more and more sophisticated way, and are closely interwoven with their preferences in contemporary equilibrium notions as well as in selection between corresponding equilibrium points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00133986
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  • 8
    Electronic Resource
    Electronic Resource
    Interpersonal dependency of preferences (1996)
    Springer
    Theory and decision 41 (1996), S. 257-280 
    Details
    ISSN: 1573-7187
    Keywords: Preference ; decision theory ; utility ; rationality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract Standard decision theoretic models disregard the phenomenon of interpersonal dependency of preferences. In this paper it is argued that interpersonal dependency of preferences is a serious challenge for standard utility theory. First we sketch the more philosophical aspects of the problem and then, using a simple, formal model for the two-person case, we show that interpersonal dependency of preferences generally results in indeterminacy of preferences (resp. of subjective utility).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00136128
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  • 9
    Electronic Resource
    Electronic Resource
    Biting the Bayesian bullet: Zeckhauser's problem (1988)
    Springer
    Theory and decision 25 (1988), S. 117-122 
    Details
    ISSN: 1573-7187
    Keywords: Bayesian decision theory ; sure thing principle ; independence axiom ; rationality ; irrationality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract A troubling challenge to the basic principles of Bayesian decision theory is analyzed as a case where irrationality is no intellectual flaw but a characterological one, i.e., not stupidity but funk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00134155
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  • 10
    Electronic Resource
    Electronic Resource
    Nonrational actors and financial market behavior (1991)
    Springer
    Theory and decision 31 (1991), S. 257-287 
    Details
    ISSN: 1573-7187
    Keywords: financial market ; decision theory ; behavioral decision ; financial flows ; rationality ; herd behavior
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract The insights of descriptive decision theorists and psychologists, we believe, have much to contribute to our understanding of financial market macrophenomena. We propose an analytic agenda that distinguishes those individual idiosyncrasies that prove consequential at the macro-level from those that are neutralized by market processes such as poaching. We discuss five behavioral traits — barn-door closing, expert/reliance effects, status quo bias, framing, and herding — that we employ in explaining financial flows. Patterns in flows to mutual funds, to new equities, across national boundaries, as well as movements in debt-equity ratios are shown to be consistent with deviations from rationality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00132995
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