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  • 1
    Electronic Resource
    Electronic Resource
    A solidarity value forn-person transferable utility games (1994)
    Springer
    International journal of game theory 23 (1994), S. 43-48 
    Details
    ISSN: 1432-1270
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we introduce axiomatically a new value for cooperative TU games satisfying the efficiency, additivity, and symmetry axioms of Shapley (1953) and some new postulate connected with the average marginal contributions of the members of coalitions which can form. Our solution is referred to as the solidarity value. The reason is that its interpretation can be based on the assumption that if a coalition, sayS, forms, then the players who contribute toS more than the average marginal contribution of a member ofS support in some sense their “weaker” partners inS. Sometimes, it happens that the solidarity value belongs to the core of a game while the Shapley value does not.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01242845
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On an axiomatization of the banzhaf value without the additivity axiom (1997)
    Springer
    International journal of game theory 26 (1997), S. 137-141 
    Details
    ISSN: 1432-1270
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We prove that the Banzhaf value is a unique symmetric solution having the dummy player property, the marginal contributions property introduced by Young (1985) and satisfying a very natural reduction axiom of Lehrer (1988).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01262517
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  • 3
    Electronic Resource
    Electronic Resource
    On an Axiomatization of the Banzhaf Value without the Additivity Axiom (1997)
    Springer
    International journal of game theory 26 (1997), S. 137-141 
    Details
    ISSN: 1432-1270
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract:  We prove that the Banzhaf value is a unique symmetric solution having the dummy player property, the marginal contribution property introduced by Young (1985) and satisfying a very natural reduction axiom of Lehrer (1988).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01262517
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  • 4
    Electronic Resource
    Electronic Resource
    An alternative characterization of the weighted Banzhaf value (2000)
    Springer
    International journal of game theory 29 (2000), S. 127-132 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Cooperative games, Banzhaf value, weighted value.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. We provide a new characterization of the weighted Banzhaf value derived from some postulates in a recent paper by Radzik, Nowak and Driessen [7]. Our approach owes much to the work by Lehrer [4] on the classical Banzhaf value based on the idea of amalgamation of pairs of players and an induction construction of the value. Compared with the approach in [7] we consider two new postulates: a weighted version of Lehrer’s “2-efficiency axiom” [4] and a generalized “null player out” property studied in terms of symmetric games by Derks and Haller [2].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001829900027
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  • 5
    Electronic Resource
    Electronic Resource
    A counterexample on overtaking optimality (1999)
    Springer
    Mathematical methods of operations research 49 (1999), S. 435-439 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Markov decision chains ; overtaking optimality criteria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. Brown [3] constructed an aperiodic Markov decision chain in which no overtaking policy (stationary or nonstationary) exists. However, in his example a strong overtaking optimal policy exists in the class of all stationary policies. We provide another example of an aperiodic and geometric ergodic Markov decision chain which shows that the existence of a strong overtaking optimal stationary policy may fail inclusively in the class of stationary policies. We also give a brief survey of the existing literature on overtaking optimality in Markov decision chains.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050059
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  • 6
    Electronic Resource
    Electronic Resource
    Weighted Banzhaf values (1997)
    Springer
    Mathematical methods of operations research 45 (1997), S. 109-118 
    Details
    ISSN: 1432-5217
    Keywords: Cooperative transferable utility games ; Banzhaf values ; nonsymmetric values
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194250
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  • 7
    Electronic Resource
    Electronic Resource
    Sensitive equilibria for ergodic stochastic games with countable state spaces (1999)
    Springer
    Mathematical methods of operations research 50 (1999), S. 65-76 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Stochastic games ; countable state space ; sensitive optimality ; unbounded payoffs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. We consider stochastic games with countable state spaces and unbounded immediate payoff functions. Our assumptions on the transition structure of the game are based on a recent work by Meyn and Tweedie [19] on computable bounds for geometric convergence rates of Markov chains. The main results in this paper concern the existence of sensitive optimal strategies in some classes of zero-sum stochastic games. By sensitive optimality we mean overtaking or 1-optimality. We also provide a new Nash equilibrium theorem for a class of ergodic nonzero-sum stochastic games with denumerable state spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050035
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  • 8
    Electronic Resource
    Electronic Resource
    Optimal strategies in a class of zero-sum ergodic stochastic games (1999)
    Springer
    Mathematical methods of operations research 50 (1999), S. 399-419 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Discrete-time zero-sum stochastic games ; Borel state space ; average optimal strategies ; overtaking optimal strategies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. In this paper we study zero-sum stochastic games with Borel state spaces. We make some stochastic stability assumptions on the transition structure of the game which imply the so-called w-uniform geometric ergodicity of Markov chains induced by stationary strategies of the players. Under such assumptions and some regularity conditions on the primitive data, we prove the existence of optimal stationary strategies for the players in the expected average payoff stochastic games. We also provide a first result on overtaking optimality in zero-sum stochastic games.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050078
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  • 9
    Electronic Resource
    Electronic Resource
    A note on strong 1-optimal policies in Markov decision chains with unbounded costs (1999)
    Springer
    Mathematical methods of operations research 49 (1999), S. 475-482 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Markov decision chains ; countable state space ; sensitive optimality ; unbounded costs.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. We extend a result by Cavazos-Cadena and Lasserre on the existence of strong 1-optimal stationary policies in Markov decision chains with countable state spaces, uniformly ergodic transition probabilities and bounded costs to a larger class of models with unbounded costs and the so-called V-uniform ergodic transition structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050062
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  • 10
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    Existence of Stationary Markov Perfect Equilibria in Stochastic Altruistic Growth Economies (2014)
    Springer
    Details
    Publication Date: 2014-04-02
    Print ISSN: 0022-3239
    Electronic ISSN: 1573-2878
    Topics: Mathematics
    Published by Springer
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