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  • Articles  (9)
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  • Nash equilibrium  (9)
  • Springer  (9)
  • American Institute of Physics
  • Bremen
  • 2020-2024
  • 1990-1994  (9)
  • Economics  (9)
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  • Books
  • Articles  (9)
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  • Springer  (9)
  • American Institute of Physics
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  • 1
    Electronic Resource
    Electronic Resource
    Interconnected games and international environmental problems, II (1994)
    Springer
    Annals of operations research 54 (1994), S. 97-117 
    Details
    ISSN: 1572-9338
    Keywords: Modelling ; interconnection ; side payments ; game theory ; environment ; transboundary pollution ; multiple objective games ; repeated games ; tensor games ; tradeoff ; Pareto equilibrium ; Nash equilibrium ; Folk theorem ; prisoners' dilemma ; JEL C70 ; Q28
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Some features of international environmental problems are considered. A basic problem is to induce countries to adopt a cooperative approach. One of the instruments to induce countries to cooperate is an exchange of concessions in fields of relative strengths, such as swapping trade concessions for cooperation on international environmental problems. This instrument will be modelled in this paper with tensor games. Both tradeoff and non-tradeoff tensor games will be addressed, with emphasis on tradeoff tensor games with linear strict weights. The relationship between the Pareto equilibria of a non-tradeoff tensor game and the Nash equilibria of the associated tradeoff tensor games will be studied. Due to structural similarities between tensor games and repeated multiple objective games, some attention will also be paid to the latter. Relationships between objects related to Folk theorems for the tradeoff tensor game with completely additive weights and the corresponding objects for its constituting isolated games will be studied. Since many international environmental problems have prisoners' dilemma characteristics, it is analyzed how interconnection may enhance cooperation in prisoners' dilemma games.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02031729
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  • 2
    Electronic Resource
    Electronic Resource
    On the evaluation of solution concepts (1994)
    Springer
    Theory and decision 37 (1994), S. 49-73 
    Details
    ISSN: 1573-7187
    Keywords: solution concepts in game theory ; Nash equilibrium ; rationalizability ; strong rationalizability ; common belief ; modal logic ; Kripke structures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract It is proposed that solution concepts for games should be evaluated in a way that is analogous to the way a logic is evaluated by a model theory for the language. A solution concept defines a set of strategy profiles, as a logic defines a set of theorems. A model theoretic analysis for a game defines a class of models, which are abstract representations of particular plays of the game. Given an appropriate definition of a model, one can show that various solution concepts are characterized by intuitively natural classes of models in the same sense that the set of theorems of a logic is characterized by a class of models of the language. Sketches of characterization results of this kind are given for rationalizability, Nash equilibrium, and for a refinement of rationalizability —strong rationalizability — that has some features of an equilibrium concept. It is shown that strong rationalizability is equivalent to Nash equilibrium in perfect information games. Extensions of the model theoretic framework that represent belief revision and that permit the characterization of other solution concepts are explored informally.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01079205
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  • 3
    Electronic Resource
    Electronic Resource
    Finding a Nash equilibrium in noncooperativeN-person games by solving a sequence of linear stationary point problems (1994)
    Springer
    Mathematical methods of operations research 39 (1994), S. 365-375 
    Details
    ISSN: 1432-5217
    Keywords: noncooperative game ; Nash equilibrium ; stationary point
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we present an algorithm for finding a Nash equilibrium in a noncooperative normal formN-person game. More generally, the algorithm can be applied for solving a nonlinear stationary point problem on a simplotope, being the Cartesian product of several simplices. The algorithm solves the problem by solving a sequence of linear stationary point problems. Each problem in the sequence is solved in a finite number of iterations. Although the overall convergence cannot be proved, the method performs rather well. Computational results suggest that this algorithm performs at least as good as simplicial algorithms do. For the special case of a bi-matrix game (N=2), the algorithm has an appealing game-theoretic interpretation. In that case, the problem is linear and the algorithm always finds a solution. Furthermore, the equilibrium found in a bi-matrix game is perfect whenever the algorithm starts from a strategy vector at which all actions are played with positive probability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01435463
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  • 4
    Electronic Resource
    Electronic Resource
    Are game theoretic concepts suitable negotiation support tools? From Nash equilibrium refinements toward a cognitive concept of rationality (1993)
    Springer
    Theory and decision 34 (1993), S. 235-253 
    Details
    ISSN: 1573-7187
    Keywords: Game theory ; Nash equilibrium ; perfect equilibrium ; trembling hand procedure ; backward induction ; common knowledge ; strategic deviation ; forward induction ; dynamic rationality ; cognitive rationality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract If game theory is to be used as a negotiation support tool, it should be able to provide unambiguous recommendations for a target to aim at and for actions to reach this target. This need cannot be satisfied with the Nash equilibrium concept, based on the standard instrumental concept of rationality. These equilibria, as is well known, are generally multiple in a game. The concept of substantive or instrumental rationality has proved to be so pregnant, however, that researchers, instead of re-evaluating its use in game theory, have simply tried to design concepts related to the Nash equilibrium, but with the property of being unique in a game — i.e., they have devised ways ofselecting among Nash equilibria. These concepts have been labeledrefined Nash equilibria. The purpose of this paper is to show the following. (a) The different types of refined Nash equilibria, based on the principle of backward induction, can lead to severe contradictions within the framework itself. This makes these concepts utterly unsatisfactory and calls for a new appraisal of the reasoning process of the players. (b) The degree of confidence in the principle of backward induction depends upon the evaluation of potential deviations with respect to the extended Nash equilibrium concept used and upon the possible interpretations of such deviations by the different players. Our goal is to show that the nature of these possible interpretations reinforces the argument that a serious conceptual reappraisal is necessary. (c) Some form of forward induction should then become the real yardstick of rationality, extending Simonianprocedural rationality towards the concept ofcognitive rationality. This could open the way to a renewed game theoretic approach to negotiation support systems. Such a research program, which would be a revision of the basic game theoretic concepts, is dealt with in the end of the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01075191
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  • 5
    Electronic Resource
    Electronic Resource
    Endogenizing the order of moves in matrix games (1993)
    Springer
    Theory and decision 34 (1993), S. 47-62 
    Details
    ISSN: 1573-7187
    Keywords: Nash equilibrium ; endogenous timing ; Cournot ; Stackelberg
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract Players often have flexibility in when they move and thus whether a game is played simultaneously or sequentially may be endogenously determined. For 2 × 2 games, we analyze this using an extended game. In a stage prior to actual play, players choose in which of two periods to move. A player moving at the first opportunity knows when his opponent will move. A player moving at the second turn learns the first mover's action. If both select the same turn, they play a simultaneous move subgame. If both players have dominant strategies in the basic game, equilibrium payoffs in the basic and extended games are identical. If only one player has a dominant strategy or if the unique equilibrium in the basic game is in mixed strategies, then the extended game equilibrium payoffs differ if and only if some pair of pure strategies Pareto dominates the basic game simultaneous play payoffs. If so, sequential play attains the Pareto dominating payoffs. The mixed strategy equilibrium occurs only when it is not Pareto dominated by some pair of pure strategies. In an alternative extended game, players cannot observe delay by opponents at the first turn. Results for 2×2 games are essentially the same as with observable delay, differing only when only one player has a dominant strategy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01076104
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  • 6
    Electronic Resource
    Electronic Resource
    A silent duel over a cake (1993)
    Springer
    Mathematical methods of operations research 37 (1993), S. 119-127 
    Details
    ISSN: 1432-5217
    Keywords: Nash equilibrium ; Game of timing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The division of a cake by two players is modelled by means of a silent game of timing. It is shown that this game has a unique Nash equilibrium. The strategies of the Nash equilibrium are explicitly given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01414151
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Monetary policy interaction within or without an exchange-rate arrangement (1992)
    Springer
    Open economies review 3 (1992), S. 61-82 
    Details
    ISSN: 1573-708X
    Keywords: EMS ; exchange-rate feedback ; Nash equilibrium ; asymmetric policy ; exchange-rate bands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract In a simple stochastic two-country model in which each country uses monetary policy to offset shocks that impinge on its national income, the policy rule chosen by each country is affected by the rule chosen by the other. A monetary union emerges as a Nash equilibrium (and is Pareto optimal) if the variance of shocks affecting the real exchange rate is small. An exchange-rate arrangement, and in particular a system of exchange-rate bands such as the European Monetary System (EMS), may create a need for more policy cooperation and may give scope for strategic asymmetries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01886182
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  • 9
    Electronic Resource
    Electronic Resource
    A procedure for finding Nash equilibria in bi-matrix games (1991)
    Springer
    Mathematical methods of operations research 35 (1991), S. 27-43 
    Details
    ISSN: 1432-5217
    Keywords: bi-matrix game ; Nash equilibrium ; complementarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In diesem Beitrag entwickeln wir ein neues Verfahren zur Berechnung eines Nash-Gleichgewichtspunktes für Zweimatrizen-Spiele. Das Standardverfahren zur Lösung dieser Spiele ist der Lemke-Howson Algorithmus. Dieses Pivotverfahren löst ein lineares Komplementaritätsproblem. Da dieses Verfahren nur in einer beschränkten Anzahl Punkte beginnen kann, können nicht alle Gleichgewichtspunkte berechnet werden. Unser Verfahren löst ein stationäres Punktproblem definiert auf die Strategiemenge und darf in einem beliebigen Punkt angefangen werden. Der Weg der Punkte des Algorithmus hat eine einladende spieltheoretische Interpretation. Wenn im Startpunkt alle Strategien mit positiver Wahrscheinlichkeit gewählt werden, dann ist das gefundene Nash-Gleichgewicht perfekt. Auch dürfen alle Gleichgewichtspunkte berechnet werden durch mehrere Startpunkte zu wählen.
    Notes: Abstract In this paper we consider the computation of Nash equilibria for noncooperative bi-matrix games. The standard method for finding a Nash equilibrium in such a game is the Lemke-Howson method. That method operates by solving a related linear complementarity problem (LCP). However, the method may fail to reach certain equilibria because it can only start from a limited number of strategy vectors. The method we propose here finds an equilibrium by solving a related stationary point problem (SPP). Contrary to the Lemke-Howson method it can start from almost any strategy vector. Besides, the path of vectors along which the equilibrium is reached has an appealing game-theoretic interpretation. An important feature of the algorithm is that it finds a perfect equilibrium when at the start all actions are played with positive probability. Furthermore, we can in principle find all Nash equilibria by repeated application of the algorithm starting from different strategy vectors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415958
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