154 research outputs found
Doubly Strong Equilibrium
We present a new concept for (generalized) strategic form games, called \emph{doubly strong equilibrium}, and give an existence result when the players have non-ordered and discontinuous preferences. Since a doubly strong equilibrium is a strong equilibrium in the sense of Aumann, we get the existence of strong equilibria in discontinuous games. The result has been obtained by using the \emph{quasi-Ky Fan minimax inequality}. Applications to exchange economies are given. We prove the existence of \emph{doubly strong allocations}, which maximize consumers' preferences on the set of feasible allocations. The doubly strong allocations belong to the core of the economy. When consumers' preferences are selfish, we have that the doubly strong allocations are fair in the sense of Schmeidler and Yaari. So, we get the existence of fair allocations in the setting of non-ordered and discontinuous preferences.
Doubly Strong Equilibrium
We present a new concept for (generalized) strategic form games, called \emph{doubly strong equilibrium}, and give an existence result when the players have non-ordered and discontinuous preferences. Since a doubly strong equilibrium is a strong equilibrium in the sense of Aumann, we get the existence of strong equilibria in discontinuous games. The result has been obtained by using the \emph{quasi-Ky Fan minimax inequality}. Applications to exchange economies are given. We prove the existence of \emph{doubly strong allocations}, which maximize consumers' preferences on the set of feasible allocations. The doubly strong allocations belong to the core of the economy. When consumers' preferences are selfish, we have that the doubly strong allocations are fair in the sense of Schmeidler and Yaari. So, we get the existence of fair allocations in the setting of non-ordered and discontinuous preferences.
Game Theory Relaunched
The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy
Isomorphic Strategy Spaces in Game Theory
This book summarizes ongoing research introducing probability space
isomorphic mappings into the strategy spaces of game theory. This approach is
motivated by discrepancies between probability theory and game theory when
applied to the same strategic situation. In particular, probability theory and
game theory can disagree on calculated values of the Fisher information, the
log likelihood function, entropy gradients, the rank and Jacobian of variable
transforms, and even the dimensionality and volume of the underlying
probability parameter spaces. These differences arise as probability theory
employs structure preserving isomorphic mappings when constructing strategy
spaces to analyze games. In contrast, game theory uses weaker mappings which
change some of the properties of the underlying probability distributions
within the mixed strategy space. Here, we explore how using strong isomorphic
mappings to define game strategy spaces can alter rational outcomes in simple
games . Specific example games considered are the chain store paradox, the
trust game, the ultimatum game, the public goods game, the centipede game, and
the iterated prisoner's dilemma. In general, our approach provides rational
outcomes which are consistent with observed human play and might thereby
resolve some of the paradoxes of game theory.Comment: 160 pages, 43 figure
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