Generalized projection dynamics in evolutionary game theory
AbstractWe introduce a new kind of projection dynamics by employing a ray-projection both locally and globally. By global (local) we mean a projection of a vector (close to the unit simplex) unto the unit simplex along a ray through the origin. Using a correspondence between local and global ray-projection dynamics we prove that every interior evolutionarily stable strategy is an asymptotically stable fixed point. We also show that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ several projections on a wider set of functions derived from the payoff structure. This yields an interesting class of so-called generalized projection dynamics which contains best-response, logit, replicator, and Brown-Von-Neumann dynamics among others.
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Bibliographic InfoPaper provided by Max Planck Institute of Economics, Evolutionary Economics Group in its series Papers on Economics and Evolution with number 2008-11.
Date of creation: Oct 2008
Date of revision:
Find related papers by JEL classification:
- A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-11-04 (All new papers)
- NEP-EVO-2008-11-04 (Evolutionary Economics)
- NEP-GTH-2008-11-04 (Game Theory)
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