پديد آورنده :
پرنيان، حسين
عنوان :
فرم هاي نرمال و شكافت هاي توابع استراتژي تكين
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد مشاور :
رضا مزروعي سبداني
واژه نامه :
به فارسي و انگليسي
تاريخ نمايه سازي :
1394/09/15
استاد داور :
مليحه يوسف زاده، محمدرضا رئوفي
تاريخ ورود اطلاعات :
1396/10/05
چكيده انگليسي :
Normal Forms And Unfolding Of Singular Strategy Functions Hossein Parnian hossein parnian@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Majid Gazor mgazor@cc iut ac ir Advisor Dr Reza Mazrooei Sebdani mazrooei@cc iut ac ir 2010 MSC 05C15 53C42 Keywords strategy function singularity theory universal unfolding Abstract This thesis is to study the adoptive local dynamics of strategy functions These functions haveapplication in game theory and adaptive dynamics of many real world problems In this directionwe rst de ne certain properties of singular points of strategy functions namely the evolutionarystable strategy ESS convergence stable strategy CvSS and singular strategy Next an equivalencerelation strategy equivalence is de ned so that it naturally preserves these properties Singularity theory is a well known theory for the dynamics study of zeros of singular functions However it is not well suited for our purpose In fact due to the di erences in equivalence relationsbetween these functions the algebraic structures are completely di erent from the ones in the classicalsingularity theory Therefore we establish a non standard singularity theory for the study of singularstrategy functions so that it would be compatible with ESS and CvSS properties of singular strategies The complete classi cation list of all normal forms universal unfoldings transition sets and persistentbifurcation diagrams of all singular strategies of codimension less than and equal to three is given This would give a comprehensive insight to the understanding of adaptive local dynamics of strategyfunctions The rst and second chapters deal with the literature on singularity and game theories basic ideas theorems and de nitions In the third chapter we will study some local properties of smooth strategyfunctions near their singular points and will concentrate on some properties including zero sets CvSSand ESS Then we will de ne the strategy equivalence The strategy functions will be classi ed
استاد مشاور :
رضا مزروعي سبداني
استاد داور :
مليحه يوسف زاده، محمدرضا رئوفي
