LectureFeb24_MATH4321_12S

LectureFeb24_MATH4321_12S - Equilibrium Principle: BR to...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Equilibrium Principle: BR to each other Maximin Principle: Safety First For Player I: Find p so that Min q p T Aq is largest. p is called the Safety Strategy or Optimal Strategy. Min q p T Aq is the lower value. For Player II: Find q so that Max p p T Aq is smallest. q is called the Safety Strategy or Optimal Strategy. Max p p T Aq is the upper value. Minimax Theorem: Maximin=Minimax Solution of All 2 by 2 Matrix Games. Consider the general 2 × 2 game matrix We will use the Maximin Principle to find the safety strategies and the value. Given a mixed strategy of Player I, , we will find the minimum of the payoff. Recall that the minimum is achieved by a pure strategy of Player II. a b A d c        The minimum is then Min(pa+(1-p)d),pb+(1-p)c), for 0  p  1. The graph of the function p  Min(pa+(1-p)d),pb+(1-p)c) is the lower envelope of the graphs of the two linear functions p  pa+(1-p)d, for 0  p  1 and p  pb+(1-p)c, for 0  p  1 1 p a b p d c  The maximum of Min(pa+(1-p)d),pb+(1-p)c) is...
View Full Document

This note was uploaded on 03/13/2012 for the course MATH 4321 taught by Professor Cheng during the Spring '12 term at HKUST.

Page1 / 17

LectureFeb24_MATH4321_12S - Equilibrium Principle: BR to...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online