QABE_Slides10

# QABE_Slides10 - Introduction The Basics The Fundamentals of...

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Introduction The Basics The Fundamentals of Markov Chains Markov Chains in Game Theory QABE Lecture 10 Markov Chains 2011 c ± School of Economics, UNSW

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Introduction The Basics The Fundamentals of Markov Chains Markov Chains in Game Theory Agenda 1 Markov chain, defnition and characteristics. 2 Markov chain and Game Theory. c ± School of Economics, UNSW
Introduction The Basics The Fundamentals of Markov Chains Markov Chains in Game Theory WhyMa rkovCha ins? Calculating Probabilities We have been thinking about calculating the probability of events Involving large numbers of possibilities (permutations and combinations) Conditional on other events having occurred (conditional probability, Bayes’ Rule) We now focus on problems involving calculating the probability that an event occurs at some point in the future. c ± School of Economics, UNSW

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Introduction The Basics The Fundamentals of Markov Chains Markov Chains in Game Theory WhyMa rkovCha ins? Calculating Probabilities Simple (but boring) Example Toss a coin N times What is the probability of H on the n th trial? c ± School of Economics, UNSW
Introduction The Basics The Fundamentals of Markov Chains Markov Chains in Game Theory WhyMa rkovCha ins? Calculating Probabilities Simple (but boring) Example Toss a coin N times What is the probability of H on the n th trial? Outcomes are all independent events That is, “history does not matter” P ( H on n th trial )=1 / 2 for all n c ± School of Economics, UNSW

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Introduction The Basics The Fundamentals of Markov Chains Markov Chains in Game Theory WhyMa rkovCha ins? Calculating Probabilities But many outcomes of interest are dependent! Employment: More likely to be employed tomorrow if employed today Demand: More likely to be strong tomorrow if strong today Basketball: More likely to hit the next shot if you hit this shot? Government: A Party is more likely to win the next election if it won the previous one We use Markov Chains to analyse such cases. c ± School of Economics, UNSW
Introduction The Basics The Fundamentals of Markov Chains Markov Chains in Game Theory An Illustrative Example Example (Employment States) At each date n =0 , 1 , 2 , ..., T a worker is either Employed or Unemployed. The probability of being Employed at date n +1 conditional on being Employed at date n is 0.9. The probability of being Employed at date n conditional on being Unemployed at date n is 0.2. c ± School of Economics, UNSW

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Introduction The Basics The Fundamentals of Markov Chains Markov Chains in Game Theory An Illustrative Example Example (Employment States) At each date n =0 , 1 , 2 , ..., T a worker is either Employed or Unemployed. The probability of being Employed at date n +1 conditional on being Employed at date n is 0.9. The probability of being Employed at date n conditional on being Unemployed at date n is 0.2.
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## This note was uploaded on 09/23/2011 for the course ECON 1202 taught by Professor Lorettiisabelladobrescu during the One '11 term at University of New South Wales.

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QABE_Slides10 - Introduction The Basics The Fundamentals of...

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