Find steady-state probabilities for each policy

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Reference no: EM132256168

Stochastic Process Modeling Assignment - Project - Markov Decision Processes

Note - Read Appendix A, and then, solve the following problem. Need help with part II and part III only.

PROBLEM - Every Friday night a man plays poker at his home with the same group of friends. If he provides refreshments for the group (at an expected cost of $14) on any given Friday night, the group will begin the following Friday night in a good mood with probability 7/8 and in a bad mood with probability 1/8. However, if he fails to provide refreshments, the group will begin the following Friday night in a good mood with probability 1/8 and in a bad mood with probability 7/8, regardless of their mood this Friday. Furthermore, if the group begins the night in a bad mood and then he fails to provide refreshments, the group will gang up on him so that he incurs expected poker losses of $75. Under other circumstances, he averages no gain or loss on his poker play. The man wishes to find the policy regarding when to provide refreshments that will minimize his (long-run) expected average cost per week.

PART I -

a) Formulate this problem as a Markov decision process by identifying the states and decisions and then finding the C_ik.

b) Identify all the (stationary deterministic) policies. For each one, find the transition matrix and write an expression for the (long-run) expected average cost per period in terms of the unknown steady-state probabilities (π₀, π₁, . . . , π_M).

PART II -

a) Find these steady-state probabilities for each policy. Then evaluate the expression obtained in Part I (b) to find the optimal policy by exhaustive enumeration. Describe the optimal policy briefly in "plain English".

b) Formulate a linear programming model for finding an optimal policy.

PART III -

Use the policy improvement algorithm to find an optimal policy. Describe the optimal policy briefly in "plain English".

Attachment:- Appendix A.rar

Reference no: EM132256168

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3/13/2019 11:11:46 PM

Read Appendix A, and then, solve the following problem. Need help with part II and part III only. The project report should be prepared on a word processor and should contain tables and/or figures that are necessary to make the report easy to read. Be concise in your writing and consult technical writing references as needed.

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