10. Describe the Principle of Insufficient Reason.

• This criterion might appeal to a decision maker who is neither pessimistic nor optimistic.

  • It assumes all the states of nature are equally likely to occur.

  • The procedure to find an optimal decision.

    • For each decision add all the payoffs.

    • Select the decision with the largest sum (for profits).

10. Describe the Principle of Insufficient Reason.

- The principle of insufficient reason (Laplace criterion) says that if we ignore a posibility, it will happen with the same probability as if New it.

11. Compare the prior and posterior probabilities. Posterior probability (The revised values of prior probabilities after receiving additional information)

Prior probability (The probability which describes the decision maker's judgement about the states of the environment, future events, or hypotheses, before obtaining additional information)

12. Describe the calculation of the posterior probabilities.

13. Describe the expected value of sampling information.

The expected value of sample information (EVSI) represents the increase of the best expected payoff in consequence of obtaining a free imperfect information.

The EVSI is equal to the difference between the best expected value of payoff with sample information (EVMS) and the best expected value of payoff without sample information.

The following formulas hold:

EVSI = EVMS – max(EMV) for a maximization criterion

EVSI = min(EMV) – EVMS for a minimization criterion

14. Describe the decision tree.

Decision tree is a graphic tool for describing the actions available to the decision maker, the events that can happen and the relationship between these actions and events. The decision point is represented by a square box or decision node. The decision alternatives are represented as branches from the decision node. The possible events are represented by event nodes – circles. In the decision making under certainty there are only decision nodes ( boxes).. At the end of each branch is the conditional profit

15. How do we calculate the value for the decision node and for the chance (event) node?

the value for the decision node - value * probability approved

for the chance (event) node -value * probability denied

16. How we can find the optimal strategy using the decision tree?

-Work backward from the end of each branch.

-At a state of nature node, calculate the expected value of the node.

-At a decision node, the branch that has the highest ending node value represents the optimal decision.

Game theory

17. Classify the games according to total return.

Zero Sum - the amount won and amount lost by all competitors are equal (Matching pennies, Rock, paper, scissors)

Nonzero Sum - the amount won and the amount lost by all competitors are not equal (Poker in A Casino)

18. What is the goal of all intelligent players?

- the intelligent players cares about the result ( win ), maximaise profit

19. Describe the optimal solution of the matrix game with constant return of two intelligent players.

If the matrix has 2 saddle points then the value is 0 therefore the game is fair.

20. How does the saddle point indices the optimal strategies?

- It’s a point where the best strategy for each player cross over.

21. What is the mixed strategy?

Its opposite to pure strategy, we choose from available strategies or we assign probabilities.