Decision Analysis and Game Theory v Decision Analysis

의사결정분석과 게임 이론 Decision Analysis and Game Theory

v Decision Analysis : Wikipedia • In Decision analysis(DA) is philosophy, theory, methodology, the discipline comprising the and professional practice necessary to address important decisions in a formal manner. • The Decision analysis includes many procedures, methods, and tools for identifying, clearly representing, and formally assessing important aspects of a decision, for prescribing a recommended course of action by applying the maximum expected utility action axiom to a well-formed representation of the decision, and for translating the formal representation of a decision and its corresponding recommendation into insight for the decision maker and other stakeholders. .

15. 1 확실성하의 의사결정-계층분석과정(AHP) v AHP (Analytic Hierarchy Process) : Wikipedia § The analytic hierarchy process (AHP) is a structured technique for organizing and analyzing complex decisions, based on mathematics and psychology. § It has particular application in group decision making, and is used around the world in a wide variety of decision situations, in fields such as government, business, industry, healthcare, and education. § Rather than prescribing a "correct" decision, the AHP helps decision makers find one that best suits their goal and their understanding of the problem.

(Martin, Jane) Hans의 대학 선택 과정

15. 2 위험하의 의사결정 예제 15. 2 -1) 주식투자 – 의사결정나무(decision tree) § which stock do you choose? 2200 의사결정시점 (decision point) 1100 확률적 사건 (chance event)

Petersburg paradox Toss a fair coin. Toss the coin until the first occurrence of tails. Payoff=2 the number of heads Expected payoff=

15. 2 위험하의 의사결정 v 효용함수(utility function) risk averse(위험 회피적) risk neutral(위험 중립적) risk seeker(위험 선호적)

15. 4 게임 이론 (game theory) v Game Theory : wikipedia § Game theory is a study of strategic decision making. Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers". § An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory. § Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. § The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant(s).

Summer campsite: cost matrix s 1 s 2 s 3 s 4 sum a 1 5 10 18 25 58 a 2 8 7 12 23 50 a 3 21 18 12 21 72 a 4 30 22 19 15 86 A: campsite size S: level of attendance Laplace: 58/4=14. 5, 50/4=12. 5, 72/4=18, 86/4=21. 5 Minimax: 25, 23, 21, 30

Regret matrix s 1 s 2 s 3 s 4 Max a 1 5: 0 10: 3 18: 6 25: 10 10 a 2 8: 3 7: 0 12: 0 23: 8 8 a 3 21: 16 18: 11 12: 0 21: 6 6 a 4 30: 25 22: 15 19: 7 15: 0 25 Hurwicz: min max a=0. 5 a 1 5 25 25 -20 a 15 a 2 7 23 23 -16 a 15 a 3 12 21 21 -9 a 16. 5 a 4 15 30 30 -15 a 22. 5

Another example: B 1 B 2 min A 1 1 -1 -1 A 2 -1 1 -1 max 1 1 No pure strategy Mixed strategy: P(A 1)=p B 1 expected 2 p-1 B 2 expected 1 -2 p

15. 4 게임 이론 (game theory) •

15. 4 게임 이론 (game theory) •

15. 4 게임 이론 (game theory) •

게임의 예(non-cooperative game) 용의자 2 용의자 1 부인 자백 부인 3, 3 0, 5 자백 5, 0 1, 1 B A 광고자제 광고공세 광고자제 50, 50 20, 60 광고공세 60, 20 30, 30 Dominant strategy and dominated strategy

Home works 15. 6 : A professor of political science wants to predict the outcome of a school board election. 15. 17 Tri. Star plans to open a new plant in Arkansas. 15. 37 An investment of 10, 000 in a high-risk venture has a 50 -50 chance over the next year of increasing to 15. 49 Consider the following two-person, zero sum game: (a) verify that the strategies (1/6, 0, 5/6)….