Outline. Decision Making Theory and Homeland Security. Readings. AGEC689: Economic Issues and Policy Implications of Homeland Security

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1 Decision Making Theory and Homeland Security AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 1 Readings Kunreuther and Heal (003). Interdependent Security. The Journal of Risk and Uncertainty, 6:/3: AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU Outline Risk and Decision making under risk Brief discussion of Game Theory AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 3 1

2 Risk and Decision Making Under Risk Degree of risk Decision making under risk Risk attitudes AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 4 Minimizing Variance or Standard Deviation The payoffs of all s: x 1, x,, x The probability of each : p 1, p,, p Expected value of x: EV ( x) = x1 p1+ xp xp= xipi σ Variance: = ( x1 EV ) p1+ ( x EV ) p ( x EV ) p = ( xi i= 1 Standard deviation: square root of variance σ Coefficient of variation: CV = EV i= 1 EV ) p i AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 5 Risk Measurement Absolute Risk: Overall dispersion of possible payoffs Measurement: variance, standard deviation The smaller variance or standard deviation, the lower the absolute risk. Relative Risk Variation in possible returns compared with the expected payoff amount Measurement: coefficient of Variation (CV), The lower the CV, the lower the relative risk. σ CV = EV AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 6

3 Decision Making Under Uncertainty Criteria: Maximize expected value Minimize variance or standard deviation Coefficient of variation Maximin criterion Maximax criterion Incorporate risk attitudes: certainty equivalent AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 7 Maximize Expected Value Animal Disease Outbreak Yes Expected profit Prob Profit proj. A proj. B $5,000 $6,000 $,000 $0 $4,400 $4,800 Questions: Which project you will choose based on this criteria? What are your concerns? AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 8 Minimizing Variance/Standard Deviation Animal Disease Outbreak Yes Expected profit Prob Profit proj. A proj. B $5,000 $,000 $4,400 $5,500 $0 $4,400 Questions: Which project you will choose based on this criteria? What is ignored using this criterion? AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 9 3

4 Coefficient of Variation Expected value Variance Coefficient of Variation A $5, B $5, Questions: Which project you will choose based on this criterion? What is ignored? AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 10 Maxmin and Maxmax Criterion Animal Disease Outbreak Yes Prob Profit proj. A proj. B $5,000 $6,000 $,000 $0 Questions: Which project you will choose? Based on Maxmin? Based on Maxmax? What is ignored? AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 11 Risk Attitudes Scenario: A person has two choices, a sure thing and a risky option, and both yields the same expected value. Risk averse: take the sure thing Risk neutral: indifferent between two choices Risk loving: take the risky option AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 1 4

5 Fundamental Reasons to Risk Attitudes Risk averter: diminishing MU Risk neutral: constant MU Risk lover: increasing MU AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 13 Incorporating Risk Attitudes: Certain Equivalent Initial wealth $1000, and you face two options: (a) Keep your initial wealth and do nothing; (b) Invest: receive $10,000 if succeed; lose 1000 if fail. After assessing these two options, you find yourself indifferent between two. Analysis: Certainty Equivalent α = Certainty Equivalent factor: Risk averse: α<1 Risk neural: α=1 Risk loving: α>1 EquivalentCertainSum ExpectedRiskSUm AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 14 Risk Premium: Prive Initial wealth=40 which results in U(40)=10. An prive investment can magically ensure no disease outbreak (not realistic). (a)without disease outbreak,u(70)=140 (b)with disease outbreak, U(10)=70 (c)0.5u(70)+0.5u(10)=105 Questions: (a)will invest on prive activities? (b)risk premium? Utility (U) U(70)=140 U(40)=10 0.5U(10)+0.5U(70) =U(6)=105 U(10)= Wealth ($) Risk premium AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 15 5

6 Risk Premium: Earthquake Insurance Josh lives in the San Francisco Bay Are of California where the prob. of an earthquake is 10%. His utility function is U(w)=w 0.5, where w is wealth. If Josh chooses not to buy insurance next year, his wealth is $500,000 without an earthquake, and $300,000 at the lose of his house with an earthquake. What s his risk premium? Answer: risk premium=$4,6361. The solution will be discussed in class. AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 16 Terminology in Game Theory Players Strategies Choice variables to each of the player Payoffs Some numerical representation of the objectives of each player AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 17 Standard Assumptions Rationality Players are perfect calculators and implementers of their desired strategy Common knowledge of rules All players know the game being played Equilibrium Players play strategies that are mutual best responses AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 18 6

7 Classifying Games Sequential (Stackelberg) vs. simultaneous (Cournot) One-shot vs. repeated games Public vs. private information Enforceable vs. unenforceable cooperative agreements AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 19 tes on Game Theory Game versus decisions Large versus small numbers Games typically thought to pertain small number of players But large number of players will be involved. AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 0 Payoff Table: ncooperative Equilibrium Two cattle farmers, A and B: Initial wealth=$00 Potential investment=$80 Loss schedule: Loss=$100 for each if no one invests; Loss=$10 for each if both invests; Loss=($30 for whom invests and $80 for whom does not invest) if only one invests. Y Y = = = = = = = =100 AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 1 7

8 ash ncooperative Equilibrium Y Y = = = = = = = =100 How to find the equilibrium? If farmer A invests, the best response for B is not to invest. If farmer A does no invest, the best response for B is not to invest. If farmer B invests, the best response for A is not to invest. If farmer B does not invest, the best response for A is not to invest. The ash equilibrium is investment for both. Both farmers can be better off if they choose to invest. Why they do not cooperate? AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU Game Tree: Pre- Prive Initial wealth=$500 =$100 Loss if adverse occurs: $400 without investment, $100 with investment Probability of the adverse = =300 made =400 ($100) = E1=Expected payoff if investment made =300(0.5)+400(0.5)=$350 E=Expected payoff if no investment=100(0.5)+500(0.5)=$300 Will choose to invest since E1>E AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 3 Pre- Prive : loss schedule matters Previous loss schedule: $400 w/o investment, $100 w/ investment ew loss schedule: $150 w/o investment, $100 w/ investment 300(0.5)+400(1-0.5)<350(0.5)+500(1-0.5) investment =300 made =400 ($100) = AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 4 8

9 Pre- Prive : prob. matters ($100) made = = = What is the probability of having the adverse becomes 0.? 300(0.)+400(1-0.)<100(0.)+500(1-0.) investment AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 5 Pre- Prive : Policy Implications Often, we do not know the probability of the adverse. What can we provide to policy makers? The critical prob. tipping the balance. ($100) made = = = (p)+400(1-p)>100(p)+500(1-p) Invest if p>1/3 AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 6 Simultaneous Game Problem statement: Two cattle farmers simultaneously choose the prive investment (K 1, K ) to maximize their wealth. Initial wealth= for both Loss function: L 1 (K 1 )=1-K 1 -K (1+K 1 +K ) for farmer 1 L (K )=1-K -K 1 (1+K 1 +K ) for farmer General Procedure to Solve Simultaneous Game Set up the objective and solve the first order condition (FOC) and best response function (BRF) for each Farmer 1: [ max K1 1 K1 K ( 1+ K1+ K ) ] K 1 FOC: + K + K = BRF: 1 K K1= AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 7 9

10 Simultaneous Game (cont ) [ ] Farm : max K 1 K K1( 1+ K1+ K ) K FOC: 1+ K + K1= 0 1 K K1 BRF: K = 1 Find the intercept of two BRFs, which determines the equilibrium. 1 K K1= 1 K1 K = 1/ 1/3 Cournot Equilibrium K1 =K = 1/ 3 1/3 1/ 1 K1 AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 8 Sequential Game Problem statement: What if farmer can observe farmer 1 s investment and then determine his own investment? Sequential game. General Procedure to Solve Sequential Game Set up the objective and solve the first order condition (FOC) and best response function (BRF) for farmer first Farmer : [ max K 1 K K1( 1+ K1+ K ) ] K FOC: 1+ K + K1= 0 BRF: 1 K1 K = AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 9 Simultaneous Game (cont ) Set up the objective function and FOC for farmer 1 taking the BRF of farmer into consideration. Farmer 1: [ 1 max K 1 K K1( 1+ K1+ K ) ] K1 where K = K FOC: / 3+ / 3K1= 0 K 1 = 1 Substitute K1=1 into the BRF for farmer. 1 K1 1 1 K = = = 0 K 1 1/ 1/3 Stackelberg Equilibrium 1/3 1/ 1 K1 AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 30 10

11 Simultaneous vs. Sequential Game Leader may have advantage by taking the action first (first-mover advantage). AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin at TAMU 31 11