Decision Theory and Risk Analysis: Some organising questions

1. Decision Theory and Risk Analysis: Some organising questions David Rios Insua Jesus Rios Risk Analysis, Extreme Event and Decision Theory Program, SAMSI Stats and OR, U. Rey Juan Carlos Interneg, Concordia U. Durham NC, September ‘07

2. Outline • Background • Risk analysis: framework • Adversarial risk analysis: several approaches • Final questions

3. Background: Risk analysis • Risk assessment. Information on the extent and characteristics of risk attributed to a hazard. • Risk management. Activities undertaken to control the hazard • Risk communication. Exchange of info and opinion concerning risk and risk-related factors among risk assessors, risk managers and other interested parties.

4. Background: Our interest in RA • Interest in risk management in project management driven by auctions • Interest in negotiation analysis in political decision making

5. Background:Risk: challenges in a complex world • Sao Paulo airport accident Population has increased: facilities previously remote, now close to lots of population • Chinese toys Use of toxic or potentially toxic materials increased, genetically modified organisms • Climate change Public much more aware of hazards posed to humans • Estonian hacker attack Need to protect critical infrastructures to assure continuity of a nation. Interconnected international infrastructures • EU Water directives Government agencies tend to involve the public, multiplicity of stakeholders Awareness about equity with respect to risks • …..

6. Back: Risk mgt in project mgt • Standard practice 1 Increase costs by a default 25%. If very uncertain, further add 5% … Risk management is current top priority for top executives • Standard practice 2 For each incurred cost: provide minimum, most likely, maximum. Fit triangular distributions. Simulate.

7. Background: risk mgt in ICT • Singpurwalla (2006) … they often do a credible job analyzing the causes of software failure, but then quantify their uncertainties using a myriad of analytical techniques, many of them ad hoc. This has caused concern about the state-of-the-art of software risk assessment… • www.enisa.europa.eu/rmra/rm_ra_tools.html • (2007) Putting numbers on such risks may be at best dubious and at worse will only result in spurious accuracy • Probabilities (ordinal scale) 1 zero, 2 very low,…., 6 very high, 7 certain • Impact (ordinal scale) 1 none, 2 small, 3 large, 4 catastrophic • Comparison with current system 1 additional, 2 increased, 3 neutral, 4 decreased, 5 eliminated

8. Background: Many criteria, guiding principles, some unformalised • Many methods for assessing (eg Covello, Merkhofer, 93) and expressing (eg Stern, Fineburg 96) • Value at Risk Maximum loss over a target horizon such that there is a low, prespecified probability (defined as the confidence level) that the actual loss will be larger • As Low as Reasonably Practicable/Achievable Ideal and Upper Limits to probability of death as a result of operation of a system

9. Question 1 • Many unformalised criteria, very different in various fields. Could we unify them through decision theory, decision analysis?

10. A framework for risk analysis/mgt: starting assumptions • Firstly informed by project management, auctions. Later by counterterrorism • Only interested in (project) cost, initially • An existing project design, initially • Only another participant (if any) • Aim. Maximise expected utility (most times)

11. Risk analysis and mgt. framework (Single DM) • Forecast costs under normal circumstances • Identify hazard events, estimate probabilities and impacts on costs (additional induced costs) • Forecast costs (a “mixture” model). Compute expected utility • Identify interventions, estimate impact on probabilities and/or costs. • Compute expected utilities. Choose best intervention

12. Basic setting • Design given (no interventions, status quo)

13. Question 2. Uncertainty in costs?? • SAMSI RA-EV-DT page To a significant extent costs are not treated as random • RAND, 2006. Better methods for analyzing Cost Uncertainty can improve acquisition decisionmaking OSD have historically underestimated the cost of buying new weapon systems • Davey (2000) Preventing project escalation costs • Garvey (2000) Probability Methods for Cost Uncertainty Analysis

14. Question 2. Uncertainty in costs?? • Model (Palomo, RI, Ruggeri, 2008) • Impact of future technological Advances (Harville, Yaschin, 2007)

15. Basic setting • Design given • Including choice of design

16. Risk assessement • Likelihood and impact of identified hazards: • Expected utility after risk assessed: • Impact of risks:

17. Question 3? Modeling hazards: Risk assessment • Extreme event models • As in Palomo, Rios Insua, Ruggeri (2007) • K potentially disruptive events+nothing happens. “Beta binomial” for their probabilities q • Independent case • Beta marginals+Deterministic constraints • Copulas • Limiting interactions (Dirichlet-multinomial) • Gravity (Additional cost). (max, min, mode) Beta

18. Risk management • Intervention to be chosen: • Gain through managed risk:

19. Adversarial risks • Other intelligent participants Auctions for large projects, Counterterrorism, Regulators,… • Their actions influence my risks • My actions influence their risks • Some nodes might be shared… • Possibly conflicting interests, but possibly cooperating,…

20. Adversarial risks: Just me

21. Adversarial risks: Me and other

22. Adversarial risks: Modelling 3

23. Adversarial risks. Solving 1 Game Theoretic approach • Forecast costs and model preferences for me • Forecast costs under normal circumstances • It. under abnormal circumstances (RA) • Model preferences • Estimate costs and preferences for others • Solve problem (Nash equilibrium??) • Summarise solutions

24. Adversarial risks. Solving 2 Game Theoretic approach Computing best responses • Computing my best intervention given… • Computing my best strategy given…

25. Adversarial risks. Solving 3 Game Theoretic approach • Iterative elimination of dominated actions Mainly used in discrete settings but SEF Sample policies, Evaluate policies, Filter dominated ones May be used to focus attention on interesting policies

26. Adversarial risks. Solving 4 Game Theoretic approach • Nash equilibrium

27. Adversarial risks. Solving 5 Game Theoretic approach • Nash equilibrium (Auctions with risk I) Decision to be made: bid If winner, win bid-costs (once costs realised) If not, win 0

28. Adversarial risks. Solving 5 bis Game Theoretic approach • Nash equilibrium (Auctions with risk II)

29. Adversarial risks. Solving 5 tris Game Theoretic approach • Nash equilibrium (Auctions with risk III) Under certain technical general conditions, if all participants are constant risk averse, there is a unique equilibrium Palomo, Rios Insua, Ruggeri (2008)….

30. Adversarial risks. Questions 4,5,6… Game Theoretic approach • Compute equilibria in influence diagrams, Common and uncommon structures (Koller and Milsch, 2003; Rios and Rios Insua, 2008;…) • Compute equilibria for various types of utility functions • Summarise solutions • Efficient implementations of SEF • Role of MCMC (Augmented probability simulation) • ….

31. Adversarial risks. Solving 6 Game Theoretic approach • Critics to game theoretic approach • Full and common knowledge of the game by the players… • FOTE, FOTID • Simultaneous decision making… • What if not unique… • Social dilemmas • Implementation of security initiatives in international networks requires contribution of all members • each member is better off if he defects and the rest contribute • But if everyone defects the result is worse than if they would cooperate • Cooperation incentives • Disclose free rider identities, reward for cooperation, punishment for defect,.. • Equilibria are not tools for giving partisanadvise

32. Adversarial risks: Bayesian approach • An symmetrically prescriptive/descriptive approach to negotiation analysis (Raiffa, Kadane, Larkey,…) • Prescriptive advice to one party conditional on a (probabilistic) description of how others will behave • Based on MABOO analysis from auctions • Estimate • Probabilities of the other’s uncertain costsThink about how the other would assess these probabilities • Preferences of the other over his costs • Treat the other participant decisions as uncertain • Assess probabilities over the others’ decision actions • Choose strategy that maximises my expected utility

33. Adversarial risks: Bayesian approach

34. Question 7 • How to assess the probability of other participant’s actions, e.g. • Sensitivity/Robustness analysis

35. Adversarial risks. A negotiation approach • Even in disputed settings, negotiate • Terrorism, example of Spain • Until a few months ago, government negotiating with Basque terrorist organisation; the opposition party strongly against it. Now, at least in public, no negotiations. • Auctions, temporary unions of (competing) enterprises • Cooperation between France and Spain against terrorism • Negotiation: a decision making process in which two or more parts communicate and exchange ideas, arguments and offers to satisfy their needs and achieve their objectives educating and informing their rivals, possibly modifying their relations and making concessions to reach an agreement (Concessions, Joint gains, Pareto frontier exploration)

36. Adversarial risks: How to reach a solution? Balanced increment method • Bliss point, Kalai-Smorodinsky solution

37. Adversarial risks: Negotiations with BIM, first steps • Desirable properties of a negotiated solution: • Feasibility • Efficiency • Fairness Discreteness Rios, Kim, Rios Insua (2007) UTILITY SPACE

38. Questions BIM and other methods like BCM? How do they compare Computational implementations in specific structures like influence diagrams Role of MCMC (augmented probability simulation) …

39. Negotiations for adversarial risks. Intervention portfolios • Security system • FMEA • Critical event (successful terrorist attack): E • Failure modes: • Logical relations between them, e.g. • Adversarial agent 's (terrorists) possible actions: • Elicit probabilities of failure modes given adversarial actions and probabilities of each adversarial action

40. Negotiations for adversarial risks. Intervention portfolios • Compute probability of critical event under the logical model (ind) • Is it below an acceptable bound,

41. Questions • Probability elicitations • Include consequences (not just successful attack) • Formalise through DT • Assess acceptable level • Should we consider values form experts, public, stakeholders?

42. Negotiations for adversarial risks. Intervention portfolios • If not acceptable • Propose interventions improving failure mode occurrence • Interventions entail limited resource consumption (money, human resources, …) • C: maximum amount of money that can be spent • H: human resources • R: other limited resources • Each proposal needs • ci euros • hi people working on it • ri units of other limited resources

43. If proposal i is implemented Choosing a portfolio of interventions to improve system security affordable under limited resources Negotiations for adversarial risks. Intervention portfolios

44. Negotiations for adversarial risks. Intervention portfolios • Portfolio of intervention proposals • A feasible portfolio F should satisfy • Select feasible portfolio of proposals which minimise failure probability p(E|F)?

45. Negotiations for adversarial risks. Intervention portfolios • Assessment of P(E|F) • probabilities of adversarial actions (may be influenced by F) • probabilities of failure modes when F is implemented

46. Negotiations for adversarial risks. Intervention portfolios • P(E|F) under the previous logical model ( ) ind • Optimization problem • Is p* below acceptable bounds,

47. Questions • Effective reassessment of probabilities • Computation of objective function (when dependencies arise) • Efficient solution of problem • Other formulations Minimise costs for acceptable solution

48. Negotiations for adversarial risks. Intervention portfolios • If optimal portfolio of interventions not acceptable? • Acceptable failure risk as a constraint • Nondominated (infeasible) portfolios: P.F.(c,h,r) • How to select a unique F* such that • Multiobjective optimization: • Goal programming: • Goal G:= (C,H,R) • Look for a point x := (c; h; r) such that

49. Question • Acceptable but infeasible interventions F.P.(c,h,r) & F* can be used as preparation for a negotiation with somebody for additional resources • How to conduct such negotiations? • Add new issues and trade them for necessary resources • Logrolling

50. Negotiations for adversarial risks. Risk sharing negotiations • Terrorism as an international problem • Uncertainty about which countries are targets of terrorism • Responses to terrorist attacks (ex-post antiterrorist actions) requires resources that not all countries have • This leads to international antiterrorist cooperation • How to negotiate a priori a contingent ex-post antiterrorist response? • Sharing risks & resources