1 decision theory and risk analysis: some organising questions david rios insua jesus rios risk...

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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

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Outline

Background

Risk analysis: framework

Adversarial risk analysis: several approaches

Final questions

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Background: Risk analysis

1. Risk assessment. Information on the extent and characteristics of risk attributed to a hazard.

2. Risk management. Activities undertaken to control the hazard

3. Risk communication. Exchange of info and opinion concerning risk and risk-related factors among risk assessors, risk managers and other interested parties.

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Background: Our interest in RA

Interest in risk management in project management driven by auctions

Interest in negotiation analysis in political decision making

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Background:Risk: challenges in a complex world

Sao Paulo airport accidentPopulation has increased: facilities previously remote, now close to lots of

population

Chinese toysUse of toxic or potentially toxic materials increased, genetically modified

organisms

Climate change Public much more aware of hazards posed to humans

Estonian hacker attackNeed to protect critical infrastructures to assure continuity of a nation.

Interconnected international infrastructures

EU Water directivesGovernment agencies tend to involve the public, multiplicity of stakeholdersAwareness about equity with respect to risks

…..

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Back: Risk mgt in project mgt Standard practice 1Increase costs by a default 25%. If very uncertain,

further add 5%…Risk management is current top priority for top

executives

Standard practice 2For each incurred cost: provide minimum, most

likely, maximum. Fit triangular distributions. Simulate.

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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 system1 additional, 2 increased, 3 neutral, 4 decreased, 5 eliminated

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Background: Many criteria, guiding principles, some unformalised

Many methods for assessing (eg Covello, Merkhofer, 93) and expressing (eg Stern, Fineburg 96)

Value at RiskMaximum 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

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Question 1

Many unformalised criteria, very different in various fields.

Could we unify them through decision theory, decision analysis?

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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)

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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

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Basic setting

Design given (no interventions, status quo)

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Question 2. Uncertainty in costs??

SAMSI RA-EV-DT pageTo 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

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Question 2. Uncertainty in costs??

Model (Palomo, RI, Ruggeri, 2008)

Impact of future technological Advances (Harville, Yaschin, 2007)

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Basic setting

Design given

Including choice of design

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Risk assessement

Impact of risks:

Expected utility after risk assessed:

Likelihood and impact of identified hazards:

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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

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Risk management Intervention to be chosen:

Gain through managed risk:

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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,…

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Adversarial risks: Just me

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Adversarial risks: Me and other

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Adversarial risks: Modelling 3

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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

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Adversarial risks. Solving 2 Game Theoretic approach

Computing best responses Computing my best intervention

given…

Computing my best strategy given…

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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

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Adversarial risks. Solving 4 Game Theoretic approach

Nash equilibrium

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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

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Adversarial risks. Solving 5 bis Game Theoretic approach

Nash equilibrium (Auctions with risk II)

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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)….

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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)

….

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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 partisan advise

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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

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Adversarial risks: Bayesian approach

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Question 7

How to assess the probability of other participant’s actions, e.g.

Sensitivity/Robustness analysis

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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)

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Adversarial risks: How to reach a solution? Balanced increment method

Bliss point, Kalai-Smorodinsky solution

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Adversarial risks: Negotiations with BIM, first steps

Desirable properties of a negotiated solution: Feasibility Efficiency Fairness

Discreteness

Rios, Kim,Rios Insua (2007)

UTILITY SPACE

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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)

…

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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

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Negotiations for adversarial risks. Intervention portfolios

Compute probability of critical event under the logical model

(ind)

Is it below an acceptable bound,

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Questions Probability elicitations

Include consequences (not just successful attack)

Formalise through DT

Assess acceptable level

Should we consider values form experts, public, stakeholders?

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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

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Negotiations for adversarial risks. Intervention portfolios

If proposal i is implemented

Choosing a portfolio of interventions to improve system security affordable under limited resources

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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)?

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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

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Negotiations for adversarial risks. Intervention portfolios

P(E|F) under the previous logical model ( ) ind

Optimization problem

Is p* below acceptable bounds,

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Questions

Effective reassessment of probabilities

Computation of objective function (when dependencies arise)

Efficient solution of problem

Other formulations Minimise costs for acceptable solution

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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

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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

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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

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Negotiations for adversarial risks. Risk sharing negotiaitions

Participants Governments of two negotiating countries (G and G’ ) Terrorists (T)

T's possible actions:

Resources needed to respond to : x*

G and G’ negotiate who contributes with how much resources

Contribution of G : x Contribution of G’ : x’

Negotiators’ bottom line Limited resources of G: R

x < R Limited resources of G’: R’

x’ < R’

x + x’ >= x*

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Negotiations for adversarial risks. Risk sharing negotiations

Set resource contributions depend on what T will do

Probabilistic assessments over Viewpoint of G :

Viewpoint of G’ :

A contingent contract specifies each one’s contribution per

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Negotiations for adversarial risks. Risk sharing negotiations

G and G’ agree on the contingent contract

Analysis of joint gain opportunities FOTE or FOTID Is agreement Q a dominated contract?

G: G’:

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Negotiations for adversarial risks. Risk sharing negotiations

R

R’

x

x’Q

G

G’

min

mi

n

Joint gains

Bliss point

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Questions

Securing insecure agreements Is agreement Q secure? Convert agreement Q in a Nash equilibrium

Do we implement BIM or BCM or …

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Some final questions Public involvement in risk analysis is increasing

Producing better decisions and outcomes Changing the manner in which decisions are made or deliberations are

conducted Better information, better communication, increased confidence in institutions,

…

More costs, Delayed processes

Deliberative polls Referenda Workshops Negotiated rule making …

How to rationally support public involvement? E-democracy, E-participation

Gregory, Fischoff, Mac Daniels (2005), Rios Insua, Kersten, Rios (2007)

Risk communication

What if not only cost??

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IT COULD BE A FUN AT RISK YEAR AT SAMSI !!!!