SDM summary 23/24
Week 1 – introduction.................................................................................................................................... 2
Basic terminology.................................................................................................................................................2
Decision theory.....................................................................................................................................................3
Elementary decision rules.....................................................................................................................................4
Decisions involving multiple objectives................................................................................................................4
MCDA....................................................................................................................................................................6
SMART..................................................................................................................................................................8
Other subtypes of MCDA....................................................................................................................................10
Week 2 – DM under risk............................................................................................................................... 11
Decision making under risk................................................................................................................................11
Heuristics and biases..........................................................................................................................................12
Decision framing and cognitive inertia..............................................................................................................14
Expected monetary value (EMV)........................................................................................................................15
Expected utility theory (EUT)..............................................................................................................................16
Prospect theory (PT) – Tversky & Kahneman 1986 and Holmes et al. 2011......................................................19
Week 3 – DM under uncertainty and structural ignorance............................................................................22
DM under uncertainty........................................................................................................................................22
DM under structural ignorance..........................................................................................................................28
Week 4 – Collective decision making............................................................................................................ 32
Social choice theory............................................................................................................................................32
Mathematical aggregation................................................................................................................................32
Behavioral aggregation......................................................................................................................................33
Voting rules........................................................................................................................................................34
Week 5 – Basics of Game Theory.................................................................................................................. 39
Basics of game theory........................................................................................................................................39
Equilibria and strategies.....................................................................................................................................40
Simultaneous versus sequential games.............................................................................................................41
Classic games.....................................................................................................................................................43
Week 6 – Game Theory part II...................................................................................................................... 45
Mixed strategies.................................................................................................................................................45
Evolutionary games............................................................................................................................................46
Repeated games.................................................................................................................................................46
1
, Week 7 – Cooperative Game Theory............................................................................................................. 48
Bargaining and negotiations..............................................................................................................................48
Coalition games..................................................................................................................................................48
Week 1 – introduction
Basic terminology
Decision making = process of selecting an alternative from a set of mutually exclusive
alternatives. We assume structure drives behavior, so we try to structure the process in the best
way.
Decision analysis = decomposing the decision problem into a smaller set of problems. Smaller
problems are then dealt with.
Strategic decision making = we can’t influence the competitors or environment in which the
decision must be made. The consequences of the alternatives we choose depend on the choices
made by competitors. We must anticipate the risk in the environment, as we cannot control this.
Rational decision making = selecting a best alternative from a set of mutually exclusive
alternatives.
Rational = selecting what is best. Identifying a “best” requires preferences regarding the
outcomes, which assumes we value some things to be more important than others. There is a
discussion regarding what rationality really is, but we see it as “being able to select a best”.
rationality has two components: behavioral (the act of selecting the best alternative) and
latent (hidden preference for an alternative that cannot be directly observed).
Type of DM problems:
- Decision making under certainty = the outcome is known for every alternative.
- Decision making under risk = multiple outcomes for (some of) the alternatives, probabilities
for arriving at each outcome can be calculated.
- Decision making under uncertainty = multiple outcomes for (some of) the alternatives,
probabilities for arriving at each outcome cannot be calculated.
- Decision making under structural ignorance = (some of the) outcomes for alternatives are
unknown. Then we don’t know the consequences and probability distribution.
In the real world the differences between these become fluid. But the calculations we make
serve to enhance the conceptual understanding of the DM situation.
Individual decision making = one individual tries to find the best decision.
- Based on values and preferences: MCDA, SMART, AHP.
- Accounting for risk: EUT
- Based on framing of risks: prospect theory
- Based on uncertainty: Bayesian logic
- In situations of structural ignorance: case-based decision making.
2
,Collective decision making = group of individuals must collectively find best decision.
- Based on DM-rules and procedures: social choice theory.
- By looking at the other players: game theory (GT).
o Without ability to make (binding) agreements: non-cooperative GT.
o With ability to make (binding) agreements: cooperative GT.
- By modelling situations with more than two players: coalition formation.
Decision theory
Hypothesis = presumption derived from a theory that can be tested with empirical research.
Theory = coherent set of propositions that serve to describe and explain a particular
phenomenon (here: decision-making).
Three branches of decision theory (DT):
1- Descriptive/positive DT = study of how real decision makers actually make decisions
behavioral model. Descriptive because want to understand how it actually works.
2- Normative DT = study of how decisions makers ought to take decisions.
3- Prescriptive/facilitated DT = study of how decision makers could take (better) decisions.
In this course we discuss descriptive and prescriptive.
When building a theory you start with a set of universal propositions, then build a formal theory
(try to decide what a good DM process looks like) and then derive a thereom. This is a general
proposition that is not self-evident (not evidently true but can be tested).
The following building blocks are needed to build the theory:
- Primitive terms = terms which meaning is immediately understood.
- Definitions = to define meaning of terms that are not immediately understood.
- Propositions = universal statements that can be true/not true and must be tested.
- Statements = made with the building blocks above.
o Primitive statements = propositions that are plausible a priori or evidently true.
o Derived statements = deduced from primitive statements using logic.
o Empirical statements = hypotheses propositions that are true or not true based on
the empirical evidence.
Axiom = set of generally accepted propositions or a formalization of common sense.
To build a theory and find the best decision, the following axioms must be fulfilled:
- Completeness = choices must be preferences and ranked.
- Transitivity = there must be an ending choice. Non-transitivity is when there is a cyclical
preference, so not 1 option ranked the highest.
transitivity = x>y, and y>z, then x > z.
Decision problem = set of mutually exclusive alternatives, denoted by X.
One alternative = denoted by x.
Existence preferences = each decision maker has preferences, denoted by R. Having preferences
and being able to order them, means there is a best alternative in the set of options.
Choice function = denoted by C.
Attribute = used to measure performance in relation to an objective.
Value/utility function = assign to each alternative x a value u, to order the preferences.
value = decision involves no risk and uncertainty.
3
, utility = decision involves risk and uncertainty.
Elementary decision rules
Decision matrix
- Rows: alternatives (options/choices)
- Columns: consequences (outcomes)
- Cells: value/utility of outcome.
Decision tree sequential DM.
Influence diagrams sets of interconnected decisions and events.
Two decision rules:
1- Regret rule = minimize the maximal regret
after making the choice.
DM under certainty.
Step 1- construct decision matrix.
Step 2- what is the max. utility per column.
6, 2 and 5.
Step 3- construct regret matrix. Utility in every
cell is the max. regret if that option is chosen.
Column 1 money, science has value of 0, so
regret of 6.
Step 4 – choose minimum of the maximum
regret.
Column 1, lowest regret is 3.
2- Maxmin rule = select the best of the worst.
DM under uncertainty.
Step 1- take the minimum of each row.
Step 2- take the maximum of the minimum
values.
Step 3- corresponding row is decision.
Decisions involving multiple objectives.
Intuitive decision making = making decisions without structure from DM method.
Bounded rationality = limitations of the human mind makes them use ‘heuristics’ to deal with
most decision problems. They seek satisfactory instead of optimal courses of action.
Heuristics = simple strategies/mental processes that humans, animals, organizations, and
machines use to quickly form judgments, make decisions and find solutions to complex
problems. Can be compensatory (poor performance on one attribute is compensated by good
performance on others, requires more effort) or non-compensatory.
Type of heuristics:
4
Week 1 – introduction.................................................................................................................................... 2
Basic terminology.................................................................................................................................................2
Decision theory.....................................................................................................................................................3
Elementary decision rules.....................................................................................................................................4
Decisions involving multiple objectives................................................................................................................4
MCDA....................................................................................................................................................................6
SMART..................................................................................................................................................................8
Other subtypes of MCDA....................................................................................................................................10
Week 2 – DM under risk............................................................................................................................... 11
Decision making under risk................................................................................................................................11
Heuristics and biases..........................................................................................................................................12
Decision framing and cognitive inertia..............................................................................................................14
Expected monetary value (EMV)........................................................................................................................15
Expected utility theory (EUT)..............................................................................................................................16
Prospect theory (PT) – Tversky & Kahneman 1986 and Holmes et al. 2011......................................................19
Week 3 – DM under uncertainty and structural ignorance............................................................................22
DM under uncertainty........................................................................................................................................22
DM under structural ignorance..........................................................................................................................28
Week 4 – Collective decision making............................................................................................................ 32
Social choice theory............................................................................................................................................32
Mathematical aggregation................................................................................................................................32
Behavioral aggregation......................................................................................................................................33
Voting rules........................................................................................................................................................34
Week 5 – Basics of Game Theory.................................................................................................................. 39
Basics of game theory........................................................................................................................................39
Equilibria and strategies.....................................................................................................................................40
Simultaneous versus sequential games.............................................................................................................41
Classic games.....................................................................................................................................................43
Week 6 – Game Theory part II...................................................................................................................... 45
Mixed strategies.................................................................................................................................................45
Evolutionary games............................................................................................................................................46
Repeated games.................................................................................................................................................46
1
, Week 7 – Cooperative Game Theory............................................................................................................. 48
Bargaining and negotiations..............................................................................................................................48
Coalition games..................................................................................................................................................48
Week 1 – introduction
Basic terminology
Decision making = process of selecting an alternative from a set of mutually exclusive
alternatives. We assume structure drives behavior, so we try to structure the process in the best
way.
Decision analysis = decomposing the decision problem into a smaller set of problems. Smaller
problems are then dealt with.
Strategic decision making = we can’t influence the competitors or environment in which the
decision must be made. The consequences of the alternatives we choose depend on the choices
made by competitors. We must anticipate the risk in the environment, as we cannot control this.
Rational decision making = selecting a best alternative from a set of mutually exclusive
alternatives.
Rational = selecting what is best. Identifying a “best” requires preferences regarding the
outcomes, which assumes we value some things to be more important than others. There is a
discussion regarding what rationality really is, but we see it as “being able to select a best”.
rationality has two components: behavioral (the act of selecting the best alternative) and
latent (hidden preference for an alternative that cannot be directly observed).
Type of DM problems:
- Decision making under certainty = the outcome is known for every alternative.
- Decision making under risk = multiple outcomes for (some of) the alternatives, probabilities
for arriving at each outcome can be calculated.
- Decision making under uncertainty = multiple outcomes for (some of) the alternatives,
probabilities for arriving at each outcome cannot be calculated.
- Decision making under structural ignorance = (some of the) outcomes for alternatives are
unknown. Then we don’t know the consequences and probability distribution.
In the real world the differences between these become fluid. But the calculations we make
serve to enhance the conceptual understanding of the DM situation.
Individual decision making = one individual tries to find the best decision.
- Based on values and preferences: MCDA, SMART, AHP.
- Accounting for risk: EUT
- Based on framing of risks: prospect theory
- Based on uncertainty: Bayesian logic
- In situations of structural ignorance: case-based decision making.
2
,Collective decision making = group of individuals must collectively find best decision.
- Based on DM-rules and procedures: social choice theory.
- By looking at the other players: game theory (GT).
o Without ability to make (binding) agreements: non-cooperative GT.
o With ability to make (binding) agreements: cooperative GT.
- By modelling situations with more than two players: coalition formation.
Decision theory
Hypothesis = presumption derived from a theory that can be tested with empirical research.
Theory = coherent set of propositions that serve to describe and explain a particular
phenomenon (here: decision-making).
Three branches of decision theory (DT):
1- Descriptive/positive DT = study of how real decision makers actually make decisions
behavioral model. Descriptive because want to understand how it actually works.
2- Normative DT = study of how decisions makers ought to take decisions.
3- Prescriptive/facilitated DT = study of how decision makers could take (better) decisions.
In this course we discuss descriptive and prescriptive.
When building a theory you start with a set of universal propositions, then build a formal theory
(try to decide what a good DM process looks like) and then derive a thereom. This is a general
proposition that is not self-evident (not evidently true but can be tested).
The following building blocks are needed to build the theory:
- Primitive terms = terms which meaning is immediately understood.
- Definitions = to define meaning of terms that are not immediately understood.
- Propositions = universal statements that can be true/not true and must be tested.
- Statements = made with the building blocks above.
o Primitive statements = propositions that are plausible a priori or evidently true.
o Derived statements = deduced from primitive statements using logic.
o Empirical statements = hypotheses propositions that are true or not true based on
the empirical evidence.
Axiom = set of generally accepted propositions or a formalization of common sense.
To build a theory and find the best decision, the following axioms must be fulfilled:
- Completeness = choices must be preferences and ranked.
- Transitivity = there must be an ending choice. Non-transitivity is when there is a cyclical
preference, so not 1 option ranked the highest.
transitivity = x>y, and y>z, then x > z.
Decision problem = set of mutually exclusive alternatives, denoted by X.
One alternative = denoted by x.
Existence preferences = each decision maker has preferences, denoted by R. Having preferences
and being able to order them, means there is a best alternative in the set of options.
Choice function = denoted by C.
Attribute = used to measure performance in relation to an objective.
Value/utility function = assign to each alternative x a value u, to order the preferences.
value = decision involves no risk and uncertainty.
3
, utility = decision involves risk and uncertainty.
Elementary decision rules
Decision matrix
- Rows: alternatives (options/choices)
- Columns: consequences (outcomes)
- Cells: value/utility of outcome.
Decision tree sequential DM.
Influence diagrams sets of interconnected decisions and events.
Two decision rules:
1- Regret rule = minimize the maximal regret
after making the choice.
DM under certainty.
Step 1- construct decision matrix.
Step 2- what is the max. utility per column.
6, 2 and 5.
Step 3- construct regret matrix. Utility in every
cell is the max. regret if that option is chosen.
Column 1 money, science has value of 0, so
regret of 6.
Step 4 – choose minimum of the maximum
regret.
Column 1, lowest regret is 3.
2- Maxmin rule = select the best of the worst.
DM under uncertainty.
Step 1- take the minimum of each row.
Step 2- take the maximum of the minimum
values.
Step 3- corresponding row is decision.
Decisions involving multiple objectives.
Intuitive decision making = making decisions without structure from DM method.
Bounded rationality = limitations of the human mind makes them use ‘heuristics’ to deal with
most decision problems. They seek satisfactory instead of optimal courses of action.
Heuristics = simple strategies/mental processes that humans, animals, organizations, and
machines use to quickly form judgments, make decisions and find solutions to complex
problems. Can be compensatory (poor performance on one attribute is compensated by good
performance on others, requires more effort) or non-compensatory.
Type of heuristics:
4
