Introductory description
This module runs in Term 1 and is available for students on a course where it is a listed option and as an Unusual Option for students who have taken the prerequisites.
Prerequisites: ST115 Introduction to Probability OR ST111 Probability A.
Module web page
Module aims
Throughout their history, game and decision theories have used ideas from mathematics and probability to help understand, explain and direct human behaviour.
Questions explored in the module include: What is probability? A set of axioms, a relative amount of outcomes, a belief? And how can this be elicited? What guides decisionmaking when outcomes are uncertain? What happens when information is only partial or ambiguous? What if there is more than one person, or how are decisions made in games? How do people perceive and evaluate probabilities and risks? Are they acting rationally or not? Which heuristics and biases come into play? Under which conditions do they occur, and how do they impact decisionmaking?
Answer will be embedded into theories and illustrated with practical examples from a wide range of applications including engineering, economics, finance, business, sciences, psychology and medicine.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Introduction and motivation
 Examples covering all parts of the module
 Some inspiring questions
 Overview
 Concepts of probability
 Axiomatic
 Propensity interpretation
 Frequentist interpretation
 Subjective probability
 Descriptive aspects of probability (empirically demonstrated aspects of perception of randomness and risk)
 Normative theory for decisionmaking under uncertainty and ambiguity
 Preferences
 Elicitation (with explicit examples who this can be done via interviews, expert opinions etc)
 Expected unitility theory
 Descriptive theory for decisionmaking under uncertainty and ambiguity
 Empirically demonstrated confirmation of and deviation from normative theory:
e.g. representativeness heuristic, anchoring, conjunction fallacy, availability heuristics, hindsight bias, ambiguity effect (Allais, Ellsberg paradox)  Models: prospect theory (Kahneman & Tversky), bounded rationality: the adaptive toolbox (Gigerenzer & Selten)
 Discussion: model comparison, feasibility of reduction of nonnormative behaviour through training
 Games
 Combinatorial games (winning strategy, examples, unsolved examples)
 Zerosum games (von Neumann's Minimax theorem, separability, domination, symmetry)
 Generalsum games (Nash equilibrium, evolutionary games, signaling and asymmetric information)
 Cooperative games (Shapley value)
Learning outcomes
By the end of the module, students should be able to:
 Describe the mathematical and philosophical basis for a number of alternative approaches to probability including subjective probability.
 Apply normative decision theory to model decision making in practical examples from a range of applications.
 Understand the foundations of and motivation for descriptive decision theory; describe and model deviations from normative theory in examples.
 Describe the elements of mathematical game theory, apply these to simple mathematical example games and suitable real world scenarios.
Indicative reading list
View reading list on Talis Aspire
Subject specific skills
TBC
Transferable skills
TBC
Study time
Type 
Required 
Optional 
Lectures 
30 sessions of 1 hour (23%)

2 sessions of 1 hour

Private study 
90 hours (68%)


Assessment 
12 hours (9%)


Total 
132 hours 

Private study description
Weekly revision of lecture notes and materials, wider reading, working on practice exercises and preparing for examination.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D

Weighting 
Study time 
Multiple Choice Quizzes

10%

12 hours

A number of multiple choice quizzes which will take place during the term that the module is delivered.

2 hour examination (April)

90%


The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.
~Platforms  Moodle

Assessment group R

Weighting 
Study time 
2 hour examination (September)

100%


The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.
~Platforms  Moodle

Feedback on assessment
Solutions and cohort level feedback will be provided for the examination.
Past exam papers for ST222
Postrequisite modules
If you pass this module, you can take:

EC34115 Mathematical Economics 2: Mechanism Design and Alternative Games
Courses
This module is Optional for:

Year 2 of
USTAG302 Undergraduate Data Science

Year 2 of
USTAG304 Undergraduate Data Science (MSci)

Year 2 of
USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)

Year 2 of
USTAGG14 Undergraduate Mathematics and Statistics (BSc)
This module is Option list A for:

Year 2 of
USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

Year 2 of
UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)

Year 2 of
USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
This module is Option list B for:

Year 2 of
UCSAG4G1 Undergraduate Discrete Mathematics

Year 2 of
UCSAG4G3 Undergraduate Discrete Mathematics

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)

Year 2 of
G105 Mathematics (MMath) with Intercalated Year

Year 3 of
G105 Mathematics (MMath) with Intercalated Year

UMAAG100 Undergraduate Mathematics (BSc)

Year 2 of
G100 Mathematics

Year 3 of
G100 Mathematics

UMAAG103 Undergraduate Mathematics (MMath)

Year 2 of
G103 Mathematics (MMath)

Year 3 of
G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe

Year 2 of
G106 Mathematics (MMath) with Study in Europe

Year 3 of
G106 Mathematics (MMath) with Study in Europe

Year 2 of
UMAAG1NC Undergraduate Mathematics and Business Studies

Year 2 of
UMAAG1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)

Year 2 of
UMAAGL11 Undergraduate Mathematics and Economics

UMAAG101 Undergraduate Mathematics with Intercalated Year

Year 2 of
G101 Mathematics with Intercalated Year

Year 4 of
G101 Mathematics with Intercalated Year