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 pre-requisites.

Pre-requisites: ST115 Introduction to Probability OR ST111 Probability A.

Module web page

Module aims

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.

1. Introduction and motivation

• Examples covering all parts of the module
• Some inspiring questions
• Overview

1. Concepts of probability

• Axiomatic
• Propensity interpretation
• Frequentist interpretation
• Subjective probability
• Descriptive aspects of probability (empirically demonstrated aspects of perception of randomness and risk)

1. Normative theory for decision-making under uncertainty and ambiguity

• Preferences
• Elicitation (with explicit examples who this can be done via interviews, expert opinions etc)
• Expected unitility theory

1. Descriptive theory for decision-making 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 non-normative behaviour through training

1. Games

• Combinatorial games (winning strategy, examples, unsolved examples)
• Zero-sum games (von Neumann's Minimax theorem, separability, domination, symmetry)
• General-sum 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