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Evolutionary Game Theory (MATH 30050)

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Administrative Information

  1. Unit number and title: MATH 30050 Evolutionary Game Theory
  2. Level: H/6
  3. Credit point value: 10 credit points
  4. Year: 12/13
  5. First Given in this form: 2008-9
  6. Unit Organiser: John McNamara, FRS
  7. Lecturer: Prof J M McNamara
  8. Teaching block: 2
  9. Prerequisites: MATH11300 Probability 1

Unit aims

To introduce evolutionary game theory; a modelling framework in biology which can be used to analyse optimal decision making by organisms when the fitness of an organism depends on the behaviour of others.

General Description of the Unit

Behavioural ecology is a branch of biology which is concerned with the natural behaviour of organisms, the evolution of this behaviour and its ecological consequences. Activities which are important for reproduction and survival will be shaped by natural selection so that behaviour is approximately optimal given the animal's environment and constraints. It is thus possible to explain much behaviour in terms of maximisation of fitness.

The fitness of one organism in a population often depends on the behaviour of other population members. When this is the case we can model the outcomes of the process of natural selection using evolutionary game theory. This course will concentrate exclusively on evolutionary game theory. It will introduce basic concepts and basic examples. It will then go on to outline a variety of conceptual issues, ranging from deciding the sex of offspring, to the conflict between parents over care of common young and the evolution of cooperation.

Although the concepts in this course are motivated by biology, many are relevant to other areas. In particular, many of the concepts are common to both evolution and economics.

Although the course will be mathematical, using fairly simple results from probability, the emphasis will be on concepts and their application rather than mathematical proofs.

Relation to Other Units

The units Financial Mathematics, Introduction to Queuing Networks, and Evolutionary Game Theory apply probabilistic methods to problems arising in various fields.

Teaching Methods

Lectures, lecture notes and material on problems sheets cover the syllabus. Problem sheets with full solutions are supplied.

Learning Objectives

After taking this unit, the student should:

  • be aware of a range of important issues within the field of behavioural ecology;
  • have developed skills in constructing mathematical models of biological and other systems;
  • have learnt the basics of game theory.

Assessment Methods

The final assessment mark for Evolutionary Game Theory is calculated from a 1 ½-hour written examination in May/June consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators are not permitted.

 

Award of Credit Points

Credit points are gained by:

  • either passing the unit,
  • or getting an examination mark of 30 or over, and also handing in satisfactory attempts at four specified homework questions, to be given out at various times over the course.

Transferable Skills

Construction of mathematical models of phenomena: that is the ability to translate a real world problem into mathematics.

Texts

 As there is no ideal course book lecture notes will be available on Blackboard. An overview written for biologists will also be available on Blackboard.

The following also contains useful background:

J Maynard Smith, Evolution and the Theory of Games, Cambridge University Press (1982).

Syllabus

NOTE: The numbers of lectures given here are rough approximations only.

Introduction and motivation. The Hawk-Dove game. Sex ratio games. Nash equilibria (3 lectures).

Evolutionary stability: refinement of the Nash concept to that of an ESS (2 lectures).

Two-player games with well-defined roles. Respect for ownership. (1 lecture).

Altruism. The prisoner's dilemma game and the evolution of cooperation (2 lectures).

Games between parents over care of their young. The importance of decision processes (1 lecture).

Credible threats and promises. Informational asymmetries and self binding. Limit ESS (1 lecture).

Honest signalling and the handicap principle (1 lecture).

Replicator dynamics (2 lectures).

Continuous stability and adaptive dynamics (2 lectures).