Mathematical Economics - ECO00007H

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Module summary

Game theory models conflict and cooperation between rational decision-making agents. It has applications in a wide variety of areas, including statistical decision theory, artificial intelligence (online learning, multi-agent systems), economics and business (auctions, pricing, bargaining), biology (evolution, signaling behavior, fighting behavior), political science (stability of government, military strategy), and philosophy (ethics, morality and social norms).

Related modules

Additional information

Game theory analyses strategic interaction using abstract mathematical models and formal reasoning. The module requires some basic calculus and algebra as well as familiarity with concepts such as sets, probability and mathematical optimisation.

Module will run

Occurrence	Teaching period
A	Autumn Term 2022-23 to Spring Term 2022-23

Module aims

Teach students to use game theoretic reasoning to understand how individual incentives can shape strategic outcomes in a range of hypothetical situations and real-life applications.

Module learning outcomes

On completing the module a student will be able to:

• Have acquired a small set of analytical methods of argument and proof
• Have developed problem solving skills in formally stated economic problems
• Appreciate the links between economic theory and formal mathematical analysis
• Have acquired a set of analytical methods, and practice and skill in using them in problem solving; and an appreciation of how the economic theory works in these areas

Module content

In Mathematical Economics, we discuss the essential elements and tools of analysis for game theory. We will consider “one-shot” and sequential games and discuss different solution concepts to form predictions for strategic outcomes. In the later part of the module, we study games with incomplete information in which one or more players may have private information about some aspect of the game. In this case, some players will face uncertainty about the actual game that they are playing, and as a result must form beliefs about the other players and the game when making decisions. We also look at social choice and mechanism design which turns the analysis that we have done so far on its head: instead of fixing a game and analysing the potential outcome, we fix the desired outcome, and ask what type of game can induce this outcome as equilibrium. You can think of this as some sort of economic engineering process which has been applied for the design of auctions and the distributions of food among food banks among others.

Indicative assessment

Task	% of module mark
Online Exam -less than 24hrs (Centrally scheduled)	100

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Online Exam -less than 24hrs (Centrally scheduled)	100

Module feedback

• Procedural: Through seminars and problem sets for these seminars. In advance of each seminar you should work on the problem set and prepare your answer. You will be expected to be able to participate in analysing and discussing these questions. The precise format of seminars may vary. Your tutor will give you further guidance on this.
• Final: There will be a 3-hour unseen examination in the Summer Term.

Indicative reading

• Osborne, M.J. (2004). An Introduction to Game Theory. Oxford.
• Watson, Joel (2013, 3 edition) Strategy: An Introduction to Game Theory. Norton.
• Mas-Colell, A., Whinston, M.D. and Green, J.R. (1995). Microeconomic Theory. Oxford University Press.
• Gibbons, R. (1992). A Primer in Game Theory. Prentice-Hall.