This account contains the report *A survey of Game Theory*, by Graeme Taylor, adapted in various ways to better fit E2's nodal structure (and the confines of imageless HTML). This is fine by Graeme, because I'm him. I check messages here every week or so, but if you find major flaws /msg my main account instead!

Details on the print version are at http://maths.straylight.co.uk/archives/48. Translation from that to this has probably introduced numerous typos or broken layout; let me know if you spot any.

### Notable differences between the print and E2 versions:

- The print version is LaTeX formatted, and thus easier to read and print (cunning, that).
- The E2 version is comprised of multiple nodes, rather than a continuous narrative. I've attempted to make each E2 entry stand alone to a greater extent than the corresponding sections of the print version.
- Two big proofs- Nash's theorem and Shapley's theorem- are offered without proof here on E2, but the proofs are available in the print version. They just wouldn't work in HTML.
- Topics have been reorganised in various ways.

## Contents

### Section 1: Two player zero-sum games

- Strategic Form
*covers 2 player general sum and n player general sum cases which were considered later in the print version.* - Two finger Morra
*motivating example.* - Saddle Points and dominated strategies
*combined, these allow for an easy proof of the minimax theorem for 2×2 zero-sum games.* - Minimax Theorem
*Main result of section, the full result with demonstration of feasible proof by linear programming.*

### Section 2: Two player general sum games and cooperation

- Bimatrix Games
*a particular instance of strategic form*. - Nash Equilibrium
*Main result of section.* - Stag Hunt
*A game with multiple Nash equilibria.* - Cooperation in the Prisoner's dilemma
*The most famous bimatrix game.* - Iterated Prisoner's Dilemma
*emergence of cooperation.* - simple majority
*motivating example for the next section.*

### Section 3: Cooperative game theory- coalitional games

- coalitional form
- coalitional form of a strategic form game
- S-veto games
*basis for the coalitional form games.* - Shapley Value
*Measuring influence within coalitions.* - Shapley axioms
*Desirable properties for value functions.*

## Additional Resources

- Some MATLAB code I wrote for running Iterated Prisoner's Dilemma tournaments is somewhat documented, and available for download, at http://maths.straylight.co.uk/archives/44