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.
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.