**Game Theory: Syllabus - 2013**

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Studies

York College (CUNY)

Jamaica, New York

email:

__malkevitch@york.cuny.edu__

web page:

__http://york.cuny.edu/~malk__

**Syllabus**

0. What is Game Theory? (Mathematics has provided insight into two types of games - situations which involve "conflict" or the making of decisions: i. *combinatorial games* include chess, checkers, Nim, etc. and ii. *political and economic games* include Prisoner's Dilemma and Chicken. We will deal primarily with the latter but will also deal with related topics such as elections and voting, two-sided markets, bankruptcy, and apportionment. Often the issue is to understand what it means to be fair and/or behave in a rational fashion in a wide variety of contexts. Examples will be chosen involving mathematical techniques that support content within the CCSS-M as well as Practice Standard 4, Model with Mathematics.)

1. Taxonomy of games (Number of players, zero-sum games, non-zero-sum games, cooperative and non-cooperative games. Utility: transferable and non-transferable utility. Values for games: equilibrium concepts, Shapley value.)

2. 2-person zero-sum games (Matrix games, pure strategies, using spinners to find optimal mixed strategies; fair games; connections with linear programming. Applications in economics and political science.)

3. 2-person non-zero sum games (Prisoner's Dilemma, Chicken, Nash equilibria, congestion games; Braess's Paradox, price of anarchy. Rationality - connections to behavioral and experimental economics.)

4. Two-sided markets (Gale/Shapley models) (Matchings. Stable marriage. Gale/Shapley models, deferred acceptance algorithm; male optimal - female optimal stable solutions; school choice and other applications.)

5. Elections and voting (Plurality, run-off, IRV, Borda count, Condorcet methods, approval voting. Arrow's Theorem.)

6. Bankruptcy (Proportionality, Maimonides gain and loss, the contest-garment rule and the talmudic method.)

7. Apportionment (Hamilton's, Jefferson's, Webster's and Huntington-Hill's methods. House and population monotonicity. Balinski-Young Theorem.)

8. Combinatorial Games (Nim, graph games. Nim addition and hackenbush.)

Note: Game Theory is not a standard topic in the K-12 curriculum. This course will show how game theory topics can be infused into the usual curriculum (now CCSS-M) as ways of illustrating results in arithmetic, algebra, geometry, probability and statistics.

**Text:
**Gura, Ein-Ya and M. Maschler, Insights into Game Theory, Cambridge U. Press, New York, 2008.