Mathematics and politics
Lecture notes, 3/25/03
Current assignments:
- Short homework set: pg. 183. Exercise 4 (do decision trees for each of the four starting positions) and Exercise 5 (do this problem using the "draw" rule; if any player chooses to go back to the starting position of (2,3), the game ends). Due on Tuesday, April 3.
- Midterm exam will be posted on the web site Tuesday, April 1, and will be due Thursday, April 3.
- It will cover: logic, dollar auction models, O'Neill's theorem, ordinal games, and the theory of moves, plus an essay question.
The course so far: review
We have studied mathematical models of conflict between two parties. There are three basic models, which are applicable in different situations. They are:
- Escalation models -- used for situations where taking an action changes the possible responses of the other party.
- e.g. in the dollar auction, if you bid $0.80, the other player cannot bid $0.50.
- e.g. in the U.S.-North Korea model, once North Korea decides to build nuclear weapons, its only options are to go to war or dismantle them.
We model these with a decision tree, and prune it to find the optimal strategy for both parties. We assume that each player knows the preferences of the other and behaves rationally.
- Game theoretic models -- used for situations when each party has a fixed set of options and both choose their options simultaneously.
- e.g. in chicken, once the player makes a choice to get out of the car, the game is over
- e.g. in the chicken model of the Cuban Missile Crisis, if either player chooses nuclear war, the game is over
These situations are modeled by a matrix; players choose their strategy based on the possibilities, without knowing what the other might do.
- Theory of moves -- used for situations when each party has a fixed set of options but they can move alternately (not simultaneously).
- e.g. in the prisoner's dilemma, we can let both parties negotiate a good outcome (both keep silent) rather than settling for the bad outcome (both confess).
- In the game theory model, if one cheats, the other is screwed.
- In the theory of moves model, if one cheats, the other can also cheat in response; knowing this, the first player will prefer not to cheat.
- e.g. in the Israel-Palestine conflict, both parties will rationally prefer to negotiate a land-for-peace deal than to continue with the war, even though the war is a Nash equilibrium.
These situations are modeled with both a matrix and a decision tree. Players can move around the matrix by changing their strategy; each knows the other's preferences, and they determine the optimal movement strategy together.
Decision Tree Projects
- Nicole Lovelock, Steven Stolk, and Arshad Hasan: North Korea spy-plane incident
- Julie Rifkin, Stephanie Buswell, and Andrea Herrero: U.S. Civil War
- Missy Robbins and Deborah Busis: Israel-Palestine conflict
- Michel Khoury and Samora Noguera: Russo-Japanese War
- Andrew Goodman: War of 1812
- Megan Wellington and Emily Sutherland: India-Pakistan War
- Sureyya Wille and Adam Glant: Cyprus conflict
- Robin Watson and Monica Silvestre: Persian Gulf War
- Brian Savage: French-American Quasi-War
- Morgan Olson, Agnes Terry, and Vickie Lika: Cuban Missile Crisis
- Joanne Danifo and Nina Mirarchi: U.S. Civil War
- Libby Bersot, Caroline Johnson, and Jessica Papesh: Pearl Harbor
- Ryan Gilman: World War I
- Ashley Muscarelle, Jill Siegrist, and Shannon Fair: U.S. Civil War
- Ryan Pisarri and Jon Kluft: U.S.-Nicaragua conflict
- Dan Brooks and Anna Haigh: Cuban Missile Crisis
- Oren Gur: Vietnam War
- Sherri Cohen, Rachel Moskowitz, and Dena Weisberg: Arab-Israeli War of 1948
- Yinka Green: World War II
- Scott Ramsey and Joe Stumm: U.S.-Panama War
- Lauren Pratto: U.S.-Colombia conflict
- Mark Concepcion and Linda Chang: Cyprus Conflict
- Catherine Larkin: French-American Quasi-War
- Erin Chiappini: U.S.-Colombia conflict
- Jamie Helwig and Todd Saligman: Israel-PFLP (Entebbe)
- Kia Holifield and Leconie Archer: Persian Gulf War
- Christina Verigan: Cuban Missile Crisis
- Scott Grossman, Matt Frisch, and Steph Gantman: Berlin Airlift
- Meira Levinson: Israel-Palestine conflict
- Meredith Gamer: Cuban Missile Crisis
- Irene Park and Nicole Riley: Breakup of Yugoslavia
- Marina Begun: Persian Gulf War
- Ellie Berens and Nolie Gephart: Cuban Missile Crisis
- Liz Freedman, Zoey Grossman, Patrick Lang: Cuban Missile Crisis
- Elizabeth Ivester, Jennifer Linden, and Jennifer Price: Israel-Palestine conflict
- Alexis Lerro: Six Day War
- Joshua Thompson: Current war with Iraq
- Joanna Holsten and Kristen Novack: U.S.-China spy-plane crisis
- Scott Reich and Ari Goldman: U.S. Civil War
- Liz Peterson, Meg Pittman, and Carolyn Cross: U.S.-El Salvador
- Maren McCauley and Matt Valenti: American Revolution
- Audrey Hutt and Yael Barzideh: Cuban Missile Crisis
- Eve Mayer: U.S. Civil War
- Louisa Roeder and Jenny Scott: American Revolution
- Aaron Searson: Russia-Chechnya conflict