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.