Intro to Game Theory

Tutors: Will Braynen, Simon Angus

Content (provisional)

1. Why Game theory? When Game theory?
2. Simultaneous Games
   1. The Nash Equilibrium (NE)
   2. Some standard games (Prisoner's Dilemma, Stag Hunt)
3. Sequential Games
   1. Sub-game perfect NE
4. Repeated Games
5. Computational Examples (NetLogo)
   1. Games and Interaction structures
6. Applications and Links to other fields
   1. Biology
   2. Economics
   3. Philosophy
   4. Psychology

Additional reading and concepts

1. Nash Equilibrium (NE): Kreps, D.M. (1987). "Nash equilibrium" in J. Eatwell, M. Milgate, and P. Newman (Eds.), The New Palgrave, 167-177.
2. Prisoner's dilemma (PD):
   1. one-shot PD - this is the only one we talked about
   2. a PD iterated a finite number of times - using backwards induction, you can show that the optimal strategy is to defect. (NB: optimal strategy does not imply optimal or pareto efficient outcome; instead it means best response to the other players.)
   3. a PD iterated an infinite number of times - can't use backwards induction here, so cooperation is rational.
   4. Kreps et al's analytic result: if you relax rationality assumptions about other players, cooperation can become rational in a finite iterated PD. Kreps, Milgrom, Roberts, and Wilson in Journal of Economic Theory 27, 245-252 (1982)
3. Aumann's Correlated Equilibrium (CE) concept (1974), which allows all players get higher payoffs than with Nash Equilibria (NE) in some games: http://en.wikipedia.org/wiki/Correlated_equilibrium
4. Von Neumann's maximin decision rule (1928), which results in an NE in two-player zero-sum (and hence constant-sum) games. Maximin is a decision rule which tells you to choose an action that will maximize your minimum (worst-case) payoff. Equivalently, you can think of this as minimizing your possible loss. Hence, maximin is a very risk-averse rule and most likely not result in an equilibrium when followed by all players outside (two-player) zero-sum games. In Political Philosophy, John Rawls's difference principle is derived from maximin.
5. Socal Dilemmas are defined by the order of the payoffs (so you could formalize this notion) and are characterized by having a dominant strategy that leads to a suboptimal outcome for all players. One type of a social dilemma is the Prisoner's Dilemma. Further readings on public goods and social dilemmas:
   1. Robyn Dawes, Social Dilemmas
   2. G. Hardin, Mutual Coercion Mutually Agreed upon by the Majority of the People Affected (This paper implicitly assumes certainly about the size of the public good)
   3. Amnon Rapoport (not Anatol Rapoport) has done excellent work in behavioral game theory where there is uncertainty about the size of the public good, which is a more realistic model of real-world problems (e.g. overfishing).
6. More on behavioral game theory: Camerer, Loewenstein, and others.
7. Cooperative game theory, which includes bargaining theory. (We only talked about non-cooperative game theory.)
8. Evolutionary game theory (tutorial on Wednesday)

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