Intro to Game Theory: Difference between revisions
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= Additional reading and concepts = | = Additional reading and concepts = | ||
# Prisoner's dilemma (PD): | |||
## one-shot PD - this is the only one we talked about | |||
## 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.) | |||
## a PD iterated an infinite number of times - can't use backwards induction here, so cooperation is rational. | |||
## Krepps et al's analytic result - if you relax rationality assumptions about other players, cooperation can become rational in a finite iterated PD. | |||
# 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 | # 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 | ||
# 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 d''ifference principle'' is derived from ''maximin''. | # 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 d''ifference principle'' is derived from ''maximin''. | ||
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## Amnon Rapoport (not Antol 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). | ## Amnon Rapoport (not Antol 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). | ||
# More on behavioral game theory: Camerer, Loewenstein, and others. | # More on behavioral game theory: Camerer, Loewenstein, and others. | ||
# Cooperative game theory, which includes bargaining theory. (We only talked about non-cooperative game theory.) | |||
= Interested? Please put below ... = | = Interested? Please put below ... = | ||
Revision as of 16:10, 19 June 2007
Tutors: Will Braynen, Simon Angus
Content (provisional)
- Why Game theory? When Game theory?
- Simultaneous Games
- The Nash Equilibrium (NE)
- Some standard games (Prisoner's Dilemma, Stag Hunt)
- Sequential Games
- Sub-game perfect NE
- Repeated Games
- Computational Examples (NetLogo)
- Games and Interaction structures
- Applications and Links to other fields
- Biology
- Economics
- Philosophy
- Psychology
Additional reading and concepts
- Prisoner's dilemma (PD):
- one-shot PD - this is the only one we talked about
- 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.)
- a PD iterated an infinite number of times - can't use backwards induction here, so cooperation is rational.
- Krepps et al's analytic result - if you relax rationality assumptions about other players, cooperation can become rational in a finite iterated PD.
- 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
- 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.
- 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:
- Robyn Dawes, Social Dilemmas
- 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)
- Amnon Rapoport (not Antol 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).
- More on behavioral game theory: Camerer, Loewenstein, and others.
- Cooperative game theory, which includes bargaining theory. (We only talked about non-cooperative game theory.)
Interested? Please put below ...
Paul H.
Kristen
Saleha
Frederic
Alex Healing
Aaron
nathan menke
Brian Lawler
Mollie Poynton
Heather
rafal
Monika
Olaf Bochmann