Game Theory might be better described as Strategy Theory, or Theory of Interactive Decision Making. A strategic situation involves two or more interacting players who make decisions while trying to anticipate the actions and reactions by others. Game theory studies the general principles that explain how people and organizations act in strategic situations.
Game theory studies strategy mainly through the analysis of different "games". A "game" in game theory is a fully explicit structure which characterizes each player's set of actions, payoffs and possible outcomes under given rules of playing. Given this conditions, rational players act in such a way, that they maximize the expected value of their von Neumann-Morgenstern Utility. Games provide a simplified world within which to study strategy (as opposed to the real world where complexities get in the way of developing general principles).
Table of Contents
1 Introduction to Game Theory
- Short history
- Theory of rational choice
Part I - Games with Perfect Information
2 Nash Equilibrium
- Strategic games
- Example: Prisoner's Dilemma
- Matrix Notation In Game Theory - How To Set Out A Game
- Example: Battle of the sexes (a.k.a. Bach or Stravinsky?)
- Example: Matching Pennies
- Nash equilibrium
- Best response functions
- Cournot's model of oligopoly
- Bertrand's model of oligopoly
3 Mixed Strategy Equilibrium
- Mixed strategy Nash equilibrium
- Dominated actions
- Dominant Strategies
- Example: expert diagnosis
- Formation of beliefs
4 Extensive Games with Perfect Equilibrium
- Introduction to Extensive games
- Strategies and outcomes
- Nash equilibrium
- Subgame perfect equilibrium
- Stackelberg's model of duopoly
- Adding simultaneous moves
- Adding uncertainty
5 Coalitional Games
Part II - Games with Imperfect Information
6 Bayesian Games
- Motivational Examples
- Cournot's duopoly with imperfect information
7 Extensive Games with Imperfect Information
- Nash equilibrium
- Signaling games
Part III - Real World Examples
8 TV Game Shows
- Deal Or No Deal
- Mutually assured destruction
Wikipedia Articles on Game Theory Related Topics
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Game theory studies strategic interaction between individuals in situations called games. Classes of these games have been given names. This is a list of the most commonly studied games
Explanation of features
Games can have several features, a few of the most common are listed here.
- Number of players: Each person who makes a choice in a game or who receives a payoff from the outcome of those choices is a player.
- Strategies per player: In a game each player chooses from a set of possible actions, known as pure strategies. If the number is the same for all players, it is listed here.
- Number of pure strategyNash equilibria: A Nash equilibrium is a set of strategies which represents mutual best responses to the other strategies. In other words, if every player is playing their part of a Nash equilibrium, no player has an incentive to unilaterally change his or her strategy. Considering only situations where players play a single strategy without randomizing (a pure strategy) a game can have any number of Nash equilibria.
- Sequential game: A game is sequential if one player performs her/his actions after another player; otherwise, the game is a simultaneous move game.
- Perfect information: A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceded them.
- Constant sum: A game is constant sum if the sum of the payoffs to every player are the same for every single set of strategies. In these games one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
List of games
- Arthur, W. Brian “Inductive Reasoning and Bounded Rationality”, American Economic Review (Papers and Proceedings), 84,406-411, 1994.
- Bolton, Katok, Zwick 1998, "Dictator game giving: Rules of fairness versus acts of kindness" International Journal of Game Theory, Volume 27, Number 2
- Gibbons, Robert (1992) A Primer in Game Theory, Harvester Wheatsheaf
- Glance, Huberman. (1994) "The dynamics of social dilemmas." Scientific American.
- H. W. Kuhn, Simplified Two-Person Poker; in H. W. Kuhn and A. W. Tucker (editors), Contributions to the Theory of Games, volume 1, pages 97–103, Princeton University Press, 1950.
- Martin J. Osborne & Ariel Rubinstein: A Course in Game Theory (1994).
- McKelvey, R. and T. Palfrey (1992) "An experimental study of the centipede game," Econometrica 60(4), 803-836.
- Nash, John (1950) "The Bargaining Problem" Econometrica 18: 155-162.
- Ochs, J. and A.E. Roth (1989) "An Experimental Study of Sequential Bargaining" American Economic Review 79: 355-384.
- Rapoport, A. (1966) The game of chicken, American Behavioral Scientist 10: 10-14.
- Rasmussen, Eric: Games and Information, 2004
- Shor, Mikhael. "Battle of the sexes". GameTheory.net. Retrieved September 30, 2006.
- Shor, Mikhael. "Deadlock". GameTheory.net. Retrieved September 30, 2006.
- Shor, Mikhael. "Matching Pennies". GameTheory.net. Retrieved September 30, 2006.
- Shor, Mikhael. "Prisoner's Dilemma". GameTheory.net. Retrieved September 30, 2006.
- Shubik, Martin "The Dollar Auction Game: A Paradox in Noncooperative Behavior and Escalation," The Journal of Conflict Resolution, 15, 1, 1971, 109-111.
- Sinervo, B., and Lively, C. (1996). "The Rock-Paper-Scissors Game and the evolution of alternative male strategies". Nature Vol.380, pp. 240–243
- Skyrms, Brian. (2003) The stag hunt and Evolution of Social Structure Cambridge: Cambridge University Press.
- ^For the cake cutting problem, there is a simple solution if the object to be divided is homogenous; one person cuts, the other chooses who gets which piece (continued for each player). With a non-homogenous object, such as a half chocolate/half vanilla cake or a patch of land with a single source of water, the solutions are far more complex.
- ^ abcdefghThere may be finite strategies depending on how goods are divisible
- ^ abSince the dictator game only involves one player actually choosing a strategy (the other does nothing), it cannot really be classified as sequential or perfect information.
- ^Potentially zero-sum, provided that the prize is split among all players who make an optimal guess. Otherwise non-zero sum.