The (Braess) Transportation Paradox - Route 1 Bridge A A - slow road: 15 minutes - Bridge B Route 2 slow road: 15 minutes - B
1000 cars must commute from point A to point B. East-West roads take 15 minutes, no matter how many cars are on the
Cooperative Game Theory
Cooperative games are often defined in terms of a characteristic function, which specifies the outcomes that each coalition can achieve for itself. For some games, outcomes are specified in terms of the total amount of dollar
Perfect Bayesian Equilibrium
For an important class of extensive games, a solution concept is available that is simpler than sequential equilibrium, but with similar properties.
In a Bayesian extensive game with observable actions, nature moves fir
Extensive Games with Imperfect Information
In strategic games, players must form beliefs about the other players' strategies, based on the presumed equilibrium being played.
In Bayesian games, players must form beliefs about the other players' stra
Repeated Games
A repeated game (say, infinitely repeated prisoner's dilemma) is a special case of an extensive game.
The additional structure of the same game being repeated allows for new results. "Folk theorems" show that any payoffs that are fea
Extensive Games with Perfect Information
There is perfect information if each player making a move observes all events that have previously occurred. Start by restricting attention to games without simultaneous moves and without nature (no randomnes
Knowledge and Common Knowledge
Game Theory requires us to be interested in knowledge of "parameters" like costs, valuations, and demand, but also knowledge about what other players know.
Consider a finite probability space (, p) and an information
Pearce, "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica 1984 Rationalizability is a weaker (broader) solution concept than Nash equilibrium. It looks at the implications of common knowledge of rationality, without impo
Mixed Strategy Nash Equilibrium
Let G = hN, (Ai), (ui)i be a strategic game. Preferences must be specified over lotteries on A, which we assume are represented by the expectation of ui(a). Let (Ai) be the set of probability distributions over Ai. i
Bayesian Games
How do we model uncertainty about the payoffs or (more generally) knowledge of the other players? The traditional distinction (see Fudenberg and Tirole) is that uncertainty about payoffs is called incomplete information, and uncertain
Games in Strategic Form
Definition 11.1: A strategic game consists of: 1. a finite set N (the set of players), 2. for each player i N, a nonempty set Ai (the set of actions available to player i), 3. for each player i N, a preference relation %i o
Department of Economics The Ohio State University Economics 817: Game Theory
Syllabus and Reading List
James Peck and David Schmeidler Autumn 2007 www.econ.ohio-state.edu/jpeck/Econ817.htm M-W 11:30 - 1:18 Derby 47
Course Objectives: This course aim
Department of Economics The Ohio State University Econ 817-Game Theory Fall 2007 Prof. James Peck Homework #2-Due Wednesday October 17 Directions: Answer all questions, and be neat. If you discuss the questions in study groups, list the members of yo
Department of Economics The Ohio State University Econ 817-Advanced Game Theory Fall 2007 Prof. James Peck Homework #2 Answers 1. O-R, exercise 56.4. Answer: By the symmetry of the game, the set of rationalizable pure actions is the same for both pla
Department of Economics The Ohio State University Econ 817-Game Theory Homework #1-Due Monday October 8 Directions: Answer all questions, and be neat. If you discuss the questions in study groups, list the members of your study group, and make sure t
Department of Economics The Ohio State University Econ 817-Game Theory Fall 2007 Prof. James Peck Homework #1 Answers 1. O-R, exercise 19.1. Answer: There are n players, and each player i has the action set, Ai = {out} [0, 1]. Each player prefers an
Myerson and Satterthwaite, "Efficient Mechanisms for Bilateral Trading," JET 1983 In many bilateral bargaining situations with asymmetric information, ex post efficiency is inconsistent with incentive compatibility and individual rationality. One can