Topic 1 Game Theory Lecture 1

Topic 1 Game Theory Lecture 1 -...

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ECON1401 topic 1 Game theory lecture 1 28/02/2011 1 ECON 1401: Economic Analysis Topic 1: Game theory Gautam Bose Lecture 1 Games and their solutions Today’s Agenda What is a game, and what is “game theory”? Simultaneous Games and Their Solution Concepts The game matrix (game table) g (g ) Examples. Nash equilibrium multiple equilibria Sequential Games and Their Solution Concepts ECON1401 Semester 1 2011 Lecture 22 How to write down and solve a Sequential Game. Rollback (subgame perfect) equilibrium. Examples. Game Theory Game theory is a unified method for analysing rategic interactive situations which span the strategic, interactive situations which span the spectrum from tic tac toe to nuclear arms races. It is a “theory” because it abstracts the essential, common features of these situations, and analyses them in the abstract. use game eoretic insights and shed light on ECON 1401 Semester 1 2011 Lecture 23 To use game theoretic insights and shed light on a particular situation (e.g. enterprise bargaining at UNSW), we have to colour in the specific details. Games What is a game? A situation involving two or more agents (“players”) hite and black in chess White and black in chess Management vs union Obama and the Republican challenger Each of whom can adopt one of several permissible courses of action (“strategies”) Mgmt offers small/medium/large pay rise, union threatens strike if demands are not met (other strategies) ECON 1401 Semester 1 2011 Lecture 24 ( g) The combination of strategies together determine the outcome for each player (“payoffs”) Medium pay raise for union, little work loss combined with high worker morale for management (other outcomes)
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ECON1401 topic 1 Game theory lecture 1 28/02/2011 2 Simultaneous and sequential games In some games, all players choose their actions the same time (without knowing the at the same time (without knowing the choices of other players). sealed bid auction, or tender Scissors, paper, rock In other games, there is a given sequence in which players choose their actions/strategies. ECON 1401 Semester 1 2011 Lecture 25 Bargaining over a price (offer counteroffer) Tic tac toe and chess Different analysis for the two kinds of games What do we want to determine? Given the specifications of a game, how will the players play? This cannot usually be answered for one player in isolation, because the best that one can do depends on what the other does. The test of whether a player has done the best is that the player does not in retrospect wish she ad done something ifferent ECON 1401 Semester 1 2011 Lecture 26 had done something different. If we can find an outcome in which this criterion is satisfied for each player, we have found an equilibrium .
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