8 Introduction to Game Theory Ch 15

8 Introduction to Game Theory Ch 15 - Chapter 15...

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4/2/2008 1 Chapter 15 Introduction to Game Theory Game theory is a branch of mathematics used to find equilibrium in situations where the interaction of players is important. It is a good approach to understanding how firms in oligopolistic markets reach the outcomes they do. In this chapter, we’ll become acquainted with the basic concepts. Basic Definitions Players - entities like individuals or firms that make choices. Strategies - the choices made by the players (how much to produce, what prices to charge, etc.). Strategy combinations - a list of strategies for each player. Payoff - the outcome (profit, etc.) from selecting a strategy.

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4/2/2008 2 The payoff for each player is dependent upon the strategy he/she selects and that selected by other players. The player has a best response function to other players’ strategies. An equilibrium strategy combination arises if every player’s strategy is a best response to the strategies of all other players. This is called a Nash equilibrium , after John Nash, 1950. We often call it a Cournot-Nash equilibrium because the concept is based on the work of Cournot a century earlier. We define: Cournot-Nash equilibrium : An equilibrium strategy combination where there is nothing any individual player can independently do that increases that player’s payoff. Each player’s own strategy maximizes that player’s own payoff. A strategy better than all others, regardless of the actions of others, is a dominant strategy . If one strategy is worse than another for some player, regardless of the actions of other players, it is a dominated strategy .
3 Example This is a game between two players who can move in different directions. Each player gets a dollar payoff based on their move and the move the other player makes. So, if Player 1 moves up and Player 2 moves to the middle, Player 1 gets \$5 and Player 2 gets \$1 and so forth. The first number in each cell is always Player 1’s payoff and the second number is always Player 2’s payoff. The aim of each player is to maximize their

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This note was uploaded on 06/18/2011 for the course ECON 2X03 taught by Professor Jamesbruce during the Fall '10 term at McMaster University.

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8 Introduction to Game Theory Ch 15 - Chapter 15...

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