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8 Introduction to Game Theory

# 8 Introduction to Game Theory - Introduction to Game Theory...

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Introduction to Game Theory

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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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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.

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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 .
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.

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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.

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8 Introduction to Game Theory - Introduction to Game Theory...

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