Microeconomics Course E

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Presentation transcript:

Microeconomics Course E John Hey

Chapter 30 GAME THEORY Up to now we have considered situations in which individuals take decisions independently of the decisions of others. Today we consider situations of interdependence – games. It will be useful when we examine duopoly.

GAMES In general many players and many decisions. We start by considering games in which there are two players (1 and 2) each with two decisions (A and B). Their payoffs depend on the decisions of both players.

A Dominating Choice A player has a dominating choice if it is best independently of the choice of the other player.

A Nash Equilibrium A combination of choices in a game is called a Nash equilibrium if neither player wants to change his or her choice given the choice of the other player. Does a Nash Equilibrium always exist?

Pareto Dominance When one outcome is better for both players than some other outcome, we say that the first outcome Pareto Dominates the second. We note that the Nash Equilibrium (AA) in the Prisoners’ Dilemma is Pareto Dominated by BB.

A Continuum of Choices When we consider duopoly, the two players do not choose just from two choices but choose the value of some variable. We have exactly the same concepts.

Chapter 30 A player has a dominating choice if this choice is best independently of the choice of the other. A combination of choices in a game is called a Nash equilibrium if neither player wants to change his or her choice given the choice of the other player Games may have no Nash Equilibria (in pure strategies), a unique Nash Equilibrium of several Nash equilibria.

Chapter 30 Goodbye!