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In the last lecture we extended the basics of game theory to think about ways in which we could find solutions to normal and extensive form games. Watch that lecture here. Thanks to Jason and Emma, you should have a good handle on the prisoner’s dilemma now.
In this lecture we’ll finish off talking about game theory by spending time talking about dominant and mixed strategies, subgame perfect equilibria, best response functions, and bac
kward induction.
Dominant Strategies
A dominant strategy refers to the best response to any strategy chosen by the other player. When a player has a dominant strategy in a game, there is good reason to predict that this is how the player will play the game.
A mixed strategy, in contrast, refers to situations when the player randomly selects from several possible actions.
The strategies in which a player chooses one action or another with certainty are called pure strategies.
We’ll illustrate these concepts using two famous games: Matching Pennies, which we have seen before, and the battle of the sexes.
Best Response Function
The function which gives the payoff-maximizing
choice for one player in each of a continuum of actions of the other player is referred to as the best-response function.
Image via Wikipedia
Subgame Perfect Equilibria
Game theory offers a formal way of selecting the reasonable Nash equilibria in sequential games using the concept of subgame-perfect equilibrium.
A proper subgame consists of the part of the game tree including an initial decision not connected to another in an oval and everything branching out below it.
Backward Induction
A shortcut to finding the subgame-perfect equlibrium directly is to use backward induction. Backward induction solves for the equilibrium by working backwards from the end of the game to the beginning. We’ll see this working in the battle of the sexes.
Click the link below to download the slides for the lecture. I’ll have them up at slideshare.net as well, and you can get a podcast of the lecture after the fact.
Right click to download Slides
In the next lecture, we’ll move on to talk about Production. The first half of the course is nearly over!
