ExtensivePart1

ExtensivePart1 - PS 30-Notes on Extensive Form Games (WK 2)...

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Extensive form games are used when the game is played in order (you know which player played what strategy). While it can be converted into strategic form games, it is different in that finding Nash equilibria does not mean that you’ve solved the game. You have to find the subgame perfect equilibrium (SPE), which is discussed below. Introduction—How to Draw a Game Tree A game tree consists of a decision node, branches, and payoffs. Decision nodes = the players; we label the decision node with the player that make the choices. Branches = strategies. We first draw the line coming from the decision node, then we label the lines with the strategies available to the player (each branch line consists of a single strategy). Remember that there can be multiple branches from a decision node, but we cannot have multiple decision nodes going to a single branch. If two players have the same strategies, draw a branch from each node and label the branch like this: Strategy A, Strategy A’. ( ) = Payoffs. the number on top should be the first player’s payoff, the one in the middle the second player’s, etc. How Do We Make a Prediction? One option is to convert the extensive form game into a strategy form game and find the Nash equilibrium (NE). But then a problem occurs if there are more than 2 NEs. If more than one NEs exist, you then have to check whether or not they are sub-game perfect equilibria (SPE) or not o Definition of SPE: NE = SPE if in every subgame of the original game, people’s selection corresponds to and NE of that subgame o SPE is related to credibility of strategy: Credible vs. non-credible promises to play strategies First, start at subgame at the very bottom of the game tree to determine the NE of that game (the strategy = branch that gives her a better payoff) Then, work up the game tree (find the next subgame) to determine what the player chooses. If the player chooses a strategy that leads to consecutive arrows down a game tree, then that strategy profile is a SPE. Credibility of control central => if the first player knows that the second will never choose a particular strategy, then he assumes that the player will choose the NE strategy because the “threat” of using that strategy is low. SPE determines whether a NE is conceivable
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ExtensivePart1 - PS 30-Notes on Extensive Form Games (WK 2)...

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