Sequential Move Games I

# Sequential Move Games I - UNC-Wilmington Department of...

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UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas Discrete Action, One-Shot, Sequential Move Games 1 Sequential Move Game : A game in which the players select actions sequentially, one after the other. Extensive Form/Game Tree Representation of a Sequential Move Game: A sequential move game is "represented" (that is, written down in a way that explains the game to others) in what is called extensive form , or game tree form . A game tree consists of three components: o Nodes : Circles that represent a point at which a player makes a decision (chooses an action). The deciding player's name is typically written inside the node. The node for the first decision made in a game is typically written on the left, and succeeding decisions/nodes are added to the game moving from left to right. o Branches : Lines extending from a node. Each line represents a possible actions that could be chosen by the player who is making a decision at the node. The name of the action represented by the branch is typically written beside the branch. o Payoffs : Final payoffs to the players, depending on the sequence of actions selected during the game. 1 Payoffs to Player 1, Player 2 Player 1 Name Possible Player 1 Action Another Possible Player 2 Action Player 1 , Player 2 Payoff , Payoff Player 2 Name Player 2 Name Possible Player 2 Action Possible Player 2 Action Another Possible Player 2 Action Another Possible Player 1 Action Player 1 , Player 2 Payoff , Payoff Player 1 , Player 2 Payoff , Payoff Player 1 , Player 2 Payoff , Payoff

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UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas Example: The "Car Dealership" Game as a Sequential Move Game Recall the "Car Dealership" game from the Game Theory 2 handout. In the Game Theory 2 handout, this game was a Non-cooperative, Simultaneous Move , Repeated Game with Multiple Equilibria, NO Focal Point, and a Randomized Strategy Equilibrium. Car Manufacturer Big Advertising Campaign Small Advertising Campaign Car Dealership Good Servic e 30, 50 10, 40 Bad Servic e 20, 10 40, 20 Now, suppose that instead of the players moving simultaneously, as in the game above, suppose instead that the Car Dealership moves first, and then the Car Manufacturer moves second; that is, suppose that the players move sequentially , with the Car Dealership moving first. This sequential game would have the following Extensive Form/Game Tree Representation: Sequential move games are typically solved by Backward Induction . That is, sequential move games are typically solved by determining which actions players will choose in the last (right-most)
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Sequential Move Games I - UNC-Wilmington Department of...

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