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# Class_7 - Econ171Introductionto GameTheory Lecture 7...

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Econ 171 – Introduction to  Game Theory Lecture 7

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Outline Today: The extensive form basics; properties; strategy spaces; information sets Extensive vs. Normal form Sequential rationality Subgames Tomorrow Practice finding SPNE Application: Stackelberg duopoly
Grab game

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The Pirate game Variant of the Ultimatum game . Suppose there are 5 pirates who have just captured a chest containing 100 gold coins. The pirates have rankings based on their status from captain (#1) to sailor (#5). As the captain, it is her duty to divide the loot amongst the crew, but since piracy is often a democracy, everyone gets to vote on the allocation. If more than half of the crew votes against the allocation, the captain is throw overboard and the lieutenant (#2) becomes captain.
The Pirate game This process is repeated if the lieutenant's allocation is not approved, and so on. Each pirate's objective is first to stay alive, second to get the most gold as possible, and third to see others thrown overboard (or advance rank). What will the captain propose? Who will survive and what amounts will each get? Justify your answer with an intuitive explanation or reasoning.

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Dynamic game representation In many games players have knowledge of the moves of other players. Behavior and resulting equilibria are likely to change. We can use the order of actions to learn information not available in static settings and refine our NE strategy profiles. Refine rationalizability and Nash equilibrium to be consistent with the new information gained from the dynamic setting.
Extensive form Game ‘tree’ Nodes : points that represent places where events occur (e.g. game ends, a decision is made). Branches : represent actions individual can take. Player 1 Player 2 Initial node Terminal nodes Player 2

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Extensive form Game ‘tree’ Nodes : points that represent places where events occur (e.g. game ends, a decision is made). Branches : represent actions individual can take. 1 2 2 Initial node Terminal nodes U D v w x y z
Extensive form Game ‘tree’ Nodes : points that represent places where events occur (e.g. game ends, a decision is made). Branches

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## This note was uploaded on 11/03/2011 for the course ECON 1171 taught by Professor Bof during the Spring '11 term at UCSB.

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Class_7 - Econ171Introductionto GameTheory Lecture 7...

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