note9 - Microeconomic Theory Econ 101A Fall 2008 GSI: Eva...

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Unformatted text preview: Microeconomic Theory Econ 101A Fall 2008 GSI: Eva Vivalt Section Notes 9: Sequential Equlibrium, Imperfect Information, and Signalling Games 1 Sequential Equilibrium In solving for Nash equlibria, we assume that firms move simultaneously. Things change considerably if one firm moves before the other in a sequence. Assume now that firm 1 moves before firm 2 and that each is able to anticipate the others reaction. These types of scenarios are often known as Stackelberg Games . 1.1 Backwards Induction The optimization technique used to solve for how the firms will behave is known as backwards induction. This means that (assuming there are only 2 rounds in this example, with firm 1 moving first) we will first solve for how firm 2 will act in the second round in response to how firm 1 acts in the first round, and then we will move back in time to solve for how firm 1 will act in the first round, using our solution for the second round to model firm 1s anticipation of how firm 2 will react. The technique of backwards induction is a fundamental technique in determining how to solve for optimal strategies in a number of game theoretic situations. 1.2 Solving by BI in a Two-Round Game: First, Round Two Firm 2s problem is identical to that found in the Nash equilibrium. It takes a 1 as given and maximizes its profit over a 2 , producing a best response function r 2 ( a 1 )....
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note9 - Microeconomic Theory Econ 101A Fall 2008 GSI: Eva...

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