POLSC 135 1st Edition Lecture 11 Outline of Last Lecture Solving the Game Matrices Outline of Current Lecture Solving the Game Revisited Current Lecture I Solving the Game In this lecture we went over how to solve the game in conjunction with homework questions that refer to Lecture 7 The following is copy and pasted from lecture 7 Please review for it is vital for solving the homework which will be posted in the next lecture update Game Theory Example Say for example that a citizen lives within a state The state decides to raise taxes The following chart below is a representation of how the citizen may react Presumptions The state starts with 1 representing tax income Key L Loyal E Exit V Voice 1 taxes C Cost Citizen State Loyal 0 C 1 L Voice Citizen State Loyal L 1 L Citizen Ignore Exit E C 1 Respond 1 C L Exit E 1 state loses Loyal 0 C 1 L Citizen Exit E C 1 The citizen is making a choice If I stay loyal I get 0 C If I exit I get E C Easy to see that the choice will depend on whether E 0 If E 0 we say the citizen has a credible exit threat cost to state The citizen will choose to exit Due to the cost of remaining Loyal These notes represent a detailed interpretation of the professor s lecture It is best used as a supplement to your own notes not as a substitute Now we ask what the state will do at the previous decision node Loyal 0 C 1 L State Ignore Citizen Exit E C 1 Respond 1 C L The state is making a choice If I respond I get L If I ignore I get 1 The choice will depend on whether L 1 If L 1 we say the state is dependent on the citizen If L 1 we say the state is autonomous Assume the state is dependent In this case the state will choose to respond Now we ask what the citizen will do at the initial node Loyal 0 C 1 L Voice Citizen State Loyal L 1 L Ignore Respond 1 C L Exit E 1 state loses If the citizen exits she gets E If the citizen remains loyal she gets 0 If the citizen uses voice she gets 1 C The citizen will use voice Conclusion to Scenario Assumptions E 0 E 1 C note here that C 1 because E 0 L 1 Subgame Perfect Nash Equilibrium Voice Exit Respond Outcome The citizen uses voice the state responds Payoffs The citizen gets 1 C the state gets L Equilibria Citizen Exit E C 1 How to write down the equilibria Equilibrium in scenario 1 is Voice Exit Respond The citizen s 1st action the citizen s 2nd action the state s 1st action End Lecture
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