POLSC 135 1st Edition Lecture 7 Outline of Last Lecture Game Theory cont Outline of Current Lecture Solving the Game Current Lecture I II Solving the Game We typically solve extensive form games like this for a particular type of Nash equilibrium called a subgame perfect Nash equilibrium or SPNE A subgame is the part of a game beginning at one choice node and including all succeeding choice nodes A SPNE is a set of strategies such that each player plays a Nash equilibrium in every subgame Players in the game care about the consequences of their choices and therefore think ahead They try to anticipate how the other player will respond to their choices We find SPNEs by using a method called backward induction What would the other player do if I chose X What would the player do if I chose Y Game Example solving by working backwards 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 Voice Citizen State Loyal L 1 L Ignore Citizen Loyal 0 C 1 L Exit E C 1 Respond 1 C L Exit E 1 state loses 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 Citizen Loyal 0 C 1 L 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 Now we ask what the state will do at the previous decision node State Ignore Citizen Loyal 0 C 1 L 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 Voice Citizen State Loyal L 1 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 Ignore Citizen Loyal 0 C 1 L Exit E C 1 Respond 1 C L 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 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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