POL%20130%20Lecture%204

POL%20130%20Lecture%204 - POL 130 Lecture 4 POL 130 Lecture...

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Unformatted text preview: POL 130 Lecture 4 POL 130 Lecture 4 Social Science Tools: Part II January 25, 2011 Game Theory Game Theory A means to evaluate how two or more people, interacting with each other, make choices while mindful of one another’s maneuvering Elements to a “Game” Elements to a “Game” At least 2 players Each player must make at least one decision/choice (move) Decisions lead to outcomes Each outcome has a utility (or payoff) for each player What is a Strategy? What is a Strategy? A strategy is a complete plan of action for the game Specifies a contingency plan for every move/action that the other player/s could select Rationality Rationality We assume that players are rational: They choose the strategy that gives them the highest payoff Rational players do what they believe is in their own best interest: Given what they know at the time of decision Taking into account what the other player will do Nash Equilibrium Nash Equilibrium A solution concept: A set a strategies such that no player has a unilateral incentive to switch to another strategy Given the expectation about what the other player will do in each contingency of the game, a player plays his or her “best response” at that contingency Players’ interests are reflected by the payoffs Games Games We draw a game to understand or predict behavior Two ways to represent games: The extensive form game The strategic form game Extensive Form Games Extensive Form Games The extensive form game is represented by a “tree” of choices up 2 Up 1 left Down 2 right (-1, 0) down (1,1) (2 , -1) (1,2) Extensive Form Games Extensive Form Games Choice nodes Terminal nodes Payoffs Sequence of play 2 Up 1 up (1,2) down (1,1) (2 , -1) left Down 2 right (-1, 0) Backwards Induction Backwards Induction We can solve an extensive form game using a method called backwards induction: Look ahead by working backwards Starting at the end of the tree and working back to the beginning, a player can decide which choices are best given the other player’s anticipated move Players make choices that maximize their payoff from that stage of the game forward Solving the Game­ Step 1 Solving the Game­ Step 1 What is the rational choice for Player 2 do at each of his decision nodes? up 2 Up 1 left Down 2 right (-1, 0) down (1,1) (2 , -1) (1,2) Solving the Game­ Step 2 Solving the Game­ Step 2 Now, given what he anticipates Player 2 will do in each contingency of the game­ what will Player 1 do? up 2 Up 1 left Down 2 right (-1, 0) down (1,1) (2 , -1) (1,2) Solving the Game­ The Solution Solving the Game­ The Solution The outcome would be that Player 1 would move Up and Player 2 would move up Their payoffs would be 1 and 2, respectively up 2 Up 1 left Down 2 right (-1, 0) down (1,1) (2 , -1) (1,2) Equilibrium Equilibrium The solution from backwards induction is called the sub­game perfect Nash Equilibrium Trade Concession Game Trade Concession Game U.S. and Japan Recip r cal o Ag reemen t Expanded Free Trade J apan Co cessio n n No F o w-u llo p Ag reemen t US No Cn cessio o n Trade Shrinkage Status Q uo Trade Concession Game Trade Concession Game U.S. President’s preferences: Expanded Free Trade > Status Quo > Trade Shrinkage/Japanese Advantage What will the President do? Trade Concession Game Trade Concession Game It depends on how he thinks Japan will respond The Japanese government’s preferences are: Japanese Advantage > Status Quo > Expanded Free Trade Trade Concession Game Trade Concession Game Then the game would look like this: Rec ip ro cal A g reemen t (50 ,10 ) Japan Co n cessio n N o Fo llo w - u p A g reemen t ( - 15 , 30) US N o Co n cessio n (25 ,20 ) Trade Concession Game Trade Concession Game Japan would choose not to reciprocate with a concession over making a concession: R eci pr ocal A eem ent gr (5 0 , 0 ) 1 Jap an C onces s i on N Fol l ow- up o A eem ent gr ( -1 5 , 3 ) 0 US NC o onces s i on (2 5 , 0 ) 2 Trade Concession Game Trade Concession Game Therefore, the rational choice for the U.S. President would be to not make a concession: Rec ro c ip al Ag re m t e en (50 , 10 ) J apan Co n c essio n No F ll w - u oo p Ag re e t em n (-15 , 30) US No Co c n essio n (25 , 20 ) Outcome of the Trade Game Outcome of the Trade Game The outcome would be the status quo Even though the President would most prefer expanded free trade, he is constrained by how he anticipates Japan will react Trade Game II Trade Game II Let’s say a new Japanese government comes to power… The new Japanese government’s preferences are: Status quo > Expanded Free Trade > Japanese Advantage Trade Game II Trade Game II Will this affect the equilibrium outcome? Recip r cal o Ag reemen t (50 , 20 ) J apan Co cessio n n No F o w -u llo p Ag reemen t (-15 , 10) US No Cn cessio o n (25 , 30 ) Trade Game II Trade Game II Japan will choose to reciprocate over not reciprocating: Recip r cal o Ag reemen t (50 , 20 ) J apan Co cession n No F o w-up llo Ag reemen t (-15 , 10) US No Cn cessio o n (25 , 30 ) Trade Game II Trade Game II Therefore, the rational choice for the U.S. President would be to make a concession: Recip r cal o Ag reemen t (50 , 20 ) J apan Co cessio n n No F o w -u llo p Ag reemen t (-15 , 10) US No Cn cessio o n (25 , 30 ) Outcome of Trade Game II Outcome of Trade Game II The outcome would be expanded free trade Lessons from Game Theory Lessons from Game Theory 1. 2. 3. Players (policymakers) do not always do what they like best­ they are constrained The sequence of moves in foreign policy often shapes the final outcome Game theory can help us understand decisions that were mistakes in retrospect Outcomes vs. Choices Outcomes vs. Choices Game theory demonstrates the outcomes and choices are not the same thing We should analyze decisions rather than the outcomes of decisions­ better way to understand the choices of policymakers Components of a Good Model Components of a Good Model A story that answers 4 questions: Who are the actors? What are they trying to achieve? What constraints do they face? How do these actors with these goals produce the outcome they are trying to achieve under these constraints? ...
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