3-5-2012Lecture 1:2No lecture on 4-12-2012.I. Payoffs and UtilityA. Comparing Apples and OrangesB. Intensity and Order of PreferenceII. Solving Game Trees with RollbackA. Strategies vs. actionsB. Equilibrium vs. outcomesIII. Counting StrategiesIV. Scope of Game TheoryA. Assumptions of A GAMEB. Basic Assumption of Game TheoryLast lecture, we went over Game Tree:RF NotStrategic Equivalents (5, 0) (0, 5)counterfactual RF Not RF NotInc wins Inc wins Chal wins Inc wins(5, -2) (5, 0) (0, 5) (7, 0) payoffs- big intellectual tradition- utility framework: allows you to compare people’s preferences and how they make decisions- Each player- winning election (+7)- raising funds (-2)IA. Comparing Apples and Oranges- by adding up components of the payof- payofs = part of communication aspect of game theory - add up numbers / variables that represent the stakes- components of the situations- (+) : a good thing / what they like- (-) : what they don’t likeIncChal ChalIB. Intensity and Order of Preference- aggregate outcomes- to get net payofs: components reflect intensity of preference- magnitudes show how intense the preferences are (+7 vs. -2)- couldn’t do game theory without intensity of preferences- but this is risky because they are based on assumptions- Intensity of Preference: can’t measure this directly- understanding what matters to people and what is reasonable to people - allows us to compare apples to oranges- dangerous though because we make preferences across people- →benefits some while others lose- in game theory: NEVER compare 1 person’s payoff to another- because utility = individualistic framework- assume that the player compared his own payoffs- NEVER compare within the parenthesis- need a baseline- there is a natural baseline often (zero point)- but you don’t have to choose zero although it usually is easiest to- ex. if the baseline = -100- Each player- winning election (+7)- raising funds (-2)- start off with 100 → just add 100 to ( , ) because at first, we assumed that the baseline = 0- Strategic Equivalent: The Professor highlights the right choice from the Incumbent’s point of view.RF Not(10, 100) (100, 105) RF Not RF NotIncChal ChalInc wins Inc wins Chal wins Inc wins(105, 98) (105, 100) (100, 105) (107, 100) - We can choose different numbers for baselines for each player but this → the same results, so we might as well keep it simple and use the same number. Afterall, we need to compare the results.IIA. Strategies vs. Actions- solve bottom up- “look forward, reason backward”- strategically anticipate what other is going to do- Strategic Equivalent- Warning: the book does this diferently- Think about “dogs that don’t bark”- what could’ve happened but didn’t? = clue to what actually happens- counterfactuals- ~parallel universe; alternate ways the world could work- Strategy: a set of planned actions for each node the player controls- Incumbent only controls 1 node (RF / N) - →simple.- Challenger strategy has 2 components- →4 possible strategies- 1) RF if Inc RF, RF if Inc Not- 2) Not if Inc RF, RF if Inc Not (equilibrium)- 3) Not if Inc RF, Not if Inc Not- 4) RF if Inc RF, RF if Inc NotIIB. Equilibrium vs. Outcomes- It is not wrong to use more words for strategies. In fact, it may be helpful!- It is fine to abbreviate as the professor did.- The book way is too abbreviated. [RF, RF] [N, RF]- It is useful to list all strategies- because dogs that don’t bark explanation- Warning: some are so weird that it’s going to be weird to write