POLSC 135 1st Edition Lecture 16 Outline of Last Lecture: Guest Speaker and the StateOutline of Current Lecture: Present Value and the StateCurrent Lecture:I. Present Value (Discount Factor = DF)- Say something is worth $1.00 in the first period or day. It will be worth 1*DF in the second period, 1*DF2 in the third period, 1* DF3 in the fourth period. And so on. - A useful fact (if the promise is $1.00): - 1 + DF + DF2 + DF3 +… = 1/(1-DF)- PV of a stream of benefits tells us how much this stream of future benefits is worth to us today. II. State of Nature Game Again- What happens now when we repeatedly play the state of nature game? - One strategy they might use is called a “grim trigger strategy”. - If you refrain, I will refrain- If you ever steal, I will choose to steal from this point on regardless of what you do.- Individuals will choose to cooperate/refrain if:- 3/(1-DF) > 4 + 2DF / 1-DF- 3/(1-DF) > (4 – 4DF + 2DF)/(1-DF)- 3 > 4 – 2 DF - 2DF > 1- DF > ½ - Refrain is possible even if individual preferences are structured as in the state of nature as long as the game is infinitely repeated.- “Don’t Steal” can be sustained as a SPNE using a grim trigger strategy as long as individuals are sufficiently concerned about the potential benefits of future cooperation. - Other strategies also support cooperation. (tit for tat) - The state is not strictly necessary for cooperation in non-complex societies. III. Preparation for problems: - Drawing the game in matrix format- Identify players and strategies- Draw, determine, and write payoffs 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.- Solve the game- Put yourself in each player’s shows and identify the “best replies”- Identify SPNE- Identify cells where players play their best replies- List actions chosen by each player by using semi-colon - NOTE: there may be no SPNE- Identify which player has a dominant strategy (A player has a DS if they make the same choice no matter what the other player does)- If both players have a DS, then there is a DS Nash equilibrium End
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