POLSC 135 1st Edition Lecture 16 Outline of Last Lecture Guest Speaker and the State Outline of Current Lecture Present Value and the State Current Lecture I II III 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 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 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 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 Lecture
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