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ECON 3801, Cooperation Games and Final Lecture

I am too tired to write the abstract

D-period trigger

If non-cooperation action is taken, the other party will take the same action for a D period before returning to C.

Consider a repeatedly-played Prisoner’s Dilemma game, where the payoff matrix is:

Player 1	C	D
C	6,6	1,8
D	8,1	2,2

Under the D-period Trigger situation, the action sequence will be (D,C)->(C,D)->(D,C)->… where the payoff for each player will be 8,1,8,1 … (Bad) Which is lower the cooperation scenario of 6,6,6,6 … (Good)

Consider the discount factor delta, PV(Bad) = 8 + 1delta + 8delta^2 + 1delta^3 + … = 8 + 8^delta^2 + 8^delta^4 + … + delta + delta^3 = 8/(1-delta^2) + delta(1/1-delta)

PV(Good) = 6 + 6delta + 6delta^2 + 6*delta^3 + … = 6/(1-delta)

and the PV(Bad) < PV(Good) when delta …

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Utility Function

Consider a household with utility function U1 that consumes a vector of goods (x). Add up all posible vector of goods, with the condition of diminishing marginal utility, the feasible set will be a outward curve.