This is an exercise in the Steve Tadelis An Introduction to Game Theory book:

(10.12) Folk Theorem Revisited: Consider the infinitely repeated trust game described in Figure 10.1

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(a) Draw the convex hull of average payoffs.

So, this is pretty easy:

The vector of payoffs is $V=\{(0,0),(0,0),(-1,2),(1,1)\}$

So, here is my sketch in paint:

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(b) Are the average payoffs $(\overline{v_1}, \overline{v_2}) = (−0.4, 1.1)$ in the convex hull of average payoffs? Can they be supported by a pair of strategies that form a subgame-perfect equilibrium for a large enough discount factor $δ$?

I don't have an idea how to do (b). If someone could explain that would be great.

  • 3
    $\begingroup$ Your "vector of possible payoffs" in (a) is actually a set and needs only one $(0,0)$ entry. The first part of (b) shouldn't be a problem. Just draw the given point into your diagram. Is it contained in the red triangle? For the second part, consider the following question: What minimum average payoff can player 1 guarantee for himself? $\endgroup$ – VARulle Jun 14 '20 at 0:28

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