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I am reading George J. Mailath and Andrew Postlewaite (2001), and this is the lemma 1 in this paper. I don't understand the induction process in this proof. I think that we should use the fact that $x_{i+1} + p_{k+1}< v(b_{i+1}, s_{i+k})$ to show $x_{i+k-1}+p_{i+k} < v(b_{i+k-1}, s_{i+k})$.

At first, I did induction with respect to $k$. Since $k>1$, the first step of induction is $k=2$. Then, we should show that $x_{i+1} + p_{i+2} < v(b_{i+1}, s_{i+2})$. But, I have no idea of how to show this.

Is my approach of induction correct? I appreciate if you give any help. Please tell me if more context is needed.

  • $\begingroup$ Can you give the actual reference? 2001b is not informative and I'm pretty sure you are missing an author. $\endgroup$ Nov 25 '18 at 6:16
  • $\begingroup$ Here is the reference. Cole, H.L., Mailath, G.J. and Postlewaite, A., 2001. Efficient non-contractible investments in finite economies. Advances in Theoretical Economics, 1(1). $\endgroup$
    – shk910
    Nov 26 '18 at 2:34

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