# proof verification in George J. Mailath and Andrew Postlewaite (2001b)

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.

• Can you give the actual reference? 2001b is not informative and I'm pretty sure you are missing an author. – Michael Greinecker Nov 25 '18 at 6:16
• 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). – shk910 Nov 26 '18 at 2:34