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<p>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 <span class="math-container">$x_{i+1} + p_{k+1}&lt; v(b_{i+1}, s_{i+k})$</span> to show <span class="math-container">$x_{i+k-1}+p_{i+k} &lt; v(b_{i+k-1}, s_{i+k})$</span>.</p>
<p>At first, I did induction with respect to <span class="math-container">$k$</span>. Since <span class="math-container">$k&gt;1$</span>, the first step of induction is <span class="math-container">$k=2$</span>.  Then, we should show that <span class="math-container">$x_{i+1} + p_{i+2} &lt; v(b_{i+1}, s_{i+2})$</span>. But, I have no idea of how to show this.</p>
<p>Is my approach of induction correct? I appreciate if you give any help.  Please tell me if more context is needed.</p>

CC BY-SA 4.0
2018-11-25T06:16:50.477Z
Can you give the actual reference? 2001b is not informative and I'm pretty sure you are missing an author.
Michael Greinecker
CC BY-SA 4.0
2018-11-26T02:34:01.450Z
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
<microeconomics><game-theory><theory><matching>
proof verification in George J. Mailath and Andrew Postlewaite (2001b)
shk910
# proof verification in George J. Mailath and Andrew Postlewaite (2001b)

(Asked by: username_0 on 2018-11-25)

> [![enter image description here](https://i.sstatic.net/kZje6.png)](https://i.sstatic.net/kZje6.png)

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.

**Tags:** microeconomics, game-theory, theory, matching
> **Comments:**
> **username_1**: Can you give the actual reference? 2001b is not informative and I'm pretty sure you are missing an author.  
> **username_0**: 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).  

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