<p>Consider the following infinitely repeated hawk-dove game:</p>

<p>$\hspace{1cm}\hspace{1cm}\hspace{1cm}$<a href="https://i.sstatic.net/POeUE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/POeUE.png" alt="enter image description here"></a></p>

<p>For what discount rate $\delta$ can tit for tat sustain $D,D$? My professor says the answer is $\delta=1$ (discounts are applied by multiplication e.g. payoff of 1 in the next period yields $\delta$).</p>

<hr>

<p>It seems to me like two cases need to be considered:</p>

<p>1) Suppose we start with $D,D$, then tit-for-tat sustains this $\iff$ $\frac{4}{1-\delta}&gt;8+\frac{\delta}{1-\delta} \iff \delta&gt;4/7$.</p>

<p>2) Suppose we start at $H,H$, under tit-for-tat, player 1 would restore $D,D$ if $\frac{1}{1-\delta}&lt;0+\frac{4\delta}{1-\delta} \iff \delta&gt;1/4$.</p>

<p>What am I doing wrong?</p>

<microeconomics><mathematical-economics><game-theory>
When can tit-for-tat be sustained?
user526463
# When can tit-for-tat be sustained?

(Asked by: username_0 on 2018-03-29)

Consider the following infinitely repeated hawk-dove game:

$\hspace{1cm}\hspace{1cm}\hspace{1cm}$[![enter image description here](https://i.sstatic.net/POeUE.png)](https://i.sstatic.net/POeUE.png)

For what discount rate $\delta$ can tit for tat sustain $D,D$? My professor says the answer is $\delta=1$ (discounts are applied by multiplication e.g. payoff of 1 in the next period yields $\delta$).

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It seems to me like two cases need to be considered:

1) Suppose we start with $D,D$, then tit-for-tat sustains this $\iff$ $\frac{4}{1-\delta}>8+\frac{\delta}{1-\delta} \iff \delta>4/7$.

2) Suppose we start at $H,H$, under tit-for-tat, player 1 would restore $D,D$ if $\frac{1}{1-\delta}<0+\frac{4\delta}{1-\delta} \iff \delta>1/4$.

What am I doing wrong?

**Tags:** microeconomics, mathematical-economics, game-theory


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## 0 answers

