<p>This looks like a Tullock contest. I think in his model the prize from bidding (or putting in effort) is un-divisible, so <span class="math-container">$r_x$</span> will represent the probability of winning the price. But other than re-interpreting coefficients, the setting looks identical to me. There are tons of papers on these kinds of models. Hope this helps.</p>

CC BY-SA 4.0
2019-05-07T17:05:20.650Z
2019-05-07T17:05:20.650Z
Regio
<p>Here is a resource sharing model, I do not remember where I came across it, I am wondering if this is well known in econometrics. </p>

<p>Let <span class="math-container">$T &gt; 0$</span> be the total quantity of resources. For example, ad time slot between 6:00 pm to 6:10 pm, hence <span class="math-container">$T = 10$</span> minutes.</p>

<p>Two ad companies are competing for time slots by bidding in some nonnegative amount of money. Let company <span class="math-container">$1$</span>'s bid be <span class="math-container">$x$</span>, and company <span class="math-container">$2$</span>'s bid be <span class="math-container">$y$</span>.</p>

<p>Let <span class="math-container">$C &gt; 0$</span> be the cost of entering the bidding process.</p>

<p>Let <span class="math-container">$r_x$</span> be the share of ad time slot that <span class="math-container">$x$</span> gets, and <span class="math-container">$r_y$</span> be the share of ad time slot that <span class="math-container">$y$</span> gets. </p>

<p>Then <span class="math-container">$r_x = \dfrac{Tx}{C+x+y}$</span>, and <span class="math-container">$r_y = \dfrac{Ty}{C + x+y}$</span>.</p>

<p>The utility for company <span class="math-container">$1$</span> is <span class="math-container">$U_x = m_x r_x - x$</span></p>

<p>and the utility for company <span class="math-container">$2$</span> is <span class="math-container">$U_y = m_y r_y - y$</span></p>

<p>where <span class="math-container">$m_x, m_y$</span> are the margin utility.</p>

<p>I wonder if anyone has seen this type of model somewhere. </p>

CC BY-SA 4.0
2019-05-07T20:15:20.850Z
I don't see how it will be relevant for econometrics, perhaps you meant to say economics.
Regio
<game-theory><utility><optimization><resource-economics>
Is anyone familiar with the following basic resource sharing model?
Curaçao Hajek
# Is anyone familiar with the following basic resource sharing model?

(Asked by: username_0 on 2019-05-05)

Here is a resource sharing model, I do not remember where I came across it, I am wondering if this is well known in econometrics.

Let $T > 0$ be the total quantity of resources. For example, ad time slot between 6:00 pm to 6:10 pm, hence $T = 10$ minutes.

Two ad companies are competing for time slots by bidding in some nonnegative amount of money. Let company $1$'s bid be $x$, and company $2$'s bid be $y$.

Let $C > 0$ be the cost of entering the bidding process.

Let $r\_x$ be the share of ad time slot that $x$ gets, and $r\_y$ be the share of ad time slot that $y$ gets.

Then $r\_x = \dfrac{Tx}{C+x+y}$, and $r\_y = \dfrac{Ty}{C + x+y}$.

The utility for company $1$ is $U\_x = m\_x r\_x - x$

and the utility for company $2$ is $U\_y = m\_y r\_y - y$

where $m\_x, m\_y$ are the margin utility.

I wonder if anyone has seen this type of model somewhere.

**Tags:** game-theory, utility, optimization, resource-economics

> **Comments:**
> **username_1**: I don't see how it will be relevant for econometrics, perhaps you meant to say economics.  

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## 1 answers

### Answer by username_1 on 2019-05-07. Score: 1

This looks like a Tullock contest. I think in his model the prize from bidding (or putting in effort) is un-divisible, so $r\_x$ will represent the probability of winning the price. But other than re-interpreting coefficients, the setting looks identical to me. There are tons of papers on these kinds of models. Hope this helps.


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