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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.

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    $\begingroup$ I don't see how it will be relevant for econometrics, perhaps you meant to say economics. $\endgroup$ – Regio May 7 '19 at 20:15
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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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