Is anyone familiar with the following basic resource sharing model?

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.

• I don't see how it will be relevant for econometrics, perhaps you meant to say economics. May 7, 2019 at 20:15

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.