Reverse Auction bidding strategy A buyer wants to buy contiguous land plots from three landowners (sellers) who own fixed size plots. Sellers have their private valuation of their plots. The buyer will hold a closed bid procurement auction. The profit for the buyer is greater if he purchases all plots of land as compared to (any) 2 plots(without any specific order), which itself is greater than profit for a single plot. Does someone have an idea of how strategies will be developed for the sellers (in equilibrium)? I will later extend it to multiple rounds reverse auctions.
Given the very general description of the problem, I can think of the following (also very general) way of formulating it mathematically. 

Let $v_n$ be the buyer's value from owning $n$ plots of land, with $v_3&gt;v_2&gt;v_1$. 
Let $c_i$ be seller $i$'s private valuation of the plot she owns. Let $b_i$ be seller $i$'s bid, and we assume the buyer will purchase $n$ plots of land whenever $v_n$ is greater than or equal to the sum of the $n$ smallest $b_i$'s, and each seller gets the amount she asks for in the bid. 

Seller 1's objective is to choose $b_1$ to maximize the following: 
\begin{align}
&amp;\Pr(b_1+b_2+b_3\le v_3)b_1
\\&amp;\qquad+\Pr(b_1\le\max\{b_1,b_2,b_3\}\text{ and }b_1+\min\{b_2,b_3\}\le v_2\text{ and }b_1+b_2+b_3&gt; v_3)b_1
\\&amp;\qquad+\Pr(b_1=\min\{b_1,b_2,b_3\}\text{ and }b_1\le v_1\text{ and }b_1+\min\{b_2,b_3\}&gt; v_2)b_1
\end{align}
The problems for the other two sellers would be symmetric. 

If you assume that $c_i$'s are i.i.d. draws from a distribution $F$, then it seems plausible to solve for a symmetric Bayesian Nash equilibrium, where every seller bids according to the same bidding function, $b_i=\beta(c_i)$ for each $i$. 

Using $b_i=\beta(c_i)$, and perhaps with the assumption that it is strictly increasing, you should be able simplify the $\Pr(\cdot)$'s in the objective function. The rest is just to solve for the bidding function. I will leave you to finish the remaining steps.