Suppose three advertisers, I, II, III are participating in an auction for three positions for online advertising, top, middle and bottom. Assume that click per second for a position is not affected by who poses an advertisement there. For top, the click through rate is 3 click per second, for middle, it's 2, for bottom, it's 1. But advertisers have private value per click. For I, it's \$16 per click. For II, it's \$15. For III, it's \$14. The one who submits the highest wins the top position and pays the second highest bid, second highest bidder got the middle position and pays the third highest bid. The third highest bidder end up with bottom position, but pays zero. If there's a tie, then choose the winner ramdomly by a fair dice. The strategy space for each bidder is $\mathbb{R}_{+}$.
There're a lot of NE for this game. For example, I,II,III simultaneously submit bids of, \$7 per click, \$9 per click, \$11 per click respectively. Their payoff will be $1 \times (16-0)$ dollars, $2\times (15-7)$ dollars, and $3 \times (14-9)$ dollars respectively.
$$ \begin{array}{c|l|c|r} \hline &(0,7) & (7,9) & (9,11) & (11, +\infty)\\ \hline \text{player I}& \color{blue}{16} & \color{blue}{16} & 2(16-9)=14& 3(16-11)=15 \\ \hline \text{player II}& 15 & 2(15-7)=\color{blue}{16} & 2(15-7)=\color{blue}{16}& 3(15-11)=12 \\ \hline \text{player III}& 14 & 2(14-7)=14 & 3(14-9)= \color{blue}{15} & 3(14-9)= \color{blue}{15}\\ \hline \end{array} $$
How to find other NE?
Added: I want to study this numerical example, because I want to understand better the motivation of this paper.