Why social networks use bidirectional links even though unidirectional links are probably better

I think the main reason is simply to get people to invite their friends to the site, thus increasing the number of users via peer pressure.

For specialty social networks (or specialties within a general social networking site), your friends are probably not the best people to connect to. In that case, it would probably be better to use unidirectional links so that you can "subscribe" to anyone whom you would like to learn from.

Yet these unidirectional links -- while better suited in such cases -- are not great in attracting people to the site. And so such sites probably won't get enough critical mass to be interesting.

Instead of friend requests and acceptances, users should just be able to subscribe to other people via unidirectional links.

Such unidirectional links don't designate friendship at all, but rather, interest in keeping in touch with someone's activities (e.g., their subscriptions to discussion groups, the apps they add to their profile, etc.).

You could use some sort of reward to encourage people to invite their friends that has nothing to do with these links.

For example, wherever people are listed throughout the site, you could rank them based on the number of friends that they have invited to the site.

Why not let online ads fight it out in a geometric real-time game played by advertisers and consumers?

In this approach, the advertiser would display his/her ad along with all the other ads currently on display.

Larger ads have the disadvantage that they will overlap with other ads and may end up being underneath many of them.

Advertisers may resize and/or move their ads at any time to reduce overlap.

Whenever two ads overlap, they will then have to fight it out to see which one will go on top. This fight is on-going and may involve one ad appearing on top, later underneath, then on top again, and so on.

To determine which of two overlapping ads goes on top, we would compare their current scores, where the score of an ad could be the number of visits minus the number of "hide" requests from consumers say.

One can view this approach as a geometric version of social news.

For a non-geometric version of this idea, we could have something like reddit but where the submitter determines and can change the rank of his/her link on the front page.

The issue is that a link ranked highly will have to share that rank with many links. We can have the probability that a user will see a link at rank k depend on the score of that link with respect to the scores of other links with rank k.