Help: Asymmetry and Game theory

Asymmetry and Game theory

A short mathematical diversion into Game theory may be of interest here (for those who haven't encountered it yet, this is fascinating), as it is informative about dating strategies. More directly, consider the following cases:

• You can opt to show your photograph only to other members who have a photo. Likewise, you can set your profile visibility only to other (logged in) members.
  Why would you do this? It reduces the number of people who can see it, and therefore reduces the chance of your being seen by your soulmate.
  However, this provides a strong incentive for other people to sign up, and display their own profile/photo. So it actually improves both the size of the pool, and the signal/noise ratio.
  
  
• There is asymmetry in the invite system, the valentine's code, and the loveweb: the invitor (usually) knows who the invitee is, but not vice-versa.
  Anonymous channels are created, but one person usually knows more than the other: that's unfair: it gives the first person more information than the second.
  However, if the information were symmetric, it might prevent people using it, and some potential happy couples might not get together. For example:
  Alice and Bob are good friends; Alice is in love with Bob, but doesn't know whether he feels the same way about her. She also knows that, if she asks outright and he says no, it will be awkward and could spoil their friendship. So, she uses the GraduateRomance invite-system to talk to Bob, via channel #xyz. (Alice knows that #xyz is Bob; Bob can't know (though he might guess) that it's Alice. Now, she can discover (carefully) how he feels, without revealing her own identity at first. If she thinks he doesn't fancy her, then she can close the channel, and Bob will never know that it was Alice: she has "plausible deniability". This means that Alice can take a chance on love, without also taking a gamble on their friendship.
  
  
• There is asymmetry in the magnetic gallery: you can see everyone who says 'yes' to you, but not those who say 'no'.
  This information-hiding is simple tact. In the gallery, you cannot distinguish "said 'no' to you" from "didn't answer yet".
  Why? Nobody wants to hear that someone doesn't find them attractive (and most people are kind, and don't wish to cause hurt to another by visibly declining). So, if we didn't hide that information, either people would avoid the feature entirely, or they would say 'yes' when they meant 'no'... which would then trigger a mutual-match flag.
  
  

In general if Alice and Bob both use the above features of GraduateRomance here are the possibilities:

• Alice fancies Bob and Bob fancies Alice: we tell both of them; much happiness results.
• Neither Alice nor Bob is attracted to the other: both of them know that, but no harm is done to the feelings of either party.
• Alice and Bob are friends; Alice fancies Bob but Bob is not attracted to Alice: Alice has complete information (she knows her feelings and Bob's decline) but Bob does not (he knows he doesn't fancy Alice but, having said so, cannot discover that she fancies him).
• Alice and Bob are strangers; Alice fancies Bob but Bob is not attracted to Alice: Bob knows everything, but Alice is spared an unnecessary "I don't find you attractive" from Bob.