Dear Adam: Bizarre Love Triangle

I have extensive experience connecting the heart to the mind, and knows the only thing true love needs to grow is pure, brutal logic. As such, periodically, I will reach into the mailbag and answer your romantic queries. This week, I try to reduce a messy love triangle into a love… line?

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Let’s try to turn your Bizarre Love Triangle into a Familiar Line of Affection

Dear Adam,

I am desperately in love with someone. But lo! There is a competing suitor! Unfortunately, my dear, sweet, conflicted lover can’t decide if my rival or I would be a better partner. “You are both so nice and are so good for me, but for different reasons!” It would appear that my sweet peach needs time to think, and see who will persevere through the indecision longer. Oh Adam, what do I do? How long do I wait? Please help.

Sincerely,

Strung-Along

Dear Strung-Along,

I am sorry to hear about your unfortunate circumstance. Oh, to be in such demand, am I right? Your “sweet peach” (or maybe sour apple?) appears to have their pick of the orchard. But we aren’t talking about fields of trees; love is a battlefield, and what you have here is a war of attrition.

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Well, it’s not not true….

Like two starving vultures, you and your rival stare each other down over the steaming carrion that is your love, unwilling to fight directly (a good call, best avoid the Prisoner’s Dilemma), but terrified you will never find love like this again! How long do you wait? At what point have you waited too long? You certainly aren’t getting any younger… Let’s consider your options.

They say time is money, but love don’t cost a thing… but that’s nonsense, and “they” are wrong. Let’s think of your situation as an “all-pay, blind auction”, since I assume you are not on speaking terms with your rival. You both cast your maximum bid of time, and the higher bidder wins the love. However, both parties are still required to pay the lowest of the two bids.

Let’s assume you and your rival are equally desperate, so the value of love is L for both of you. If your bid is b, then losing will results in -b happiness, while winning results in L-b happiness. If you both bid the same amount of time then I assume you will engage in polygamy and end up with a happiness value of (L-b)/2.

Knowing that you can wait forever, but only have to wait as long as your rival does, suggests it may be in your best interest to indeed plan to wait forever. But what if you both decide to wait longer than (L-b)/2?  You and your rival both risking mutually assured destruction, coming out a bitter, disenchanted lover if you win, or dying cold and alone if you lose. Both are negative results, in my professional opinion. We can simplify our problem and hopefully determine our strategy by considering two resolutions:

  1. There is a high bidder, and a low bidder. If you think you will be the low bidder, the logical strategy is to quit immediately, insuring you don’t lose anything. If you think you will be the high bidder, you are incentivized to bid the lowest number that still assures victory. So if there is no tie, both parties are pressured to make the lowest possible bid, converging on zero to ensure the maximum possible payout or the minimum possible loss. 
  2. You will tie. If you think you may tie, you have no reason to bid more than (L-b)/2 for risk of winning but still coming out a loser.

Since we play nice at Dear Adam, we will only consider pure strategies. The only logical choices are to not play (no losses), or to wait up to (L-b)/2, and you must decide now. But who knows what your rival will do? We can make a table of the range of outcomes based on you and your rival’s decision:

Your Decision Stay between 0 to (L-b)/2 Go
Range of Outcomes -(L-b)/2 to L 0

In the wise words of The Clash, “should I stay or should I go, now?”

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So what’s it gonna be boy? Will you love me forever? Oops, wrong song.

I’m sorry to say, but there is no way to guarantee you come out of this happy. If you leave now, you can be sure you won’t be unhappy, but there is nothing saying you will come out ahead by staying. You can try to get in the head of your enemy and assign some probabilities to their actions, but that just turns this into gambling. I am sorry but hey, that’s life. My recommendation is to ignore the table and never give up. You might end a winner, you might end a loser, but at least you won’t be a quitter. (This also reduces competition for me by exactly one person: you.)

Illogically yours,

Adam

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