I entered the dating market for the first time two years ago. Correction, I stumbled in like a lost explorer who didn’t think to bring an extra torch. Let’s call him gym buddy (major: ECE, class: ‘24). He was a 6am gym regular and the only other one who seemed interested in powerlifting. After a few workouts, I found out he was also a foodie. This seemed like a friendship worth taking outside the gym. It was! We laughed and cooked, watched Netflix and cooked some more. Until….the fun ended a month in when, in the middle of watching Netflix, he asked me to be his girlfriend. I rejected him and lost a good friend.
Many cases of early stage miscommunication involve some level of deception or misrepresentation. In this case, both of us were being truthful. We were just REALLY bad at interpreting each others’ signals. In fact, we would likely have been better had we never communicated.
The Model
Blume and Board (2013) wrote a beautiful model of language barriers that could be tweaked to fit this. To put it simply, players need to coordinate on an action but aren’t able because they can’t understand each other’s messages. In this context, (former) gym buddy and I couldn’t coordinate because we did not understand how to translate actions (cooking, laughing, texting good morning) into intentions (romantic interest/lack of said interest). As great as it is, I’m not going to deal with this
Here is a much simpler game:
Consider two players, B and G who are looking to decide whether to get into a relationship. They interact in two stages, the communication stage where each sends a message m = i, ni, and an action stage where each makes a decision, d = A, R.
Before the game begins, the players decide their type, t = I, NI. AKA, whether they are actually interested in the other person 😉 Without any information, the probability that one party is the other party is interested (t = I) is v. Of course, people have a hard time being objective. Enter confirmation bias. If a player is interested, the perceived probability that the other player is interested is (v+b). Conversely, if a player is not interested, the perceived probability that the other player is interested is (v- b).
For simplicity, I’ll use some arbitrary numbers to show payoffs
If both B and G are both interested (t = I). Then
Two people interested in each other are happiest if they end up together and equally unhappy if they reject each other for some reason. If rejection is one sided, the rejected player feels especially crappy and the side rejecting presumably feels bad for ignoring feeling and some guilt for the emotional fallout
If the row player is interested and the other is not. Then:
No one really wins here. But guess what, getting rejected gets much more painful. Just ask (former) gym buddy ><
If both are not interested:
yeah… best if everyone rejects. Don’t need numbers for this one.
For the purposes of this article, let’s focus on the case where only one party is interested.
Solving pt 1: No Communication
Before getting to (mis)communication, let’s see what happens when there’s no communication. Notice that if a player is not interested, that player will always choose R regardless of what type is or what the other person chooses. That is, R is the dominant choice. After all, why would someone who’s not interested ever agree to be in a voluntary relationship with someone else. Now suppose that one individual is interested.
Let’s use an expected value approach: the interested player, let’s say it’s B, thinks there’s a (v+b) chance that G is also interested. Then, choosing A gives an expected payoff of
2(v+b)-5(1-(v+b))
and choosing R gives an expected payoff of
-2(v+b)-2(1-(v+b)) = -2
Given this, B will choose A if
2(v+b)-5(1-(v+b)) >-2, or in other words, B will ask G out if he believes that the probability that G is interested is greater than 3/7
At this point, I will assume that (n+b) is uniformly distributed between 0 and 1. The probability that (v+b)> 3/7 is 4/7. Therefore, the expected outcome of no communication is
(4/7)(-5)+(3/7)(-2) = -(26/7)
for B and
-1/2
for G.
Solving pt 2: Efficient Communication
Now, suppose B and G get the chance to communicate noiselessly. They can send messages m = i, ni where only interested players send m = i and only non interested players send m = ni.
Then, B will send i, which won’t impact G’s decision to choose R. G’s message (m = ni); however, will have impact. B now knows that G’s type is NI and will choose R. In response, B will also choose R resulting in a final outcome of (-2, -1/2) which is greater than the no communication outcome.
Solving pt 3: Miscommunication
Finally, let’s get to the miscommunication. Suppose that everything is the same, except that, with probability k, B confuses message ni with i. For example, (former) gym buddy interpreted my texts and willingness to cook/hangout as romantic interest when I was not interested.
Since G is not interested, G will always send ni. The updated probability that G is interested is k(1)+(1-k)(0) = k. If k>(v+b), then B will be k – (v+b) more likely to choose A => (-5)k+(1-k)(-2) < (-5)(v+b)+(1-(k+b))(-2), resulting in a WORSE outcome.
Conclusion
In conclusion, don’t get involved with gym friends make sure you understand exactly what your potential partner’s messages mean before taking any next steps.
Cheap Talk 