Full disclosure, this post is mostly for me. I know that’s not the best way to get people interested in my site and my work, but I haven’t posted for a while and I’ve spent a lot of time thinking about this. If the topic interests you, awesome. If not, no worries. I’ll post more accessible content in the future.
What is Game Theory?
Game Theory indicates the best way to handle any given situation. “Game Theory Optimal” essentially refers to how a perfect computer would choose to resolve a problem. This assumes that any problem presented to you includes an optimal solution, a best solution. Choosing to follow this option means you’re operating at the “Nash Equilibrium,” a continued series of optimal choices in order to continue operating at a Game Theory Optimal level. Here are a few examples that might make the concept clearer.
Imagine a game of Rock-Paper-Scissors, where you can choose between three different options. Often, when a player selects an option, they essentially choose one at random. Their opponent does the same and one player wins. Trouble is – humans don’t do random particularly well. You might choose Rock 50% of the time, Paper 30% of the time, and Scissors 20% of the time. I might follow a 10% / 60% / 30% ratio. I wouldn’t necessarily be doing this intentionally, but rather just because humans are bad at random. The Nash Equilibrium, however, would require choosing each of the options 33% of the time. When two players operate at the Nash Equilibrium, they each win a roughly equal amount.
Here’s another example.
Imagine you and I robbed a bank. The cops catch us and split us into two rooms, without the ability to communicate or coordinate a story. They give us each the same options – rat out your partner or deny everything. Based upon this situation, we see four possibilities:
- Neither of us cooperate with the police. If this happens, we both walk away without any jail time.
- You rat me out, but I don’t rat you out. If this happens, I get 10 years in prison and you get off without any punishment.
- I rat you out, but you don’t rat me out. If this happens, you get 10 years in prison and I get off without any punishment.
- We both rat each other out. If this happens, we each get 7 years in prison.
Look at your two possibilities. If you don’t cooperate, you either get 0 or 10 years in prison. If you rat me out, you either get 0 or 7 years in prison. A Game Theory Optimal solution requires ratting me out. Game Theory encourages each participant to act within their own, selfish interests.
What is Relational Game Theory?
Let’s change the previous examples. In the second example, known as the “Prisoners’ Dilemma,” replace jail time with paying money to a third party. Let’s also assume we’re no longer just playing once, but rather 10 times.
In this scenario, I’m going to be pretty pissed if you sell me out on the first turn. I will respond by selling you out on the second turn, regardless of your choice. This means, after 10 rounds of the game, we’d sell each other out at least 9 times. Ignoring the first round, we each give up 9×7 dollars to the third party for a total of $63.
Let’s choose something different. Let’s choose to be kind, with neither of us giving each other up. Again ignoring the first round, this means, after 9 rounds of the game, we’d each give up zero dollars. Relational Game Theory assumes we’re not just working together once, but rather a number of times. The relationship matters, since it’s not just a single interaction.
Looking at Rock-Paper-Scissors, let’s assume you recognize that your partner throws Rock 80% of the time and you respond appropriately, beginning to throw Paper 80% of the time. Now, instead of each of you winning half the rounds, you win 90% of the time. Guess whose partner isn’t going to play with them again?
How does this affect our relationships?
Affective Neuroscience actually gives us a Relational Game Theory Optimal means of interacting with our romantic partners. Rather than thinking of scripted actions, think of the Nash Equilibrium as dictating what category of responses you give. The basic nature of distress in a Relational Game Theory Optimal situation would go as follows:
- Partner A feels some painful emotion, expressing a “Distress Vocalization.” In a child, this might be a cry or a whine. In an adult, it might also be a cry or a whine, but also might look more complicated. Expressions of hurt often sound like, “You just don’t ever listen to me,” or “Look how messy the house is. We never do anything.”
- Partner B responds to this painful emotion, expressing some level of comfort. When a child expresses a Distress Vocalization, an adult is biologically wired to comfort them. This might look like a hug, or just a general sense of acceptance and love. In response to the previous examples, this might sound like, “Hey honey, your opinions are so important to me. What’s going on?” or “The house is stressing you out? Okay, I’m happy to help.”
When this happens, both partners receive an oxytocin dump, feeling closer and more loved for having the interaction.
As I’m sure many of us have experienced, however, this isn’t how the interaction often goes.
What goes wrong?
Having established the Relational Game Theory Optimal means of connecting, Pain followed by Comfort, let’s look at what often happens instead.
The Pain comment comes across as an attack. Partner B, rather than responding with Comfort, responds in a defensive or aggressive manner. This, unfortunately, means we are not operating in a Relational Game Theory Optimal manner, but rather in a traditional Game Theory Optimal manner. By choosing to protect themselves and blast one another rather than engage in a loving manner, the partners essentially chose to sell out their partner to the police. While this works for an individual interaction, it does not – in any way – lead to a close relationship that functions in the long run.
What do we do about this?
Two things need to happen to move a Game Theory Optimal situation into a Relational Game Theory Optimal situation. First, we need a sense of teamwork. Without this, no level of skills-building or communication practice will matter in any way, because operating in a pro-relationship manner is not in either partners’ best interest. They need to protect themselves rather than the team, leading to pain and hurt fired back and forth. Choosing to protect your partner makes no sense at all if they’re likely to sell you out.
After establishing the sense of teamwork, we can begin working on the actual skills. This includes practicing a Relational Game Theory Optimal means of communication, giving you and your partner the ability to use these skills and new patterns naturally and organically when conflict arises. Our bodies naturally fire us up to defend us when we feel threatened. Even at the end of couples therapy, we don’t expect this to stop. We do, however, hope both partners feel safe together after a fight, re-asserting their team. Over time, this drills in the goals of Relational Game Theory.
Bonus: Using Game Theory in Board Games
I’m addressing games with 3+ players in this final section. As I’m covering these new strategies, bare in mind the strength of both fear and desire. Both arise naturally in the brain, but fear drowns out desire when pushed too far. In couples therapy that means we need to reduce fear to help each partner feel safe pushing toward the desired connection. In board games, it means we’re playing on fear.
We tend to deviate from the Nash Equilibrium when we feel threatened or afraid of something. Ever see someone turtle up in Risk, putting all their soldiers in Australia? They lose, of course, but they get to alleviate the fear of slow attrition and losing battles, instead forestalling that pain until the end of the game. Game Theory Optimal play in Risk would require constant battling for territory in order to optimize points, but fear of that battling may cause a player to hide in Australia instead.
In a multiplayer game, you want to identify where your counterparts deviate from Game Theory Optimal play. Notice they’re consolidating troops to the North, despite minimal threat? They’re afraid of invasion up there. You can use this observation to introduce division and conflict between your enemies. Point out how your opponent is threatening the North, reinforcing that fear. You opponents will start to see one another as obstacles to their own optimal play, deviating ever further from the Nash Equilibrium in order to alleviate their fear.
The other upside? Pointing this out makes it seem you’re helping with the fear. That makes you less scary, in turn making space for affection and comradery to form naturally. Without pushing for any agenda or relationship, you move your opponent into a mindset in which you’re on their team. They work toward Relational Game Theory Optimal play with you, while working toward regular Game Theory Optimal play with one another. In short, you get credit for being the good guy while also moving closer to the finish line yourself.
Remember, though, to use this strategy in board games, not your relationship.