On Boundaries

How to apply the concept, how boundaries arise, and just more thoughts.

I have discussed Boundaries here. I still need to build a good model of the concept, but here are more thoughts while I try to form a more coherent opinion about the topic.

What do games mean without boundaries?

Without a good understanding of boundaries, it is unclear to me how Game theory can be applied.

Game theory holds as long as a situation can be modelled as a specific game, as long as its rules hold. But these rules hold as long as boundaries are respected.

When people disagree too much in a game, they can always start flipping the board, the table or throwing punches.

Myopia

Did you know the world GDP would double if we abolished borders and everyone could migrate everywhere?

If half the population of the poor region emigrates, migrants would gain $23 trillion—which is 38 percent of global GDP. For nonmigrants, the outcome of such a wave of migration would have complicated effects: presumably, average wages would rise in the poor region and fall in the rich region, while returns to capital rise in the rich region and fall in the poor region. The net effect of these other changes could theoretically be negative, zero, or positive. But when combining these factors with the gains to migrants, we might plausibly imagine overall gains of 20–60 percent of global GDP.

This is terribly misguided. By this, I do not mean their estimate is too high or too low.

What I mean is that if we abolished borders, any "rules of the game" would be thrown out. The word "country" would not mean the same anymore. Absent borders, the most physical boundaries, the game shatters. One should not just extrapolate from how things work right now; use economic models and expect everything else to stay the same.

This is the prototypical example of a Myopic Change. "Without traffic rules, I could drive faster!" Nope. Without traffic rules, we are playing a different game. It is not clear whether, in that game, there will be enough trust in the other drivers or whether governments will invest enough in maintenance so that there are still roads that we can drive at all or at the same speed as before.

Negotiations

A buyer's Willingness To Pay (WTP) is the maximum price they would pay for a product or service. The converse is the Willingness To Accept (WTA), the minimum price a seller would accept for its product or service.

If WTP > WTA, then the buyer is willing to buy at a price higher than the seller is willing to sell. A trade can occur between a buyer and a seller. Deciding the actual price is then the topic of bargaining.

How does bargaining happen? I don't know. I am not well-versed in bargaining theory. But what often happens is that when one of the parties violates some implicit rule, the other gets offended, and no trade happens whatsoever. The game breaks down. Boundaries seem quite important to model here.

Deontology on a budget

Deontology is reasoning about which actions are allowed or forbidden. It is less about the consequences of the actions than about their nature. Deontology says it might be better to do things that result in more people dying if it means we do not have to kill someone directly.

Deontology is a natural model of boundaries.

But while deontology seems absolute, it is limited by a budget. We are willing to obey deontology as long as it does not lead to too many direct losses. We are okay with helping someone starving as long as it does not cost us too much. We will avoid cheating at a game by default, but circumstances could change our minds.

(As a side note, I wrote "direct losses" because we seem willing to tank arbitrarily much counterfactual value (indirect losses) for deontological reasons. This is both a bug and a feature of deontology.)

Our budget for deontology forms boundaries on top of boundaries. And here, I start getting confused about formally modelling this.

Beyond budget considerations, deontology seems harsh, but we can recover from violations. This can be part of forgiveness, punishment, or resiliency to accidents in game theory. (You can look for Generous Tit For That / Generous TFT in this SEP entry.) This makes deontology a more fuzzy boundary than one might believe at first.

Multi-Dimensional Values

Some of our values are heterogeneous. For instance, when playing a video game with someone else, we try to have fun and win. In that case, there are sharp boundaries between those two behaviours: you can optimise for both, but you should not cheat, for instance.

In that case, a single utility function with different weights for the values (like, "I value X at 80% what I value Y") is not a good model. It is more easily represented by two games happening simultaneously, and they share some overlap.

This leads to interesting situations where we can cooperate and compete with someone simultaneously. We draw lines in the sand and thus divide the world into two games. One where we cooperate because we both stand to benefit and one where we compete harshly.

The boundaries are here to ensure that the game does not devolve into pure competition. This is a very important part of what cooperation actually means: a set of rules so that we can all benefit from the commonly agreed-upon stuff and compete on the rest.

This is how our societies work, the natural synthesis between freedom and order: strong order in the shape of laws and regulations coupled with the freedom to compete between individuals and companies.

This is how personal relationships work. We agree on values that we share and work together on them, but this does not prevent us from being our own people the rest of the time.

When the non-shared values are too opposed, we compete on them.

When the non-shared values are independent, we can work out some fair distribution of resources instead of competing destructively.

This dynamic is important in human relationships, borne by boundaries and multi-dimensionality.

Conclusion

I still need to think more about boundaries.

Cheers, and have a nice day!