preference meronomy

• aggregating collective negations needs roundabout mechanisms like tabooing.

• agents can only ever be grey boxes

• How does one add a word to a language? How does one introduce a change in grammar? How does one subvert usage - say for sarcasm, irony, or puns?

• Arendt and Anscombe: The Human as Actor

Agents can be reduced to their preferences - actually, to their strategic choices, from which preferences can be derived. Coalitions also have strategies. Do coalitions also have preferences? We can certainly derive preferences from coalitional strategies as much as we can from individual actors.

Let's say this is legal. Then preferences have part-whole relationships of some kind. They don't aggregate or accrete, because the movement of the relation can be non-monotonic (i.e. a Pareto regression); we can only say of rational agents that they obey the dominance relation for their coalition. (TODO if the dominance relation is transitive then preferences are composable. Otherwise they are used to construct each other.)

Is this a fun trick or is there any kind of rent-paying semantics to attach to the idea? One place to look is whether the firm-agent participates strategically in the game and how. Against players outside the coalition for a given game, it seems obviously to. If the conditions of the game are varied, it might not even exist, and so perhaps it can't be said to participate in any selection among those alternatives. But we have several relations from which we can derive tendencies in the movement from one preference to another. We can for eg characterize it with the Pareto update. We can also try to construct a superposition of two narrowly-deviating games, where the selection between the games is a choice that requires a coalitional consensus; and in this way see what the coalition prefers. Doing this reveals an important truth about coalitional preferences: they can only really distinguish coalitions for sections of strategies that require the whole coalition to cooperate.

This means something important for players of games that have a lot of these types of winning strategies, or are bottlenecked on coordination: player preferences about things that do not relate to coalitional winning strategies will always be ignored or superseded by preferences about things that do. In this way, we can say that firm-agents are playing against their potential members.

Players that stand to gain from the winning strategy are incentivised to block off defection of other players whenever possible. In this way we can say that firm-agents with a committed core that will act in this way can fight to stay alive.

Players acting as a coalition will ignore large swathes of the game tree in favor of acting in concert. In this way coalitions can be said to prune or narrow the game tree.

The dominance relation establishes a relationship of the coalition (size 1 and up) to a wider collection of potential coalitions. It sets up something like an awareness of context, traditionally a kind of reliance on the bounds of the defined play space that makes game theory very fragile to changes. As game designers we can model consequences but can't perfectly execute on them. However, coalitions narrow play space in a much more organic fashion - by setting up actions and conseuqneces that players inflict on each other for their own gain, you get a system where you can potentially fuzz the details of how the retaliation goes the same way you fuzz the fine structure of a game in probabilistic or epistemic games. The key is to notice that coalitions possess many paths to victory and can be meaningfully said to want things.