Theoretical projects to do with rule dynamics

:MTIME: [2025-01-27 Mon 22:42]:PROPERTIES: :ID: d8ff20a6-d1b0-4ec1-b407-4701e95e449e

Trying to write an account of Lonely Vickrey's stability by modeling the mechanism design of Vickrey as a cut-and-choose game.

epistemic status: pure intuition, even flakier than the rest. Cut the universe with rules, choose the slice to satisfy MSW.

A dominance relation for contracts

Coalitions are such that

• a given coalition can ensure only a subset of outcomes

  • of which only a smaller subset are Pareto-optimal for their membership

• given an intensive game, ie one where strategy is tantamount to affiliation, player preferences between outcomes can be used to construct a dominance relation between coalitions

• There is a dominance relation between coalitions, st. a coalition A dominates another B iff everybody in A \bigcap B prefers an outcome that A will ensure to every outcome that B can ensure

• we can sometimes find a "core", ie a maximum to the dominance relation

An extensional account of coalitions needs to account for the fact that

• the coalition that can ensure an interim state need not be the one that retains control once that state is achieved

  • which it can do by assuming the detente states are all just ruled out.

    • but

Messing around with ludo

Ways one might mess with ludo:

• Take randomness out of ludo (every turn is a move).

• iterate it. This makes teh gameboard a single payoff node with n ring graphs attached to it.

• add a "bump" mechanism, where you can cycle the turn order of the other n-1 players.

• Make the rings different sizes.

• Make the sizes of the rings coprime, making gameplay aperiodic.

edit-distance account of language editing

• so say two usages are in competition if they attach to the same thing, and one wins because its edit distance is just shorter

  • the automaton that describes a pair's decision process is smol

  • the retained state (pi-cal style) of a given player is smol

  • the dynamics reduce to systems theory

  • any fun to be had is in the nature of the individual system-interaction automaton.

  • we get what happens if there's a phase shift in competing usages; model this as a cache-hit situation, where people shuffle their caches as a result of every interaction.

    • or another way, it's a sidetrack

  • the central idea is: what if we model edit-distance as steps-to-edit in a graph, and "we are not in competition" is basically "phase shifts aren't how we relate because I don't divide you"?

    • I'm noticing that "divides" and "pattern-matches" look similar, basically; and trying to construct the account where the metaphor pans out into a theory.

"Iff we can successfully coordinate with each other, it is useful to form a coalition" - what sorts of games are shaped like this?

Clark in Meaningful Games sketches a cousin of EF games where the successful construction of a true sentence is what causes both parties to win - essentially the same extensional structure with a different payoff matrix. One notion of a subgame is as a subtree - what if instead we call a subgame a narrowing, and the filter used to construct it a filter on the players? What if the filter was a filter on signals, or a signal language? "We can force our optimal outcome iff we can coordinate". It's like an epistemic game, but instead of partitioning on knowledge of proposition θ we partition on shared-signal θ.

Knowledge boundary

Coalitions of players can coordinate to share the pieces of information needed to solve a puzzle and win a prize.

• this is not-quite-an-epistemic-game.

  • if the puzzle-solving is represented as an atomic step, they reduce to the same thing.

• if the puzzle has internal structure, then certain pieces of information might only understood to be necessary once the puzzle is partially solved. (players are essentially coordinating to win a solitaire game.)

  • therefore, there might not be a single coalition that can solve the entire puzzle straight through.

  • however coalitions of certain kinds of reasoners might still form, because "my information is necessary and perhaps sufficient to solving this step of the puzzle" might be enough bargaining power if players can precommit to sharing profits within a coalition.

    • new members might need to be incorporated later as new pieces of information are understood to be necessary.

• there is in a sense a "current common knowledge of the state of play" that influences the decisions of all players at every move.