the Knightian uncertainty of local positions within a game (“given this exact configuration, how much does my outcome depend on unknown opponent type, unknown payoff structure, unknown model of the world?”)
and
the Knightian uncertainty of some games relative to other games (“how much does the rule set, state space, opponent ontology, or payoff structure mutate as play continues?”)
I suspect that the two are related, and that when we calculate the Knightian uncertainty of local positions, we will need to factor in our uncertainty with regards to the type of game we’re playing.
For example: Tic-tac-toe has zero: the state space is fully enumerated, optimal play is strivial, every competent player forces a draw—there’s no tactical complexity to amplify mistakes.
Chess has slightly more meta-game permeability. Players cannot change the board, cannot add new pieces, cannot redefine legal moves, cannot declare “this now counts as checkmate”, cannot invent a new win condition.
Go has the same fixed-rule structure, but the state space explodes. The game-tree is too large to fully reason about, so bounded reasoning dominates.
In poker/markets, rules are mostly fixed, but information asymmetry is now part of the actual game.
In diplomacy/geopolitics, rules are soft, not hard. Players can redefine objectives and also alter the payoff structure. The game itself can change while you are playing it.
Art has even more meta-game permeability (and therefore a higher game_uncertainty coefficient): artists invent new art forms, collapse genres, redefine what counts as art, etc. Every innovation becomes part of the game for everyone else. (Publishers in 1914-1939 to James Joyce: “This isn’t a novel.” James Joyce: “Fuck you yes it is”)
Romance is the most Knightian domain maybe humans ever engage in. Signals are ambiguous, no stable payoff function, opponents mututate as agents (psychologically and physically) over time, one person’s move can redefine the entire domain, even the goal of the game is unclear, every interaction rewrites the other person’s internal model, the frame itself dissolves and reconstitutes with every gesture. There’s no discernable game tree – half the game is inventing what the game even is. Pickup artists understand this.
If the domain itself is unstable, every local position inherits that instability.
Tic-tac-toe gives no uncertainty even in the weirdest position.
Romance gives knightian uncertainty even in the most trivial position.
So, we must model the domain-level Knightian coefficient first.
Maybe we can model the game as a decision process in domain G
Game G has
State space S
Action space A
Rule space R
Transition model T
Payoff function U
Opponent skill Theta
And we don’t know what type of opponent we face, what payoff function is actually in play. So we have ambiguity sets within R, U and Theta
In Tic-tac-toe, all these sets would be singletons (zero ambiguity). in romance, none of them are.
We want to define:
Local ambiguity:
a Knightian-ness factor of G that factors in my local position under some sort of distribution of opponent types and possible moves.
“How much does the outcome of this position vary depending on unknowns?”
Rule entropy
We also care about the fact that some domains let you change the rules while playing. Maybe we want to define a rule-entropy over the rule space.
“How many different rule sets are live, or could become live?”
Meta-move ratio
“How often do people take actions that change the rules instead of acting inside them?”
In tic-tac-toe: M(G) = 0 (no one can legally change anything).
In romance: M(G) is very large (people constantly renegotiate their desires, boundaries, even the “goal” of the relationship).
Knightian_Uncertainty(G) might be a combination of how ambiguous local positions are (given the current rule set + types), how uncertain the rules are, and how often agents actually modify those rules during play
This is all very confusing and exciting and messy. Next, I suggest playing Connect-3, Connect-4, Connect-5, and Connect-6, and trying to understand the ways that when we crank n up, we crank up board complexity, ambiguity over oppoent’s goals, number of plausible futures, and local and global Knightian-ness up.
You seem to be locating two things here:
the Knightian uncertainty of local positions within a game (“given this exact configuration, how much does my outcome depend on unknown opponent type, unknown payoff structure, unknown model of the world?”)
and
the Knightian uncertainty of some games relative to other games (“how much does the rule set, state space, opponent ontology, or payoff structure mutate as play continues?”)
I suspect that the two are related, and that when we calculate the Knightian uncertainty of local positions, we will need to factor in our uncertainty with regards to the type of game we’re playing.
For example: Tic-tac-toe has zero: the state space is fully enumerated, optimal play is strivial, every competent player forces a draw—there’s no tactical complexity to amplify mistakes.
Chess has slightly more meta-game permeability. Players cannot change the board, cannot add new pieces, cannot redefine legal moves, cannot declare “this now counts as checkmate”, cannot invent a new win condition.
Go has the same fixed-rule structure, but the state space explodes. The game-tree is too large to fully reason about, so bounded reasoning dominates.
In poker/markets, rules are mostly fixed, but information asymmetry is now part of the actual game.
In diplomacy/geopolitics, rules are soft, not hard. Players can redefine objectives and also alter the payoff structure. The game itself can change while you are playing it.
Art has even more meta-game permeability (and therefore a higher game_uncertainty coefficient): artists invent new art forms, collapse genres, redefine what counts as art, etc. Every innovation becomes part of the game for everyone else. (Publishers in 1914-1939 to James Joyce: “This isn’t a novel.” James Joyce: “Fuck you yes it is”)
Romance is the most Knightian domain maybe humans ever engage in. Signals are ambiguous, no stable payoff function, opponents mututate as agents (psychologically and physically) over time, one person’s move can redefine the entire domain, even the goal of the game is unclear, every interaction rewrites the other person’s internal model, the frame itself dissolves and reconstitutes with every gesture. There’s no discernable game tree – half the game is inventing what the game even is. Pickup artists understand this.
If the domain itself is unstable, every local position inherits that instability.
Tic-tac-toe gives no uncertainty even in the weirdest position.
Romance gives knightian uncertainty even in the most trivial position.
So, we must model the domain-level Knightian coefficient first.
Maybe we can model the game as a decision process in domain G
Game G has
State space S
Action space A
Rule space R
Transition model T
Payoff function U
Opponent skill Theta
And we don’t know what type of opponent we face, what payoff function is actually in play. So we have ambiguity sets within R, U and Theta
In Tic-tac-toe, all these sets would be singletons (zero ambiguity). in romance, none of them are.
We want to define:
Local ambiguity:
a Knightian-ness factor of G that factors in my local position under some sort of distribution of opponent types and possible moves.
“How much does the outcome of this position vary depending on unknowns?”
Rule entropy
We also care about the fact that some domains let you change the rules while playing. Maybe we want to define a rule-entropy over the rule space.
“How many different rule sets are live, or could become live?”
Meta-move ratio
“How often do people take actions that change the rules instead of acting inside them?”
In tic-tac-toe: M(G) = 0 (no one can legally change anything).
In romance: M(G) is very large (people constantly renegotiate their desires, boundaries, even the “goal” of the relationship).
Knightian_Uncertainty(G) might be a combination of how ambiguous local positions are (given the current rule set + types), how uncertain the rules are, and how often agents actually modify those rules during play
This is all very confusing and exciting and messy. Next, I suggest playing Connect-3, Connect-4, Connect-5, and Connect-6, and trying to understand the ways that when we crank n up, we crank up board complexity, ambiguity over oppoent’s goals, number of plausible futures, and local and global Knightian-ness up.