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#!/usr/bin/env swipl
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%
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% M3b -- Sociological & population dynamics sims
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% Language: Prolog (game-theoretic equilibria as constraint satisfaction)
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% Protocol: line-delimited JSON on stdin/stdout to hub.tcl
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:- use_module(library(lists)).
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:- use_module(library(apply)).
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% -- Behavioral archetypes -----------------------------------------------
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% Each archetype has a strategy and population share
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archetype(herd_follower).
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archetype(contrarian_whale).
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archetype(mev_searcher).
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archetype(passive_lp).
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archetype(manipulator).
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% -- Replicator dynamics --------------------------------------------------
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% dx_i/dt = x_i * [f_i(x) - phi(x)]
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% Discretized: x_i(t+1) = x_i(t) + dt * x_i(t) * [f_i(x) - phi(x)]
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% Payoff matrix: row strategy vs column strategy
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% Returns payoff for Row when playing against Col
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payoff(herd_follower, herd_follower, 0.02).
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payoff(herd_follower, contrarian_whale, -0.01).
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payoff(herd_follower, mev_searcher, -0.03).
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payoff(herd_follower, passive_lp, 0.01).
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payoff(herd_follower, manipulator, -0.05).
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payoff(contrarian_whale, herd_follower, 0.04).
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payoff(contrarian_whale, contrarian_whale, -0.02).
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payoff(contrarian_whale, mev_searcher, 0.01).
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payoff(contrarian_whale, passive_lp, 0.02).
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payoff(contrarian_whale, manipulator, -0.01).
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payoff(mev_searcher, herd_follower, 0.06).
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payoff(mev_searcher, contrarian_whale, 0.01).
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payoff(mev_searcher, mev_searcher, -0.04).
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payoff(mev_searcher, passive_lp, 0.05).
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payoff(mev_searcher, manipulator, 0.02).
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payoff(passive_lp, herd_follower, 0.03).
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payoff(passive_lp, contrarian_whale, 0.01).
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payoff(passive_lp, mev_searcher, -0.02).
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payoff(passive_lp, passive_lp, 0.02).
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payoff(passive_lp, manipulator, -0.04).
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payoff(manipulator, herd_follower, 0.08).
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payoff(manipulator, contrarian_whale, -0.03).
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payoff(manipulator, mev_searcher, -0.02).
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payoff(manipulator, passive_lp, 0.06).
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payoff(manipulator, manipulator, -0.06).
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% Fitness of strategy I given population state Pop = [(Archetype, Share), ...]
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fitness(I, Pop, F) :-
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findall(Pij, (
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member((J, Xj), Pop),
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payoff(I, J, Pij0),
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Pij is Pij0 * Xj
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), Payoffs),
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sumlist(Payoffs, F).
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% Average fitness across population
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avg_fitness(Pop, Phi) :-
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findall(XiFi, (
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member((I, Xi), Pop),
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fitness(I, Pop, Fi),
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XiFi is Xi * Fi
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), Products),
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sumlist(Products, Phi).
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% One replicator step: x_i(t+dt) = x_i + dt * x_i * (f_i - phi)
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replicator_step(Pop, Dt, NewPop) :-
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avg_fitness(Pop, Phi),
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maplist(update_share(Phi, Dt, Pop), Pop, RawPop),
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normalize_pop(RawPop, NewPop).
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update_share(Phi, Dt, Pop, (I, Xi), (I, Xi1)) :-
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fitness(I, Pop, Fi),
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Xi1 is max(0, Xi + Dt * Xi * (Fi - Phi)).
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normalize_pop(Pop, NormPop) :-
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findall(X, member((_, X), Pop), Shares),
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sumlist(Shares, Total),
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(Total > 0 ->
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maplist(norm_share(Total), Pop, NormPop)
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;
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NormPop = Pop
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).
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norm_share(Total, (I, X), (I, Xn)) :-
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Xn is X / Total.
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% Run N replicator steps
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replicator_evolve(Pop, _, 0, Pop) :- !.
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replicator_evolve(Pop, Dt, N, FinalPop) :-
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N > 0,
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replicator_step(Pop, Dt, Pop1),
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N1 is N - 1,
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replicator_evolve(Pop1, Dt, N1, FinalPop).
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% -- Hegselmann-Krause bounded confidence ---------------------------------
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% x_i(t+1) = mean({x_j : |x_j - x_i| < epsilon})
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hk_step(Opinions, Epsilon, NewOpinions) :-
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maplist(hk_update(Opinions, Epsilon), Opinions, NewOpinions).
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hk_update(AllOpinions, Epsilon, Xi, NewXi) :-
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include(within_confidence(Xi, Epsilon), AllOpinions, Neighbors),
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length(Neighbors, Count),
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sumlist(Neighbors, Sum),
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NewXi is Sum / Count.
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within_confidence(Xi, Epsilon, Xj) :-
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abs(Xj - Xi) < Epsilon.
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hk_evolve(Opinions, _, 0, Opinions) :- !.
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hk_evolve(Opinions, Epsilon, N, Final) :-
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N > 0,
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hk_step(Opinions, Epsilon, Next),
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N1 is N - 1,
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hk_evolve(Next, Epsilon, N1, Final).
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% -- Nash equilibrium search (constraint satisfaction) --------------------
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% For 2-player symmetric games, find mixed strategy Nash equilibria
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% via support enumeration
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% Check if a mixed strategy (list of probabilities) is a Nash eq
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% for a symmetric game with payoff matrix
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is_nash_2p(Strategies, PayoffMatrix, Threshold) :-
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length(Strategies, N),
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length(PayoffMatrix, N),
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expected_payoff_vec(Strategies, PayoffMatrix, ExpPayoffs),
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max_list(ExpPayoffs, MaxPayoff),
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forall((
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nth0(I, Strategies, Si),
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nth0(I, ExpPayoffs, Ei)
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), (
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Si =:= 0 ; abs(Ei - MaxPayoff) < Threshold
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)).
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expected_payoff_vec(Strat, Matrix, Payoffs) :-
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maplist(expected_payoff_row(Strat), Matrix, Payoffs).
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expected_payoff_row(Strat, Row, EP) :-
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maplist(mul, Strat, Row, Products),
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sumlist(Products, EP).
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mul(A, B, C) :- C is A * B.
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% -- BoundedPrediction output ---------------------------------------------
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bounded_prediction(Value, Lower, Upper, Confidence, Horizon, Pred) :-
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Lower =< Value,
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Value =< Upper,
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Confidence >= 0.0,
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Confidence =< 10.0,
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get_time(Now),
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Timestamp is round(Now * 1000),
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Pred = pred(Value, Lower, Upper, Confidence, Horizon, sociological, Timestamp).
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format_prediction(pred(V, L, U, C, H, T, _)) :-
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format(" value: ~4f [~4f, ~4f]~n", [V, L, U]),
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format(" confidence: ~2f/10.00~n", [C]),
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format(" horizon: ~w type: ~w~n", [H, T]).
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% -- Self-test -------------------------------------------------------------
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default_population([
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(herd_follower, 0.30),
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(contrarian_whale, 0.15),
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(mev_searcher, 0.10),
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(passive_lp, 0.35),
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(manipulator, 0.10)
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]).
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run_self_test :-
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prolog_flag(version, V),
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format("M3b Sociological Sim -- SWI-Prolog ~w~n~n", [V]),
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format("Replicator dynamics (100 steps, dt=0.1):~n", []),
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default_population(Pop0),
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format(" initial: ", []),
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print_pop(Pop0),
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replicator_evolve(Pop0, 0.1, 100, PopFinal),
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format(" final: ", []),
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print_pop(PopFinal),
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nl,
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format("Hegselmann-Krause (epsilon=0.2, 20 steps):~n", []),
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HKInit = [0.1, 0.2, 0.25, 0.5, 0.55, 0.8, 0.85, 0.9],
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format(" initial: ~w~n", [HKInit]),
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hk_evolve(HKInit, 0.2, 20, HKFinal),
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format(" final: ", []),
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maplist(print_float, HKFinal), nl, nl,
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format("BoundedPrediction check:~n", []),
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(bounded_prediction(0.35, 0.20, 0.50, 7.80, '7d', Pred) ->
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format_prediction(Pred)
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;
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format(" FAILED~n", [])
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),
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format("~nInvariant checks:~n", []),
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(bounded_prediction(5.0, 6.0, 8.0, 7.0, '1h', _) ->
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format(" L2 bounds: FAIL~n", [])
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;
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format(" L2 bounds: PASS (rejected lower > value)~n", [])
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),
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(bounded_prediction(5.0, 4.0, 8.0, 11.0, '1h', _) ->
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format(" Confidence range: FAIL~n", [])
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;
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format(" Confidence range: PASS (rejected 11.0 > 10.0)~n", [])
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),
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format("~nAll models operational.~n", []).
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print_pop([]) :- nl.
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print_pop([(Name, Share)|Rest]) :-
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format("~w:~3f ", [Name, Share]),
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print_pop(Rest).
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print_float(X) :- format("~3f ", [X]).
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:- initialization((run_self_test, halt)).
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