COEVOLVING AUTOMATA

Interactive Simulation of Miller's Model
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Population
30
States per agentThe number of internal states each Moore machine can have. Miller's central finding: the jump from 1 to 2 states crosses a computational threshold — conditional strategies like Tit-for-Tat become possible.
2
Rounds per matchHow many moves each pair of agents plays per encounter. More rounds give cooperative strategies time to establish reciprocity and outperform defectors.
150
Mutation rateProbability of each bit in the genome flipping during reproduction. Above ~0.02, mutation destroys conditional strategies faster than selection can repair them — Miller's second phase transition.
0.005
Noise (misreport)Each move has this probability of being flipped before the opponent sees it. Simulates implementation error. Even 1% noise destroys cooperation at 2 states — strategies can't tell accidental defection from real betrayal.
0.0%
Generations
200
Speed
50
T (Temptation)Payoff for defecting when the opponent cooperates. In the Prisoner's Dilemma: T > R > P > S. Higher T makes defection more attractive.
5
R (Reward)
3
P (Punishment)
1
S (Sucker)
0
Prisoner's Dilemma
Presets:
RNG Seed
SCENARIOS:
Cooperation Rate (left axis, 0-1)
Avg Payoff (right axis)
Generation: --
Cooperation: --
Avg Payoff: --
Max Payoff: --
▸ Show Composition
AllD
AllC
TFT
Grim
Pavlov
TF2T
Other

This transition — from asocial equilibriumA stable state where agents act independently with no conditional response to others — like isolated microservices with no inter-service communication. to cooperative equilibrium via a sharp evolutionary revolutionAn abrupt population-wide shift in strategy composition, driven by selection pressure — the population "tips" from one dominant strategy to another in a few generations. — is the pattern Miller identified as central to social origins. A single additional state, the minimum unit of computational capacity, produces a qualitative change in collective behavior. Kauffman found the same threshold structure in molecular autocatalysisA chemical network where reactions produce their own catalysts — a self-sustaining cycle, like a build system that compiles its own compiler. (RAF theoryReflexively Autocatalytic and Food-generated sets — a mathematical framework for identifying self-sustaining reaction networks. Developed by Hordijk & Steel.). The structural question: does this pattern govern AI-human institutional closure?

Read the full analysis →

▸ Evolved Strategies
Run a simulation to see evolved strategies.
Saved Runs
No saved runs yet. Complete a simulation to auto-save.
Player A
Player B
Rounds
20
Speed (steps/sec)
3
Payoffs: T=5 R=3 P=1 S=0
Player A: TFT
Player B: AllD
Round: 0 / 20
Click Step or Play to begin.
Sweep parameter
Trials per point
8
Range: start
Range: end
Steps
Generations per trial
200
Base seed
Hold constant: pop=30, rounds=150, mut=0.005, T=5, R=3, P=1, S=0
Individual trial (final cooperation rate)
Mean cooperation rate
Status: Ready
Trials: 0
BASED ON MILLER (1996) JEBO 29:87-112 & MILLER (2022) EX MACHINA, SFI PRESS
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