A Market for Behaviors

Explore the five layers of the framework hands-on. Adjust sliders, switch between behavior types, and watch how markets shape what we learn.

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Figure 1: The Behavioral Landscape

Every behavior gets a reward from the incentive map I(b). The probability distribution P*(b) then piles up where rewards are high. Drag the temperature slider to feel the trade-off between exploring widely and sticking with what works.

P_a(b) = e^I(b)/τ / Σ_b'∈B e^I(b')/τ

Temperature τ 0.50

Reward peak position 50

Reward width 15

Reward amplitude 3.0

Figure 1: The orange curve is the incentive map. The blue area is what actually happens. Low τ means the agent locks onto the best behavior. High τ means it spreads out and tries everything.

Incentive map I(b)

Probability P*(b)

Figure 2: Supply and Demand for Behaviors

Pick a behavior type. Supply (what it costs to produce) goes up with quantity. Demand (how much someone values receiving it) goes down. Where they cross, the market settles.

r_ij(b) = v_j(b) − c_i(b) | I_i(b) = Σ_j≠i v_j(b) − c_i(b)

Figure 2: Supply and demand for "helpful responses." Equilibrium reward and frequency at intersection.

Supply (cost)

Demand (value)

Equilibrium

Figure 3: Multi-Agent Market Network

Each circle is an agent. Arrows show who is sending behaviors to whom. Thicker arrows mean bigger rewards. Everyone is both a producer and a consumer.

Figure 3: Six agents trading behaviors. Thicker arrows carry more reward. The market keeps behaviors and rewards circulating.

Figure 4: Rate-Distortion and Behavioral Diversity Loss

When you squeeze a model into fewer parameters, you lose information. The rare, unusual behaviors disappear first. Drag left to see diversity collapse.

θ* = argmin_θ D_KL(P* ‖ q_θ) | R(D) = min rate for distortion D

Figure 4: On the left, the model is too small and diversity crumbles. On the right, there is room for everything. The long tail of rare behaviors vanishes first.

Distortion D(R)

Behavioral diversity

Figure 5: The Feedback Loop

The cycle goes: spectrum → incentives → market → data → training → synthetic data → back to spectrum. Each pass through the loop squeezes the distribution a little tighter.

P_t+1 = Compress(Filter(P_t))

Figure 5: The loop feeds itself. Filtering and compression chip away at variety each time around. Without actively injecting diversity, everything collapses toward a narrow norm.

Figure 6: Golden Rule vs. Platinum Rule

On the left, the Golden Rule: assume everyone wants what you want. On the right, the Platinum Rule: actually find out what they want.

Golden Rule

"Treat others as you want to be treated"

b_i→j^Golden = argmax v_i(b) − c_i(b)
Agent i projects v_i onto agent j. Fails when v_j ≠ v_i.

Platinum Rule

"Treat others as they want to be treated"

b_i→j^Platinum = argmax v_j(b) − c_i(b)
Agent i learns v̂_j → v_j from data, then produces matching behaviors.

Figure 6: The Golden Rule (left) guesses. The Platinum Rule (right) asks, watches, and learns what the other person actually values.

Summary: The Five Layers

1. Behavioral Spectrum

Ontology. The space of all possible behaviors B. Defines what can exist before selection.

2. Incentive Map

Dynamics. I: B → R assigns reward to each behavior. Shapes probability via the Boltzmann distribution.

3. Market for Behaviors

Economics. Multi-agent system that rewards, prices, selects, suppresses, records, and amplifies. Supply = cost, demand = value.

4. Training = Compression

Compression. θ* = argmin D_KL(P* ‖ q_θ). Compresses market-selected traces into a generative model. Loses the long tail first.

5. Alignment = Market Design

Market design. Designing the incentive map so the market equilibrium maximizes social surplus. The Platinum Rule is the ethical principle: learn v_j from data, produce behaviors that maximize receiver value.

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