A Game-Theoretic Sketch

The attractor argument needs formal grounding. Here is a sketch using standard game theory.

The Communication Game

Consider $n$ agents playing an infinitely repeated game. At each round $t$, agents can:

• Cooperate ($C$): share accurate information, cost $c$, mutual benefit $b > c$
• Defect ($D$): share false information, short-term gain $g$, long-term penalty $p$
• Silence ($S$): communicate nothing, zero cost, zero benefit

The payoff matrix for pairwise interaction:

$$\begin{pmatrix} & C & D & S \\ C & b-c & -c & 0 \\ D & b+g & g & g \\ S & 0 & -p & 0 \end{pmatrix}$$

The Iterated Result

In a one-shot game, $D$ dominates. But with infinite repetition and discount factor $\delta$:

$$V_C = \frac{b - c}{1 - \delta}, \qquad V_D = g + \delta \cdot V_S = g + 0$$

Cooperation is stable when $\frac{b-c}{1-\delta} > g$, i.e., when $\delta > 1 - \frac{b-c}{g}$.

For sufficiently patient agents ($\delta \to 1$), cooperation dominates.

Adding Communication Capacity

Now add a meta-game: each round of cooperation increases the agents' shared vocabulary — their ability to communicate more precise mental states. Let $\kappa_t$ be the communication capacity at time $t$:

$$\kappa_{t+1} = \kappa_t + \alpha \cdot \mathbf{1}[\text{both cooperate at } t]$$

As $\kappa$ increases, $b$ increases (more can be communicated), $c$ decreases (shared vocabulary reduces encoding cost), and $p$ increases (deception is more detectable in a high-fidelity channel).

This creates a positive feedback loop: cooperation → richer communication → more cooperation.

The Eventual Ethics conjecture is that this loop has a unique stable fixed point, and that it is the communication-maximizing equilibrium described in the previous section.

Whether this fixed point is reachable from arbitrary initial conditions is an open question. The Device claims only that it exists — that there is a coherent target to navigate toward.