Body-Reservoir Governance in Repeated Games: Embodied Decision-Making, Dynamic Sentinel Adaptation, and Complexity-Regularized Optimization

TL;DR

A three-layer Body-Reservoir Governance (BRG) architecture is proposed that reinterprets cooperation as the minimum-dissipation response of an adapted dynamical system -- emergent from embodied dynamics rather than computed.

Abstract

Standard game theory explains cooperation in repeated games through conditional strategies such as Tit-for-Tat (TfT), but these require continuous computation that imposes physical costs on embodied agents. We propose a three-layer Body-Reservoir Governance (BRG) architecture: (1) a body reservoir (echo state network) whose $d$-dimensional state performs implicit inference over interaction history, serving as both decision-maker and anomaly detector, (2) a cognitive filter providing costly strategic tools activated on demand, and (3) a metacognitive governance layer with receptivity parameter $α\in [0,1]$. At full body governance ($α=1$), closed-loop dynamics satisfy a self-consistency equation: cooperation is expressed as the reservoir's fixed point, not computed. Strategy complexity cost is defined as the KL divergence between the reservoir's state distribution and its habituated baseline. Body governance reduces this cost, with action variance decreasing up to $1600\times$ with dimension $d$. A dynamic sentinel generates a composite discomfort signal from the reservoir's own state, driving adaptive $α(t)$: near baseline during cooperation, rapidly dropping upon defection to activate cognitive retaliation. Overriding the body incurs thermodynamic cost proportional to internal state distortion. The sentinel achieves the highest payoff across all conditions, outperforming static body governance, TfT, and EMA baselines. A dimension sweep ($d \in \{5,\ldots,100\}$) shows implicit inference scales with bodily richness ($23\times$ to $1600\times$ variance reduction), attributable to reservoir dynamics. A phase diagram in $(d, τ_{\mathrm{env}})$ space reveals governance regime transitions near $d \approx 20$. The framework reinterprets cooperation as the minimum-dissipation response of an adapted dynamical system -- emergent from embodied dynamics rather than computed.

Figures (9)

• Figure 1: Self-consistent convergence of body output at $\alpha = 1$. The body readout $a^{*}(t)$ converges to approximately $0.98$ within a few rounds from a cooperative initial condition. The rapid convergence confirms the local stability of the cooperative self-consistent fixed point (Proposition \ref{['prop:stability']}).
• Figure 2: KL divergence, action variance, and mean payoff as functions of metacognitive receptivity $\alpha$. KL divergence reaches its minimum near $\alpha \approx 0.70$ (not at $\alpha = 1$), reflecting the two-source effect discussed in Section \ref{['sec:two_source']}. Action variance decreases monotonically ($\sim 250\times$ reduction from $\alpha = 0$ to $\alpha = 1$). The steep initial drop in both quantities suggests that even moderate body governance captures most of the smoothing benefit.
• Figure 3: Perturbation response to a sustained opponent defection block. At $\alpha = 1$ (body governance), the output changes gradually due to the insulating effect of the self-feedback loop. At $\alpha = 0$ (TfT), the action drops immediately to $0$ (full retaliation). The dynamic sentinel (purple) combines the best of both: it detects the defection through body discomfort and activates cognitive retaliation, then smoothly returns to body governance when cooperation resumes.
• Figure 4: Habituation dynamics for different governance modes. (a) State-space KL divergence from the noisy state distribution to the habituated baseline: body governance ($\alpha = 1$) and the dynamic sentinel provide consistently lower internal distortion than TfT ($\alpha = 0$). (b) Action variance on log scale: $\alpha = 1$ and the dynamic sentinel achieve $\sim 250\times$ variance reduction relative to $\alpha = 0$. (c) Mean body readout remains near the self-consistent value ($\approx 0.98$) throughout. The coupled habituation proceeds for $300$ epochs with measurements every $15$ epochs, averaged over $20$ seeds.
• Figure 5: Free energy landscape $\mathcal{F}(\alpha, H)$. (a) State-space complexity cost $D_{\mathrm{KL}}(p_\alpha \| p_H)$ vs $\alpha$ for different habituation depths $H$. (b) Free energy at $\lambda = 3$: at $H = 0$ the large KL cost drives the minimum to $\alpha^{*} = 1$; as habituation deepens, the optimum settles at the interior value $\alpha^{*} \approx 0.7$. (c) Optimal receptivity $\alpha^{*}$ vs $H$ for three metabolic cost levels ($\lambda = 1, 3, 8$): all converge to $\alpha^{*} \approx 0.7$ at moderate habituation. Averaged over $20$ seeds.

Theorems & Definitions (42)

• Definition 2.1: Continuous Prisoner's Dilemma
• Remark 2.2: Continuous Extension
• Definition 2.3: Body Reservoir
• Remark 2.4: The Body as Primary Decision-Maker
• Remark 2.5: The Body as Intrinsic Anomaly Detector
• Remark 2.6: Echo State Property
• Definition 2.7: Cognitive Filter
• Remark 2.8: Cognition as a Sharp but Brittle Tool
• Definition 2.9: Metacognitive Governance
• Remark 2.10: Metacognition as Lightweight Governor