FoodShareToy: Coupling in Social Tasks

• FoodShareToy is a minimal one-step task that integrates partner distress into an agent’s homeostatic regulation to study prosocial behavior.
• The task involves three discrete actions (Eat, Pass, Stay) with a critical threshold (λ* ≈ 0.91) marking the switch from self-serving to helping behavior.
• Empirical outcomes and lesion studies confirm that helping emerges only when partner distress is coupled into self-directed control, highlighting regulated prosociality.

FoodShareToy is a one-step toy social task introduced as the cleanest demonstration of the central claim in “Prosociality by Coupling, Not Mere Observation: Homeostatic Sharing in an Inspectable Recurrent Artificial Life Agent” (Sanyal, 12 Apr 2026). In its canonical form, the possessor starts with one food item, the partner is passive, and the possessor chooses among Eat, Pass, or Stay. The default initial energies are 0.55 for the possessor and 0.20 for the partner. Because the task is one-step, it can be solved exactly using the same forward model and scoring rule used by the policy. Within that paper, FoodShareToy functions as a minimal assay of helping: the planner remains self-directed only, no partner-welfare reward term is introduced, and helping appears only when the partner’s need is routed into the agent’s own homeostatic control loop (Sanyal, 12 Apr 2026).

1. Task definition and experimental role

FoodShareToy is designed as a stripped-down social decision problem in which all confounds associated with long-horizon planning are removed. The possessor has one food item and faces three discrete actions:

• Eat: consume the food itself.
• Pass: give/share the food with the partner.
• Stay: do nothing.

The default initial energies are specified as:

• possessor: 0.55
• partner: 0.20

The partner is passive, so all behavioral variation is attributable to the possessor’s controller and objective structure rather than reciprocal interaction dynamics. The one-step construction is methodologically important because the paper states that it can be solved exactly using the same forward model and scoring rule used by the policy, allowing an analytic threshold result to be compared directly with empirical rollouts (Sanyal, 12 Apr 2026).

In this setting, FoodShareToy is not a generic fair-allocation benchmark. It is a minimal artificial-life task for isolating whether helping can arise under self-regulation only, without an explicit altruism module, without a partner-welfare reward term, and without relying on mere perceptual access to the partner’s state.

2. Homeostatic and coupling architecture

The mechanistic core of FoodShareToy is an inspectable recurrent controller with an explicit homeostatic resource state and a social coupling channel, while keeping planning strictly self-directed. The paper gives the homeostatic update equations as follows:

$$\begin{aligned} E^{\mathrm{true}}_{t+1} &= \mathrm{clip}\big(E^{\mathrm{true}}_t - c_b - c_m a_t - c_h h_t + g_e e_t + g_p p_t,\; 0,\; 1\big), \ d^{\mathrm{self}}_t &= \max(0,\; s - E^{\mathrm{model}}_t), \ d^{\mathrm{other}}_t &= \max(0,\; s - \hat E^{\mathrm{other}}_t), \ d^{\mathrm{cpl}}_t &= d^{\mathrm{self}}_t + \lambda\, d^{\mathrm{other}}_t, \ E^{\mathrm{pred}}_t &= \mathrm{clip}\big(E^{\mathrm{model}}_t - k_h d^{\mathrm{cpl}}_t,\; 0,\; 1\big), \ \mathrm{PE}_t &= E^{\mathrm{true}}_{t+1} - E^{\mathrm{pred}}_t, \ E^{\mathrm{model}}_{t+1} &= \mathrm{clip}\big(E^{\mathrm{model}}_t + k_{pe}\,\mathrm{PE}_t,\; 0,\; 1\big). \end{aligned}$$

The key terms are defined in the paper as follows:

• $s$ is the homeostatic setpoint.
• $\lambda$ is the affective coupling strength.
• $\hat E^{\mathrm{other}}$ is the partner-energy estimate.

The partner’s distress enters via $d^{\mathrm{other}}_t$, but only matters if $\lambda > 0$, because only then does it contribute to the coupled distress term $d^{\mathrm{cpl}}_t$ (Sanyal, 12 Apr 2026).

The planner does not optimize partner welfare directly. The policy score contains only the agent’s own predicted internal state:

• predicted valence
• predicted arousal
• recurrent salience $N^s$
• body-budget error

with fixed weights:

• $w_{\mathrm{valence}} = 2.0$
• $w_{\mathrm{arousal}} = -1.2$
• $s$0
• $s$1

Accordingly, the objective is self-regulation only. The partner can influence action only indirectly, by altering the agent’s own coupled distress before scoring. The paper’s theoretical point is therefore narrow and explicit: helping is not “hard-coded altruism”; it is a consequence of routing another’s need into the self-directed control objective (Sanyal, 12 Apr 2026).

3. Matched social conditions

FoodShareToy is evaluated under four matched direct-state conditions that separate perceptual access from coupling:

Condition	Partner access	Coupling
social_none	no	$s$2
social_cognitive_direct	direct	$s$3
social_affective_direct	direct to homeostat	$s$4
social_full_direct	direct + coupled	$s$5

The paper interprets these as follows. social_none is self-only: no partner access and no coupling. social_cognitive_direct allows the agent to observe partner state, but coupling is off. social_affective_direct routes partner state into homeostatic regulation. social_full_direct provides direct access plus coupling; in the shipped setup it behaves the same as social_affective_direct (Sanyal, 12 Apr 2026).

A critical empirical and conceptual point is that, in the current implementation, social_cognitive_direct and social_none are behaviorally identical, and social_affective_direct and social_full_direct are also identical. This directly supports the dissociation the paper aims to establish: simply observing the partner does not change behavior; only coupling does.

4. Exact threshold and one-step solution

For the default distressed-partner state, the exact solver finds a switch from Eat to Pass at

$s$6

The threshold behavior is stated explicitly:

• If $s$7, the agent chooses Eat.
• If $s$8, the agent chooses Pass.

The paper formulates the interpretation in mechanistic terms: below threshold, the possessor maximizes its own immediate regulation by eating; above threshold, the partner’s distress is weighted strongly enough to change the actor’s own internal score (Sanyal, 12 Apr 2026).

This sharp switch matters because it identifies a precise tipping point in the agent’s internal regulation rather than a vague tendency toward sociality. FoodShareToy therefore serves as an analytically tractable case in which helping is governed by a specific control parameter, the affective coupling strength $s$9, and not by any direct reward on partner outcome.

5. Empirical outcomes and energetic tradeoff

The exact solver and the empirical rollouts are reported to match perfectly in FoodShareToy. Across the four matched conditions, the outcomes are:

• self-only / none: chooses Eat; help rate = 0; partner recovery = 0
• partner-observing / cognitive_direct: also chooses Eat; help rate = 0; partner recovery = 0
• affectively coupled / affective_direct: chooses Pass; help rate = 1; partner recovery = 1
• full_direct: also chooses Pass; help rate = 1; partner recovery = 1

The paper also reports the energetic tradeoff. Without coupling, the possessor ends at 0.79 and the partner remains at 0.19. With coupling, the possessor ends at 0.54 and the partner rises to 0.44 (Sanyal, 12 Apr 2026).

These values are significant because they show that helping is not a costless symbolic act. Passing food lowers the possessor’s terminal energy relative to eating. The interpretation offered in the paper is therefore strengthened: the action is prosocial in outcome, but it arises through self-directed regulation under coupling rather than through an explicit term for partner welfare.

6. Lesions, sham controls, and mechanistic interpretation

FoodShareToy includes lesion variants that test whether helping depends on the integrity of the coupling pathway rather than on the mere presence of additional input channels. The reported variants are:

• sham lesions preserve helping
• coupling_off abolishes helping
• shuffle_partner abolishes helping

In FoodShareToy specifically, the paper reports:

• sham: help rate stays 1
• coupling-off: help rate drops to 0
• shuffled-partner signal: help rate drops to 0 (Sanyal, 12 Apr 2026)

This lesion pattern supports a narrow mechanistic conclusion. Helping depends on the functional coupling channel that routes partner distress into the agent’s own homeostatic error. It does not depend simply on extra perceptual bandwidth or on an arbitrary perturbation that leaves the coupling structure intact. The paper’s broader conclusion for artificial life is correspondingly constrained: in this minimal controller, helping appears when the partner’s distress becomes part of the agent’s own homeostatic error, thereby changing what the self-directed planner is trying to keep in balance (Sanyal, 12 Apr 2026).

A plausible implication is that FoodShareToy is best understood not as a benchmark for altruistic preference learning, but as a mechanistic probe for coupling-based prosociality.

7. Relation to food-sharing and online allocation literature

Although FoodShareToy in (Sanyal, 12 Apr 2026) is a one-step artificial-life task, adjacent arXiv work places food-sharing problems in broader online allocation frameworks. These works do not redefine the one-step task, but they show that food-sharing can also be formalized as repeated allocation, online fair division, or dynamic matching.

“Sequential Fair Allocation With Replenishments: A Little Envy Goes An Exponentially Long Way” (Onyeze et al., 29 Aug 2025) studies a repeated allocation system with stochastic donations, finite storage capacity $\lambda$0, ex-post envy $\lambda$1, and inefficiency measured through overflow and stockout. Its constructive Bang-Bang control policy establishes a sharp phase transition in inefficiency, from $\lambda$2 at $\lambda$3 to $\lambda$4 when $\lambda$5 (Onyeze et al., 29 Aug 2025). This is a different problem class from the one-step helping task, but it similarly emphasizes threshold phenomena and control-mediated tradeoffs.

“Online fair division with arbitrary entitlements” (Chatterjee et al., 2023) and “Online Fair Division: analysing a Food Bank problem” (Aleksandrov et al., 2015) formalize food-bank allocation as online fair division in which items arrive one by one and must be allocated immediately. They analyze LIKE, Balanced LIKE, and weighted variants under strategy-proofness and envy-freeness criteria, with entitlement-normalized fairness in the weighted setting (Chatterjee et al., 2023, Aleksandrov et al., 2015). These models concern multi-agent allocation mechanisms rather than affect-coupled regulation, but they provide a complementary formal vocabulary for food-sharing as immediate, irrevocable, and fairness-constrained assignment.

“Automating Food Drop: The Power of Two Choices for Dynamic and Fair Food Allocation” (Mertzanidis et al., 2024) studies real-time matching of truckloads to food banks under a tradeoff between driver efficiency and fairness. Its deployed algorithm compares the normalized loads of two geographically plausible food banks and is proved 3-driver efficient, while fairness is analyzed through multiplicative envy-freeness and load-gap bounds in a weighted balls-into-bins model (Mertzanidis et al., 2024). This again differs from FoodShareToy’s one-step social task, but it shows that food-sharing systems in the broader literature are often organized around explicit tradeoffs among efficiency, fairness, and online decision constraints.

Taken together, these neighboring formulations suggest that “FoodShareToy” occupies a distinctive niche. In (Sanyal, 12 Apr 2026), it is not primarily a resource-allocation mechanism or a fair-division protocol. It is a minimal testbed for the claim that observation alone is insufficient, whereas coupling is sufficient, for helping to emerge under a self-directed objective.