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Retained Benefit

Retained Benefit is the most abstract evolved-cooperation case study on this site. Rather than centering one specific mechanism such as patch altruism, local Prisoner's Dilemma response rules, or cooperative hunting, it evaluates a more general question: when does cooperation spread when the decisive variable is how much of the value created by cooperation is routed back toward cooperators or their copies rather than being lost through evolutionary leakage to unrelated or weakly coupled recipients?

Conceptual Focus​

Many cooperation models embed the central evolutionary problem inside a particular mechanism family.

  • altruism models embed it in local public-good production
  • reciprocity models embed it in repeated-game memory
  • hunting models embed it in ecological synergy

This model removes most of that mechanism-specific structure. It asks whether cooperation can increase when:

  • cooperation creates value
  • cooperation also carries a private cost
  • some of that value is shared broadly
  • some of it is retained by related or same-rule local recipients

So the central question becomes: how much retained feedback is enough?

Model Structure​

This is a spatial lattice model with selection on an inherited continuous cooperation trait, not a model of learning, planning, or bargaining.

Each occupied cell carries:

  • one cooperation trait h in [0, 1]
  • one inherited lineage label

The lineage label is not intended as a full kinship model. It serves as an abstract stand-in for copies of the same inherited rule or for locally clustered descendants of the same lineage.

The Core Rule​

At each step, agent i with cooperation trait hi produces gross cooperative output:

Bi = b × hi

That output is split into retained and open components:

Biretained = r × Bi

Biopen = (1 - r) × Bi

Here Biretained is the retained amount produced by site i before routing, not the accumulated retained benefit that site i eventually receives.

The producer also pays a private cost:

Ci = c × hi

Fitness is then computed as:

Wi = w0 + received_openi + received_retainedi - Ci

Variable definitions:

  • hi is agent i's cooperation trait
  • Bi is the total cooperative value produced by agent i
  • r is the retained-benefit fraction
  • b is the cooperation-benefit scale
  • Ci is the private cooperation cost paid by agent i
  • c is the cooperation-cost scale
  • Wi is the resulting fitness used in local replacement
  • w0 is fixed baseline fitness, added each step as a background term that dampens selection intensity
  • received_openi is the open benefit received by agent i from its neighborhood
  • received_retainedi is the accumulated retained benefit received by agent i from same-lineage producers in its neighborhood, not the producer-side term Biretained

The open component is shared across the full local neighborhood. The retained component is shared only across same-lineage recipients in that local neighborhood and contributes to each recipient site's accumulated retained benefit received_retainedi.

Why The Fixed Baseline Matters​

The baseline term w0 does not change from step to step. It is added to every candidate parent's fitness before local parent selection, so it dampens the strength of selection rather than changing the ordering of candidates.

Suppose five local candidate parents have cooperation-related payoff terms delta = received_open + received_retained - C = [0.30, 0.10, 0.05, 0.05, 0.00].

  • Without a baseline, parent-choice weights are [0.30, 0.10, 0.05, 0.05, 0.00], so the probabilities are [0.60, 0.20, 0.10, 0.10, 0.00].
  • With w0 = 1.0, the weights become [1.30, 1.10, 1.05, 1.05, 1.00], so the probabilities are about [0.236, 0.200, 0.191, 0.191, 0.182].
  • The ranking stays the same, but selection becomes much less extreme.

So the model turns one high-level claim into a direct experiment:

cooperation rises when enough of its return is protected from leakage

Simulation Step​

One full synchronous retained-benefit update is shown below.

Flowchart of one retained-benefit simulation step from current lattice state through benefit routing, fitness computation, local parent selection, synchronous replacement, and history recording.
Display 1: One synchronous retained-benefit update from step t to step t + 1.

Turnover is implemented as a local replacement lottery rather than as explicit death, birth, and movement.

Frozen Replay Configuration​

The browser replay below is a specific seeded run from the frozen website-demo configuration, not a schematic animation. It uses:

  • a 72 × 72 toroidal lattice
  • a von Neumann local neighborhood
  • 250 simulation steps sampled every 5 steps
  • baseline fitness 1.0
  • cooperation benefit 0.30
  • cooperation cost 0.10
  • retained-benefit fraction 0.35
  • mutation rate 0.02
  • mutation standard deviation 0.05
  • 24 initial lineage labels in 6 × 6 local blocks
  • random seed 0

In the viewer:

  • cooperation view colors low h as pale beige, mid h as light blue, and high h as burgundy-red
  • lineage view switches to lineage colors so local clustering becomes visible

Interactive Replay​

The browser replay below is based on sampled frames from that same frozen configuration.

The canonical implementation and export logic live in the EvolvedCooperation repository:

Evolved Cooperation

Retained Benefit

Sampled browser replay of the abstract Retained Benefit model. Toggle between the continuous cooperation field and the inherited lineage structure that channels retained benefit.

Replay

World State

0 / 0

Step 0

Loading replay bundle.

Selection Metrics

Mean cooperation, assortment, and dominant-lineage share

How To Read The Replay​

The replay is easiest to read as the interaction of three evolving quantities.

1. Mean cooperation​

This shows whether the inherited cooperation trait is rising or falling in the population as a whole.

2. Local assortment​

This shows how often agents are surrounded by same-lineage local recipients. When that value rises, retained benefit has a clearer channel back toward cooperators or their copies.

3. Dominant-lineage share​

This shows whether one lineage is spreading strongly enough to occupy a large share of the lattice. It is a rough indicator of successful local copying and spatial consolidation.

Together these variables let you separate:

  • trait change
  • local clustering
  • lineage expansion

instead of collapsing all three into one unexplained population curve.

Why This Belongs Under Evolved Cooperation​

This model belongs under evolved cooperation because:

  • the cooperation trait is inherited rather than learned
  • selection acts through differential local copying and reproduction-like replacement
  • mutation creates heritable variation
  • local structure changes which cooperation traits persist across generations

What changes here is not a policy inside a lifetime. What changes is the distribution of inherited cooperation levels across the population.

Within the site's evolved-cooperation set, Retained Benefit is the most abstract feedback-routing model.

Case studySelection logic
Spatial AltruismA minimal patch-based model in which altruist and selfish traits compete through local benefit, private cost, and a neighborhood lottery.
Cooperative HuntingA spatial ecological model in which predator cooperation evolves through hunting success, energetic cost, and inherited trait variation.
Spatial Prisoner's DilemmaA local-game ecology in which inherited same-vs-other Prisoner's Dilemma response rules spread through energy accumulation, local movement, and local reproduction.
Retained BenefitAn abstract lattice model in which a continuous cooperation trait spreads only when enough of the value created by cooperation is routed back toward cooperators or copies of the cooperative rule.
Display 2: How Retained Benefit fits among the site's evolved-cooperation case studies.

Why This Model Is Useful​

This model is useful because it makes one candidate near-law of cooperation unusually explicit:

there is no cooperation without feedback

In other words:

  • if cooperation creates value that is lost through evolutionary leakage to unrelated or weakly coupled recipients, cooperation is hard to sustain
  • if enough of that value is routed back toward cooperators or their copies, cooperation can spread

What "Feedback" Means Here​

On this page, feedback does not mean only a verbal response, praise, or a conscious social reaction. It means any causal return channel by which the consequences of cooperation flow back toward the cooperator, its partners, or copies of the cooperative rule rather than being lost through evolutionary leakage to unrelated or weakly coupled recipients.

Working definition. Here, feedback means any process that makes the benefits or downstream consequences of cooperation return non-randomly to cooperators, their partners, or their lineage, so that cooperation improves its own future persistence rather than being lost through evolutionary leakage to unrelated or weakly coupled recipients.

Here, weakly coupled recipients means recipients whose gain does not feed back strongly enough into the actor's inclusive fitness, lineage persistence, or recurrence of the cooperative rule, even if they are nearby or benefit in the short run.

That return can take several forms.

Material Feedback​

This is the most concrete form.

  • food, energy, money, territory, protection, or other usable resources flow back toward the cooperator
  • cooperation therefore changes the material conditions for survival, reproduction, or future action

In many biological and ecological models, this is the clearest channel because cooperative behavior changes who gets access to resources.

Immaterial Or Social Feedback​

The return does not have to be material in the narrow sense.

  • reputation can make later help or alliance more likely
  • trust can stabilize repeated cooperation
  • punishment, shame, obligation, or status can redirect future behavior
  • partner choice can reward cooperators with better future interaction opportunities

These are immaterial in the sense that they are not food or money, but they still matter if they systematically alter who benefits, who gets chosen, and who is excluded.

Informational Or Learning Feedback​

Feedback can also operate through information.

  • agents observe outcomes
  • agents remember who cooperated or defected
  • agents update expectations, policies, or strategies
  • rewards and penalties reshape future behavior within a lifetime

This is the central sense of feedback in learned-cooperation models: behavior changes because experience changes later decisions.

Ecological Or Structural Feedback​

Sometimes the return channel is embedded in the structure of interaction rather than in an explicit transfer.

  • spatial clustering makes cooperators more likely to encounter cooperators again
  • local assortment routes benefits back toward similar or related others
  • repeated interaction creates future consequences for present behavior
  • institutions or network structure can reduce leakage to defectors

This kind of feedback often determines whether a cooperative act keeps helping the same social neighborhood or is simply absorbed by outsiders.

Fitness Feedback​

In evolved-cooperation models, this is the deepest level of accounting.

  • cooperation changes survival
  • cooperation changes reproductive success
  • cooperation changes inclusive fitness or lineage persistence
  • those changes alter which inherited traits become more common over generations

So material and immaterial returns matter evolutionarily only if they eventually affect fitness.

Feedback In This Model​

In Retained Benefit, the relevant feedback is a fitness-relevant routing rule.

  • cooperation produces value
  • some of that value is shared openly
  • some of it is retained and routed only toward same-lineage recipients in the local neighborhood
  • that retained return contributes to received_retainedi
  • received_retainedi raises fitness Wi
  • higher fitness makes that lineage more likely to persist and spread

So the model uses a material-like local payoff channel, but the real question is evolutionary: does the routing of cooperative value create enough feedback into fitness to let cooperation survive selection?

That is why the slogan on this page is intentionally broad. The claim is not that cooperation requires one special substance called feedback. The claim is that cooperation requires some channel, material, immaterial, informational, structural, or fitness-relevant, through which the consequences of cooperation come back toward cooperators or their copies.

That claim is more abstract than the special-case logic of altruism, reciprocity, or hunting. Retained Benefit is therefore the site's most direct current model for asking what the minimal conditions of cooperation might look like in general.

References​