Tapes Together Strong: The Co-evolution of Computation and Cooperation

Abstract: How does cooperation evolve in complex agentic systems? Prior work in evolutionary game theory studies why individuals are incentivized to cooperate by isolating social interactions from the physical costs of behavior, while artificial life models traditionally study emergent self-replication without formalizing the dilemma between acquiring resources and preserving the shared energy needed to reproduce. In contrast, we introduce Autopoietic Game Theory, a computational model where social interactions, replication mechanisms, and their associated computational costs are endogenous and simultaneously co-evolving. We study these dynamics using a computational substrate of randomly initialized programs in Z80 machine code, showing empirically, and motivating with a simplified theoretical model, that embedding a social dilemma directly into the physics of computation can favor the emergence of self-replicating, cooperative strategies. When resources are scarce, our analysis shows that defection can become self-limiting even in well-mixed populations: parasitic stealing destroys shared energy, slows execution, and can prevent reliable replication. Empirically, evolved programs suppress stealing across several Z80 environments, while spatial assortment further supports structural complexity and task performance. We further show that the framework can incorporate exogenous pressures, such as math tasks structured as sequential social dilemmas, when rewards are tied to computation budgets. These results suggest that coupling an agent's capacity for computation to its available energy transforms cooperation into a dominant scaffolding for building sustainable, self-organizing systems.

• The paper introduces Autopoietic Game Theory (AGT), a framework where social strategy, computation, energy expenditure, and replication are interlinked components of an evolving system. The key finding is that cooperation can become evolutionarily favored when defection directly degrades the computational substrate, particularly when replication mechanisms are evolvable.
• In AGT, replication is seen as an endogenous computational process in a population of 16,384 programs. The protocol demonstrates that stealing behaviors can self-suppress when it diminishes shared energy required for replication. Experimentally, well-mixed and local populations in severe environmental inequality demonstrate that local populations remain more resilient and complex and collectively perform tasks better than the other.
• The framework identifies potential biochemical applications, suggesting evolutionary stabilization under heterogeneous energy conditions, and task-specific computing under severe constraints.

Computational substrate and research question

The paper introduces Autopoietic Game Theory (AGT), a framework in which social strategy, computation, energy expenditure, and replication are not separate modeling layers but components of one evolving dynamical system. Its central question is whether cooperation can emerge when an agent’s ability to act and reproduce depends directly on the shared energetic consequences of its interactions. This differs from standard evolutionary game theory, where payoffs and reproduction are typically imposed as external update rules, and from much artificial-life research, where replication evolves without an explicit endogenous social dilemma.

The substrate consists of a population of 16,384 programs represented as randomly initialized 32-byte sequences of modified Z80 machine code. Programs are paired either uniformly at random in a well-mixed population or with one of four spatial neighbors on a two-dimensional grid. A paired interaction concatenates the two programs into a 64-byte cyclic memory tape, while each program retains an independent CPU and register state. Programs can read and overwrite both memory segments, and replication emerges when one program writes a faithful copy of itself into the partner’s segment before the interaction terminates.

Every instruction costs one unit of energy. The probability that a program executes the next instruction is proportional to its current energy, so energy affects both survival and computational throughput. Each epoch supplies a baseline energy increment of $\epsilon=24$, and programs are subject to a maximum energy of 255 in the standard experiments. Replication, interaction, and ordinary computation therefore compete for a common budget.

Figure 1: The substrate couples paired programs through shared cyclic memory and energy-dependent execution speed.

The social dilemma is implemented through a STEAL instruction. A successful steal transfers $\delta$ units of energy from the partner, but the acting program receives only $\alpha\delta$, with $\alpha=0.8$. Consequently, every steal destroys $(1-\alpha)\delta$ units of total system energy. Stealing is locally advantageous because it increases the actor’s immediate execution budget, but it produces a negative externality by reducing the energy available for subsequent computation and replication. The paper defines non-stealing programs as cooperators and stealing programs as defectors, while acknowledging that this binary classification is a coarse-graining: non-stealing replicators still overwrite partner memory, and programs can vary their stealing frequency and magnitude.

The main conceptual claim is therefore conditional rather than universal: cooperation can become evolutionarily favored when defection directly degrades the computational substrate on which reproduction depends, particularly when the replication mechanism itself is evolvable (2609.10817).

Autopoietic Game Theory

AGT treats replication as an endogenous computational process. Programs do not receive an explicit reproduction command. Instead, they must evolve instruction sequences that locate the partner’s memory segment, write the necessary bytes, and preserve enough energy to complete the operation. At the end of an epoch, the shared tape is cleaved into two 32-byte programs. If one program has successfully overwritten the partner, both resulting segments can contain copies of the successful replicator; otherwise, the split may produce recombined or nonfunctional code.

This construction creates two linked selection pressures. First, stealing can increase the actor’s short-term execution probability. Second, the same act can reduce total energy, slow the paired computation, increase the probability of execution failure, and prevent either program from completing replication. The interaction is thus not a conventional Prisoner’s Dilemma with a subsequent Moran-style population update. The action changes the physical conditions under which the update can occur.

The paper motivates the inverse relationship between energy and execution time using thermodynamic and hardware analogies. In the model, the physical time per operation is defined as $dt=1/(E_i+E_j)$. This is a modeling assumption rather than a derivation from the Z80 instruction set or a complete physical implementation. The resulting kinetics are intended to capture metabolic drag: lower shared energy causes slower computation, which prolongs execution and increases exposure to failure.

The principal structural metrics are higher-order entropy, used as a proxy for nontrivial architectural complexity, and Hamming edit distance, used as a measure of genetic diversity. Higher-order entropy is estimated by comparing sequence entropy with a compression-based approximation to Kolmogorov complexity. These metrics distinguish populations dominated by repeated structured replicators from populations consisting primarily of independent random bytes. The interpretation is useful for population-level comparisons, although compression-based complexity remains dependent on the chosen compressor and sequence representation.

Cooperation under uniformly distributed energy

The first set of experiments examines well-mixed populations receiving the same baseline energy. With continuous mutation at $\mu=1/128$, fixed values of $\delta$, and dynamically determined steal magnitudes, evolved programs strongly suppress STEAL. This result is notable because neither spatial assortment nor memory of previous encounters is required. The programs are paired randomly and have no explicit reputational or reciprocal state.

The proposed mechanism is metabolic rather than cognitive. Mutual stealing reduces total energy, which reduces execution speed for both programs. Slow or interrupted execution makes it less likely that a program will complete the writes required for replication. By contrast, non-stealing programs can accumulate residual energy across successful epochs, increasing their execution probability in future encounters. The paper further reports traces in which a higher-energy cooperative program interrupts and overwrites a defector’s code, providing an executable mechanism by which accumulated energy changes the effective outcome of subsequent interactions.

This result should not be interpreted as showing that ordinary well-mixed Prisoner’s Dilemmas generically favor cooperation. The result depends on three substrate-specific conditions: stealing is lossy, energy controls computation, and replication occurs through the same interaction in which the social behavior is expressed. Removing any of these couplings could change the evolutionary outcome.

Starvation limits and mutation-free invasion

The authors test whether suppression of defection is merely an artifact of continuous mutation. In a mutation-free invasion assay, 1% functioning replicators and 1% STEAL-containing programs are introduced into a naive random soup. Defectors remain a minority in both well-mixed and local populations. Increasing the steal magnitude from $\delta=16$ to $\delta=32$ significantly reduces defector success, with $\delta$0 and Cohen’s $\delta$1.

The result supports a starvation mechanism: sufficiently aggressive stealing exhausts the shared budget before a defector can execute the writes required for replication. The defector’s immediate energetic gain therefore becomes counterproductive at the level of lineage propagation. Figure 2 compares the theoretical starvation boundary with empirical Z80 rollouts.

Figure 2: Theoretical and empirical defector survival decline as stealing approaches the metabolic starvation limit.

The paper also varies absorption efficiency and steal magnitude over $\delta$2 and $\delta$3. Defector frequency is not strongly determined by $\delta$4 alone. The reported correlation between the amount gained, $\delta$5, and defector proportion is weak but statistically significant ($\delta$6, $\delta$7). This is an important qualification: inefficient stealing alone does not explain the observed cooperation. The authors argue that the co-evolution of replication timing and social behavior is also necessary.

The mutation-free invasion dynamics show cooperators expanding toward carrying capacity while defectors remain below 20%.

Figure 3: Mutation-free invasion assays show cooperative replicators dominating while defectors remain at minority frequency.

The formal analysis provides sufficient-condition arguments for this regime. If the baseline pair energy is less than the expected energy needed for a defector to complete its replication writes,

$\delta$8

then a defector is expected to starve before completing replication. The paper is explicit that the proof replaces the dynamically changing energy trajectory with an expected trajectory and therefore does not establish a theorem for the full stochastic emulator. The empirical simulations do update energy after every operation, but the analytical condition should be read as a motivating approximation rather than a complete characterization.

Spatial assortment and architectural complexity

Spatial topology has a limited role under uniform energy because both well-mixed and local populations suppress stealing. Its larger effect is on the structure and resilience of the resulting replicators. Local interactions produce significantly higher higher-order entropy, with Cohen’s $\delta$9, and substantially lower edit distance, with Cohen’s $\alpha\delta$0; both comparisons have $\alpha\delta$1.

The combination of high complexity and low edit distance indicates that local populations converge toward genetically cohesive, structurally elaborate lineages. Well-mixed populations instead maintain greater genetic diversity but lower architectural complexity. The paper therefore identifies a tradeoff between diversity and complexity rather than treating either as an unqualified indicator of evolutionary success.

Figure 4: Local interactions increase architectural complexity and genetic cohesion in the presence of stealing.

Additional experiments disable stealing entirely to isolate replication dynamics. In this setting, rapid replication correlates inversely with terminal steady-state energy at $\alpha\delta$2. Well-mixed populations tend toward higher diversity, whereas local populations tend toward higher structural complexity. Historical conditions also matter: tape-bound replicators evolved in well-mixed environments can undergo architectural collapse when transferred to new test conditions, while lineages evolved under local spatial constraints retain greater complexity.

Figure 5: Historical spatial structure protects tape-bound lineages against architectural collapse.

The paper also distinguishes CPU-bound and tape-bound energy accounting. In CPU-bound systems, the executing program pays the computational cost; in tape-bound systems, the accessed memory segment pays it. Tape-bound populations can evolve interdependent mutualistic replication strategies in which one program executes writes that are charged to the partner’s segment. These strategies are more stable under local interactions, where repeated neighborhood encounters prevent rapid dilution.

Figure 6: Fixation success depends on the historical agent–environment boundary, with tape-bound lineages exhibiting interdependent replication strategies.

This result broadens the meaning of cooperation in the substrate. Cooperation is not limited to abstaining from STEAL; it can also involve the evolution of replication mechanisms whose viability depends on stable interaction partners. At the same time, it exposes a strong dependence on implementation choices concerning which entity bears computational cost.

Asymmetric energy and environmental resilience

The most severe contrast between topologies appears when baseline energy is distributed asymmetrically across space. Under strong systematic inequality, well-mixed populations suffer metabolic and structural collapse. Local populations retain substantially higher terminal energy, with Cohen’s $\alpha\delta$3, and higher structural complexity, with Cohen’s $\alpha\delta$4; both effects have $\alpha\delta$5.

Figure 7: Local spatial structure preserves energy and complexity under severe environmental inequality, whereas well-mixed populations collapse.

The mechanism is ecological and architectural. Local populations allow successful lineages to remain near high-energy regions, accumulate computational resources, and develop code capable of surviving in lower-energy regions. Well-mixed populations repeatedly expose lineages to unpredictable energy conditions, preventing the stable accumulation of the computational structure required for complex replication.

The authors describe local topology as an “architectural scaffold,” but the result is more specific than a general claim that spatial structure is beneficial. Under uniform energy, spatial structure primarily increases complexity and cohesion; under asymmetric energy, it becomes necessary for maintaining population-level energy and functional replication. The distinction matters because assortment is not simply rescuing a conventional game-theoretic equilibrium. It is stabilizing the physical and computational conditions under which an equilibrium can be represented and transmitted.

Externally imposed computational tasks

The final Z80 experiments introduce exogenous mathematical tasks whose rewards determine energy acquisition. Each agent receives an input and a location-specific constant. Programs can solve a solo task, such as $\alpha\delta$6, or a joint task, such as $\alpha\delta$7, where reading the partner’s private input requires additional computation.

Free energy is supplied only below a threshold, forcing successful programs to earn surplus energy through task completion. Solve rates decline significantly as environmental energy becomes more abundant. This establishes a direct relation between scarcity and computational engagement: when replication is already energetically affordable, solving the external task has little selective value.

Figure 8: Greater free-energy abundance reduces solve rates for both individual and joint tasks.

The mixed task mode creates a sequential social dilemma. A joint solution initially rewards both agents, but a partner can subsequently obtain a larger individual payoff by solving its solo task. If both solve jointly, both receive a substantial shared reward; if one solves jointly and the other solves alone, the solo solver gains more while the joint solver receives less. Despite this incentive structure, programs suppress the solo strategy and converge toward joint-task performance under severe scarcity.

Figure 9: Under a severe energy threshold, programs temporarily increase stealing during complexification but eventually suppress it while optimizing joint-task performance.

Joint solve rates are significantly higher under local interactions than in well-mixed populations, with $\alpha\delta$8 and Cohen’s $\alpha\delta$9. Local populations also achieve higher energy and higher-order entropy. The implication is that assortment supports not only cooperation in the narrow sense of avoiding energy theft but also the computational coordination required for multi-step collective tasks.

The paper identifies a sharp cognitive bottleneck when agents must discover a communication protocol for sharing the private variable $\alpha=0.8$0. Joint solve rates collapse, whereas individual solve rates increase. Communication is therefore not costless coordination; it consumes the same limited computational budget required for task execution and replication.

Figure 10: Requiring emergent communication reduces joint performance by diverting computation from the task itself.

This experiment places an important boundary on the paper’s claims. Cooperation is feasible when the substrate provides sufficiently direct access to partner state. It becomes much harder when programs must discover communication protocols while also preserving replication and energy management.

Replication timing as a causal mechanism

Because the open-ended Z80 substrate makes causal attribution difficult, the paper introduces a simplified finite-population model with binary strategies and evolvable replication timing. Agents retain energy across encounters, and the probability of controlling replication is proportional to energy.

Three event orderings are compared in a draining Prisoner’s Dilemma. If agents interact, update energy, and then replicate according to post-interaction energy, defectors take over: the immediate payoff from exploiting a cooperator translates directly into reproductive control. If replication priority is determined from pre-interaction energy but reproduction occurs afterward, this immediate advantage disappears and cooperation takes over. If replication occurs before interaction, cooperation is strictly favored in the specified toy setting because mutually cooperative pairs gain more energy than mutually defective pairs.

Figure 11: Changing only the temporal ordering of interaction and replication reverses the evolutionary outcome.

When both strategy and replication timing co-evolve, cooperation dominates when mutual defection drains or stagnates energy. Even when mutual defection increases energy, cooperators retain a substantial population share rather than being eliminated.

Figure 12: Co-evolving replication timing allows cooperation to persist across payoff environments, including one in which mutual defection increases energy.

These simulations sharpen the paper’s central causal claim. Energy loss is not sufficient by itself: a fixed update rule in which post-interaction payoffs determine reproduction can still favor defectors. Cooperation is supported when the replication mechanism can evolve so that immediate exploitation does not automatically determine reproductive control. The toy model consequently provides a plausible mechanism for the Z80 results, but it does not prove that the same timing rule is the dominant mechanism in the full instruction-level system.

Limitations and open questions

The framework is restricted to a modified Z80 architecture, a particular instruction distribution, fixed program length, shared read/write access, and a small set of social operations. The authors correctly note that instruction density, memory-access rules, energy caps, and replication costs may alter starvation thresholds and the reachability of cooperative programs. In particular, unrestricted access to partner memory is a strong assumption. It facilitates both cooperation and exploitation, but many biological and artificial-agent systems do not expose internal state in this way.

The cooperation classification is also deliberately coarse. Programs that do not execute STEAL are labeled cooperative even though they may overwrite partners, exploit replication asymmetries, or use other forms of interference. The additional SHARE experiments demonstrate that selection can retain social operations when they increase system energy, but they also show that the agent–environment boundary changes whether stealing, sharing, or neither operation is favored.

The analytical results rely on frozen or expected execution priorities, average energy trajectories, and simplified population-transition approximations. The paper explicitly labels several claims as conjectures rather than theorems. These approximations are useful for identifying starvation and metabolic-drag regimes, but they leave open the exact stochastic conditions under which cooperation is globally stable.

The empirical evaluation also relies on a limited number of seeds and on indirect complexity metrics. The reported effect sizes are often large, but the open-ended nature of the substrate makes replication, transfer, and causal intervention more difficult than in a fixed-strategy evolutionary model. The main unresolved questions are correspondingly specific: how cooperation changes under restricted partner-memory access; whether the observed dynamics persist across instruction sets and hardware architectures; which replication-timing motifs are causally selected in the Z80 population; and how partial copying, recombination, and communication jointly affect task performance.

Conclusion

“Tapes Together Strong: The Co-evolution of Computation and Cooperation” (2609.10817) proposes a computational model in which cooperation is selected through the same energetic and temporal constraints that govern computation and replication. In the Z80 substrate, lossy stealing can become self-limiting because it depletes the shared budget required for faithful reproduction. Evolvable replication mechanisms amplify this effect by decoupling immediate energetic advantage from reproductive success. Uniform-energy well-mixed populations can therefore suppress defection without memory or assortment, while local structure substantially increases complexity, cohesion, resilience under energy inequality, and performance on collaborative tasks.

The paper’s strongest conclusion is conditional: cooperation is favored when social behavior, computational throughput, and reproduction are physically coupled. Its results do not establish a general solution to cooperation in arbitrary evolutionary systems, but they identify a concrete class of endogenous mechanisms in which destructive individual optimization undermines the computational substrate required for lineage persistence.