An Agent-Based Modelling System of Competition and Cooperation
Cooperation is a dynamic process influenced by broader system dynamics and strategic choices of agents
I have recently tested my seminal idea that in dynamic systems, the interaction between agents' strategies and their relative productivity drives the emergence of order or disorder. And the key to that emergence is intelligence. For this, I have simulated different scenarios through agent-based modelling, using NetLogo, a multi-agent programmable modelling environment.
In the model I made, I have simulated two agents (called turtles) that represent countries or entities. Each turtle has a strategy that ranges from -5 to +5. A positive strategy means the turtle is cooperating, while a negative strategy means it is competing. These strategies evolve based on the turtle's interactions with its neighbours: if it sees other turtles being more cooperative, it becomes more cooperative too. Additionally, the turtle’s strategy is influenced by a measure called generativity, which tracks the overall productivity or cooperation of the system. If generativity is high, turtles are encouraged to cooperate; if it’s low, they are more likely to compete.
The feedback loop works in two ways: the turtles’ strategies affect the overall generativity of the system, and the generativity score influences the turtles' behaviors. When most turtles are cooperative, generativity increases, encouraging more cooperation. When most turtles are competitive, generativity decreases, pushing the system toward more competition. This dynamic process allows the system to adapt over time, with turtles shifting their strategies based on both their neighbors and the overall state of the system, demonstrating how cooperation or competition can emerge and evolve in a system. The system is adaptive, with the turtles continuously adjusting their behavior based on the balance between strategies and the state of teh system (generativity).
I have run five simulations of 20 ticks each. And here are the results
Simulation 1:
Generativity: 1.1132219806010593
Turtle 1 Strategy: 1.7889788112186131
Turtle 0 Strategy: -0.6757568306175538
Generativity: 1.312060141496469
Turtle 1 Strategy: 1.765742029126805
Turtle 0 Strategy: -0.4536818876303358
Generativity: 1.5115115817045763
Turtle 1 Strategy: 1.754770833288948
Turtle 0 Strategy: -0.2432592515843716
Generativity: 1.7215066569167599
Turtle 1 Strategy: 1.7648644042574655
Turtle 0 Strategy: -0.043357747340705605
Generativity: 1.9310272122957555
Turtle 1 Strategy: 1.7839738520565525
Turtle 0 Strategy: 0.14705336023920296
Generativity: 2.131934911066212
Turtle 0 Strategy: 0.32980708360052713
Turtle 1 Strategy: 1.8021278274656851
Generativity: 2.3406157129258753
Turtle 1 Strategy: 1.8371925921320902
Turtle 0 Strategy: 0.503423120793785
Generativity: 2.5422812892475295
Turtle 1 Strategy: 1.870504118565175
Turtle 0 Strategy: 0.6717771706823545
Generativity: 2.7442844718778225
Turtle 1 Strategy: 1.910567771171034
Turtle 0 Strategy: 0.8337167007067885
Generativity: 2.9465923442016617
Turtle 1 Strategy: 1.9567252176478218
Turtle 0 Strategy: 0.9898671265538401
Generativity: 3.154009489429397
Turtle 1 Strategy: 2.0157994583208576
Turtle 0 Strategy: 1.1382100311085392
Generativity: 3.3612034629974277
Turtle 1 Strategy: 2.0791139605282725
Turtle 0 Strategy: 1.2820895024691552
Generativity: 3.56421090185228
Turtle 0 Strategy: 1.4249481642269635
Turtle 1 Strategy: 2.139262737625317
Generativity: 3.770996688285776
Turtle 0 Strategy: 1.5606638928968812
Turtle 1 Strategy: 2.210332795388895
Generativity: 3.974372516029546
Turtle 0 Strategy: 1.696523165765252
Turtle 1 Strategy: 2.2778493502642942
Generativity: 4.180825831490794
Turtle 0 Strategy: 1.8255894749902042
Turtle 1 Strategy: 2.35523635650059
Generativity: 4.384501714287018
Turtle 0 Strategy: 1.9557477018619476
Turtle 1 Strategy: 2.428754012425071
Generativity: 4.5906842300634265
Turtle 0 Strategy: 2.079398017390104
Turtle 1 Strategy: 2.5112862126733226
Generativity: 4.794604509575219
Turtle 1 Strategy: 2.589691802909162
Turtle 0 Strategy: 2.204912706666057
Generativity: 5.000566457315827
Turtle 0 Strategy: 2.3241516614782123
Turtle 1 Strategy: 2.6764147958376148
Generativity: 5.204685799479929In Simulation 1, we observe a gradual shift toward more cooperative behaviour over time. Initially, Turtle 1 (which started with a positive strategy) remains cooperative, while Turtle 0 starts with a more negative, competitive strategy. As the simulation progresses, the overall generativity of the system increases, reaching values above 5, reflecting a trend toward cooperation. Turtle 0's strategy rises steadily, becoming more cooperative, while Turtle 1 maintains a high level of cooperation. This suggests that as the system becomes more generative, both turtles begin to adopt more harmonious strategies. The feedback loop is evident in the results: as the overall generativity increases (indicating more cooperation in the system), both turtles adjust their strategies to become more cooperative, moving closer to each other’s approach. By the end of the simulation, both turtles have similar, high positive strategies, reflecting a system that has moved towards a state of cooperation due to the positive generativity influencing their behaviour.
Simulation 2:
Generativity: 3.8669454684122115
Turtle 0 Strategy: 2.7241596406907598
Turtle 1 Strategy: 1.142785827721452
Generativity: 4.067992033879788
Turtle 1 Strategy: 1.3229010838374942
Turtle 0 Strategy: 2.7450909500422944
Generativity: 4.276547508545301
Turtle 0 Strategy: 2.7825369313975665
Turtle 1 Strategy: 1.4940105771477343
Generativity: 4.478326192659677
Turtle 0 Strategy: 2.818110613685075
Turtle 1 Strategy: 1.6602155789746014
Generativity: 4.686220930246453
Turtle 1 Strategy: 1.8181103307101252
Turtle 0 Strategy: 2.868110599536328
Generativity: 4.893845930918519
Turtle 0 Strategy: 2.9232355867670834
Turtle 1 Strategy: 1.9706103441514353
Generativity: 5.096464367811979
Turtle 0 Strategy: 2.975604324636301
Turtle 1 Strategy: 2.1208600431756786
Generativity: 5.303601228515632
Turtle 0 Strategy: 3.0400039712669216
Turtle 1 Strategy: 2.2635972572487097
Generativity: 5.510542245300677
Turtle 0 Strategy: 3.1081246523510564
Turtle 1 Strategy: 2.4024175929496203
Generativity: 5.717306512949181
Turtle 1 Strategy: 2.5377029459196923
Turtle 0 Strategy: 3.1796035670294884
Generativity: 5.923911264501955
Turtle 1 Strategy: 2.669797976975182
Turtle 0 Strategy: 3.2541132875267733
Generativity: 6.127450476225576
Turtle 1 Strategy: 2.8025529542263827
Turtle 0 Strategy: 3.3248975219991936
Generativity: 6.333756337645008
Turtle 1 Strategy: 2.9286701826150234
Turtle 0 Strategy: 3.405086155029985
Generativity: 6.5375652977139715
Turtle 1 Strategy: 3.0562999413047343
Turtle 0 Strategy: 3.4812653564092373
Generativity: 6.74150288417621
Turtle 0 Strategy: 3.560017085654012
Turtle 1 Strategy: 3.1814857985221985
Generativity: 6.947449212394041
Turtle 1 Strategy: 3.3004123628787894
Turtle 0 Strategy: 3.647036849515251
Generativity: 7.1533157736106325
Turtle 0 Strategy: 3.7355721864000193
Turtle 1 Strategy: 3.4177435872106128
Generativity: 7.357521202112659
Turtle 1 Strategy: 3.5378404456721095
Turtle 0 Strategy: 3.8196807564405493
Generativity: 7.561816601335738
Turtle 1 Strategy: 3.6562278604336105
Turtle 0 Strategy: 3.9055887409021275
Generativity: 7.766193199134566In Simulation 2, we see both turtles starting with relatively cooperative strategies, though Turtle 0 is slightly more cooperative from the start. As the simulation progresses, both turtles gradually adopt more cooperative behaviours, with their strategies steadily increasing over time. This trend is reflected in the rising generativity value, which reaches up to 7.76, signalling a high level of cooperation within the system. Turtle 1, which started with a slightly lower strategy, catches up to Turtle 0, indicating that the system is moving towards a harmonious state where both turtles are increasingly aligned in their behaviours. Compared to Simulation 1, where Turtle 0 began with a more competitive strategy and shifted towards cooperation as generativity increased, Simulation 2 starts with both turtles being more cooperative from the beginning. As a result, the system reaches a higher level of cooperation faster, with both turtles showing consistently positive strategies. In Simulation 1, Turtle 0’s strategy required a longer adjustment to catch up, while in this scenario, both turtles evolved together towards higher cooperation, demonstrating a smoother and quicker transition toward a balanced, generative state.
Simulation 3:
Generativity: -3.194313089726306
Turtle 1 Strategy: -0.6849690426930503
Turtle 0 Strategy: -2.509344047033256
Generativity: -3.394752152215456
Turtle 1 Strategy: -0.87662685539921
Turtle 0 Strategy: -2.5181252968162458
Generativity: -3.6038558983189986
Turtle 1 Strategy: -1.0587017774700618
Turtle 0 Strategy: -2.5451541208489368
Generativity: -3.8125720291774456
Turtle 1 Strategy: -1.2330243946390056
Turtle 0 Strategy: -2.5795476345384403
Generativity: -4.020938337277195
Turtle 1 Strategy: -1.4003505566339773
Turtle 0 Strategy: -2.620587780643217
Generativity: -4.2228877442171715
Turtle 1 Strategy: -1.5633118247744164
Turtle 0 Strategy: -2.6595759194427555
Generativity: -4.425147083980502
Turtle 1 Strategy: -1.7203843692711627
Turtle 0 Strategy: -2.7047627147093385
Generativity: -4.627686138116906
Turtle 0 Strategy: -2.7555437974374297
Turtle 1 Strategy: -1.8721423406794762
Generativity: -4.830477634475011
Turtle 1 Strategy: -2.019103909875479
Turtle 0 Strategy: -2.811373724599532
Generativity: -5.0374583090118215
Turtle 1 Strategy: -2.1587174006116814
Turtle 0 Strategy: -2.8787409084001396
Generativity: -5.24065825024235
Turtle 1 Strategy: -2.297918517231633
Turtle 0 Strategy: -2.942739733010717
Generativity: -5.444046197202903
Turtle 1 Strategy: -2.43354752498114
Turtle 0 Strategy: -3.010498672221763
Generativity: -5.650488575071004
Turtle 1 Strategy: -2.562395082343171
Turtle 0 Strategy: -3.0880934927278334
Generativity: -5.854174329045042
Turtle 0 Strategy: -3.1618085722086002
Turtle 1 Strategy: -2.6923657568364425
Generativity: -6.0580007220066125
Turtle 0 Strategy: -3.2383364314399925
Turtle 1 Strategy: -2.81966429056662
Generativity: -6.264047402358797
Turtle 1 Strategy: -2.9405978976102887
Turtle 0 Strategy: -3.3234495047485075
Generativity: -6.468090273340951
Turtle 1 Strategy: -3.0637833489493542
Turtle 0 Strategy: -3.4043069243915967
Generativity: -6.673941582279557
Turtle 1 Strategy: -3.1808095277214665
Turtle 0 Strategy: -3.49313205455809
Generativity: -6.879722388596649
Turtle 1 Strategy: -3.296425654063298
Turtle 0 Strategy: -3.583296734533351
Generativity: -7.084005210895474In Simulation 3, the overall system is in a degenerative state, with both turtles starting with highly competitive strategies. Turtle 0 is particularly focused on negative, competitive behaviours from the start, while Turtle 1 adopts a less extreme, but still negative, strategy. As the simulation progresses, both turtles continue to move deeper into these competitive strategies, and generativity drops further into negative territory. The system becomes increasingly uncooperative, with both turtles reinforcing their negative strategies. The final result is a continued state of degenerativity, with no shift toward cooperation or positive change, which contrasts sharply with the other simulations. When compared to Simulation 1 and 2, Simulation 3 takes the opposite trajectory. While in Simulation 1 and 2 the turtles move toward more cooperative, generative strategies over time, Simulation 3 is marked by a sustained competitive trend. Generativity continues to worsen throughout, reinforcing a scenario where the turtles’ strategies spiral into competition and harm rather than cooperation. Simulation 1 showed a gradual shift to cooperation, and Simulation 2 saw both turtles evolving together positively. In contrast, Simulation 3 highlights how both turtles, trapped in negative-sum dynamics, reinforce their destructive behaviors, resulting in a system that produces negative generativity rather than the positive or neutral generativity seen in the previous simulations.
Simulation 4:
Generativity: 0.04900867826379285
Turtle 0 Strategy: 3.5581745398024864
Turtle 1 Strategy: -3.5091658615386936
Generativity: 0.271677029267146
Turtle 1 Strategy: -3.0557988414716344
Turtle 0 Strategy: 3.3274758707387804
Generativity: 0.46071884248662043
Turtle 1 Strategy: -2.6475932926416395
Turtle 0 Strategy: 3.10831213512826
Generativity: 0.6513290789171959
Turtle 1 Strategy: -2.269187784822569
Turtle 0 Strategy: 2.920516863739765
Generativity: 0.8433548172957903
Turtle 1 Strategy: -1.9176768140158584
Turtle 0 Strategy: 2.7610316313116487
Generativity: 1.0600515884091095
Turtle 0 Strategy: 2.6437929801585924
Turtle 1 Strategy: -1.583741391749483
Generativity: 1.2544827524793396
Turtle 1 Strategy: -1.2779335090838493
Turtle 0 Strategy: 2.532416261563189
Generativity: 1.469008626905957
Turtle 1 Strategy: -0.9874160205514974
Turtle 0 Strategy: 2.4564246474574545
Generativity: 1.6653990252359347
Turtle 0 Strategy: 2.384232614057007
Turtle 1 Strategy: -0.7188335888210722
Generativity: 1.87815669074313
Turtle 0 Strategy: 2.341836969420298
Turtle 1 Strategy: -0.4636802786771682
Generativity: 2.090170483863374
Turtle 1 Strategy: -0.22340441627229488
Turtle 0 Strategy: 2.3135749001356687
Generativity: 2.301512932154394
Turtle 0 Strategy: 2.2980683826062904
Turtle 1 Strategy: 0.003444549548103304
Generativity: 2.5122494917370393
Turtle 1 Strategy: 0.21817574120101269
Turtle 0 Strategy: 2.2940737505360267
Generativity: 2.722439236760377
Turtle 0 Strategy: 2.300468595092614
Turtle 1 Strategy: 0.42197064166776344
Generativity: 2.9227429918768153
Turtle 1 Strategy: 0.6161992944554439
Turtle 0 Strategy: 2.3065436974213713
Generativity: 3.1235171308694003
Turtle 0 Strategy: 2.322026477273075
Turtle 1 Strategy: 0.8014906535963254
Generativity: 3.332318470428592
Turtle 0 Strategy: 2.3548010256484293
Turtle 1 Strategy: 0.9775174447801629
Generativity: 3.5338752614764215
Turtle 1 Strategy: 1.1479384148714056
Turtle 0 Strategy: 2.385936846605016
Generativity: 3.7419702575557556
Turtle 1 Strategy: 1.3098383364580861
Turtle 0 Strategy: 2.4321319210976697
Generativity: 3.949775991517355
Turtle 1 Strategy: 1.4659530156900653
Turtle 0 Strategy: 2.4838229758272896
Generativity: 4.157320666417698In Simulation 4, the system starts with highly competitive behaviour from Turtle 1, but Turtle 0 begins with a strongly cooperative strategy. Over time, Turtle 0 maintains its relatively high competitive strategy, while Turtle 1 slowly shifts from competitive to more neutral and eventually cooperative behaviours. As the simulation progresses, generativity steadily improves, moving from a modest positive value to a higher level of positive generativity. This indicates that Turtle 0's focus on building cooperation leads to an increasingly generative system, with Turtle 1 responding by softening its competitive strategy and gradually shifting toward more cooperative behaviour. The system's overall generativity grows as the turtles adapt to each other, ultimately entering a positive feedback loop where the balance between the two strategies creates an increasingly generative environment.
In comparison to the previous simulations:
Simulation 1 saw a relatively smooth progression toward positive generativity, with both turtles shifting to cooperative strategies over time. This trend was similar to Simulation 4, but the turtles in Simulation 4 start with more distinct strategy differences, and the improvement in generativity is more gradual and steady, especially from Turtle 1.
Simulation 2 exhibited an even more dynamic shift, with both turtles rapidly adjusting their strategies to become more cooperative. This simulation showed a faster convergence to positive generativity, whereas Simulation 4 involved a more drawn-out process, especially for Turtle 1's transition.
Simulation 3, in stark contrast, remained in a negative generativity state, with both turtles locked in competitive behaviors. Unlike Simulations 1, 2, and 4, which saw gradual improvement, Simulation 3 remained trapped in a competitive loop, unable to break free from negative-sum dynamics.
Simulation 5:
In Simulation 5, the system begins with highly entropic behaviours from both turtles, especially Turtle 0, which maintains a very competitive strategy. Turtle 1, while less extreme, still adheres to competitive strategies as well, and as the simulation progresses, both turtles continue to reinforce their negative-sum approach. The generativity remains deeply negative throughout the simulation, indicating a system that is trapped in competition. No movement toward cooperation, and the generativity does not improve, instead becoming more degenerative over time as both turtles engage in increasingly competitive strategies. The system is locked in a downward spiral of negative generativity, with the strategies of both turtles becoming more extreme in the competitive behaviour.
Comparison to previous simulations:
Simulation 1 showed a more gradual shift towards cooperation and positive generativity, where the turtles moved from competitive to cooperative strategies, leading to a positive generativity trend. In contrast, Simulation 5 is marked by an unbroken downward trajectory in generativity, as both turtles double down on their competitive strategies, leading to a stagnant or negative-sum dynamic.
Simulation 2 also saw a more rapid shift towards positive generativity, with the turtles adjusting their strategies dynamically and producing a more positive generative output. Here, as with Simulation 1, there was cooperation and mutual adjustment, but Simulation 5 continues to spiral into negative generativity, with no shift toward cooperation or strategy adjustment.
Simulation 3, much like Simulation 5, showed stagnant or negative generativity. However, Simulation 3 was characterized by more violent shifts or tension between the turtles, while Simulation 5 is more of a gradual descent into increasingly competitive behaviour. There’s no attempt by the agents to shift toward balance or cooperation, which distinguishes Simulation 5 from Simulation 3, where at least some attempts at adjustment might have been seen.
Simulation 4 saw gradual improvement in generativity over time as Turtle 0's competitive strategy led Turtle 1, who began with a highly competitive strategy, to soften its approach. In Simulation 5, no such reduction in competitive strategies occurs. Both turtles consistently double down on their competitive behaviours, maintaining negative generativity levels.
These agent-based modelling simulations extend existing understandings of cooperation by demonstrating that it is not simply a fixed or static behaviour but a dynamic process influenced by broader system dynamics and strategic choices of agents. Rather than assuming that cooperation is always beneficial or sustainable, the model reveals how changes in overall generativity of the system can shift the balance between cooperative and competitive strategies. When an agents are not benefitting from the situation, they may resort to more competitive strategies, even if the overall cooperation in the system is high. This highlights the importance of relative gains and the fluidity of cooperation, suggesting that cooperation can be fragile and contingent on ongoing adjustments in strategy and the broader system dynamics.
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