Uncertainty, cooperation, communication complexity, and social network structure

1. Uncertainty, cooperation, communication complexity, and social network structure Peter Andras peter.andras@ncl.ac.uk

2. Overview • Uncertainty and cooperation • Components of uncertainty • Communication of intentions • Uncertainty and communication complexity • Artificial social network structure

3. Cooperation • Individuals are selfish – Why do they cooperate ? • Examples: microbes, worms, ants, fish, wolves, humans

4. Theories of cooperation • Theories: • reciprocity (direct/indirect) • similarity (tags/genes/etc) • commitment inertia • assortment/segregation • Methods of study: • live experiments (bacteria, plants, animals, humans) • agent-based simulations

5. Uncertainty • Sources of uncertainty: predators, food scarcity, extreme natural conditions (cold, hot, wet, dry) • Usually more cooperation in uncertain environments • alpine plants • microbes in presence of antibiotics • mole-rats in dry environment • fish in high predation risk environment • humans during natural disasters or wars

6. Agent-based simulation • Agents play cooperation games (e.g. Prisoner’s Dilemma) with other agents • Usually: many repeated games with all possible partners

7. Usual game matrix Game matrix with uncertainty P=N(p,), Q=N(q,), R=N(r,), S=N(s,) Simulation of uncertainty

8. Agent-based simulation • Our simulation: • moving agents in 2D world • random selection of interaction partners from neighborhood • finite life • offspring generation • resource accumulation and consumption • resource generation through game playing

9. Uncertainty and cooperation • more uncertainty  more cooperation (Andras et al, 2003, in: Adaptive Agents and Multi-Agent Systems, pp.49-65; Andras et al, 2007, BMC Evolutionary Biology, 7:240)

10. Representation of uncertainty • Uncertainty is present in natural environments of living organisms in the form of the variance of outcomes of events or scenarios involving the organism • Representation: variance of resources

11. Objective uncertainty • Suppose the environment is described in terms of resources • Objective uncertainty is the variance of the resource distribution

12. Subjective uncertainty • The observable range of resources is different from the natural range of them • E.g., resource amounts too little to be worth exploring

13. Subjective 2> Objective 2 • Subjective uncertainty is higher than the objective uncertainty, given that at least half of the natural resource distribution is in the observable range

14. Effective uncertainty • Individuals share their subjective uncertainty through cooperation. The experienced uncertainty is the effective uncertainty.

15. Effective 2 < Subjective 2 • Effective uncertainty is smaller than subjective uncertainty if the individuals cooperate

16. Steady-state uncertainty • Effective uncertainty is reduced through cooperation to the level of steady-state uncertainty that allows reproduction or stable growth of the agent population (Andras et al, 2006, JASSS – Journal of Artificial Societies and Social Simulation, 9:1/7)

17. Communication of intentions • Organisms communicate with other organisms about their intentions – this plays an important role in cooperation and cheating • E.g. exposure of signal molecules on the cell surface, vocalisations and postures of animals, gestures, body language and spoken language of humans

18. Agent language – 1 • Intention of cooperation – Icoop • Language = lexicon, syntax, semantics • lexicon = {0,s,i,y,n,h,t} • syntax = probabilistic two-input automaton • E.g. s,i’ 0.6 i;0.3 y; 0.1 n • semantics = 0 – no interest, s – start of communication, i – intend to communicate further, y – want to engage in cooperation, n – lost interest, h – cooperate, t – defect • P(h|y,y’) = Icoop (Andras et al, 2003, in: Adaptive Agents and Multi-Agent Systems, pp.49-65; Andras, 2008a, in: Proceedings of the IEEE Conference on Evolutionary Computation; Andras, 2008b, in: Proceedings of the Artificial Life XI)

19. Agent language – 2 • Intention consistency: a big smile is more likely to follow a small smile than an angry face • Positivity order: n, 0, s, i, y • Intention consistency rules: • P(x1,x’  y)  P(x2,x’  y) if Pos(y)  Pos(x1)  Pos(x2) • P(x,x1’  y)  P(x,x2’  y) if Pos(y)  Pos(x) & Pos(x1) Pos(x2)

20. Uncertainty and language • Ambiguous use of the language may add to the uncertainty induced by other environmental factors • High uncertainty may lead to lower ambiguity of the language • army • surgical theatre • West-African languages • Ambiguity ~ lexical complexity

21. Language complexity • Kolmogorov complexity – description length measure • Variance of transition probabilities (e.g. P(y|i,i’)) – variability of language usage • Lexical language complexity: average of transition probability variances

22. Uncertainty and language complexity • more uncertainty  less lexical language complexity (Andras, 2008b, in: Proceedings of the Artificial Life XI)

23. Artificial social networks • Can we generate agent-based simulations of social interaction systems that have scale-free interaction networks ? (without explicitly encoding to have this interaction network in the simulation) • Does the presence of memories, gossip and uncertainty in the simulation matter for this?

24. Memory and gossip • Memory: the agents remember their interactions with other agents and accordingly adapt their willingness to cooperate • Gossip: the agents share their memories about other agents with their interaction partners

25. Social network measurement • 20 simulations for each setting running for 1000 turns, measurement for consecutive 100 turns • Settings: • low / high uncertainty • with / without memory • with / without gossip (in case of with memory) • Measurement of the interaction network • Expected connectedness distribution: • Exponent estimated as:

26. Results • Kolmogorov-Smirnov test (Matlab) was used to check the match between measured and expected distributions • The log(p) is the logarithm of the calculated significance level – the network is significantly different from a scale-free network if log(p) < –2.

28. Results • The memory and gossip settings have no significant effect on the power law nature of the connectedness distribution of the corresponding simulated social networks • The presence of uncertainty is critical for the generation of interaction networks with scale-free connectedness distribution

29. Summary • More uncertain environments induce more cooperation • Uncertainty: objective, subjective effective uncertainty; Objective 2 < Subjective 2, Effective 2 < Subjective 2 • More uncertainty induces reduction of the lexical complexity of the language used to communicate intentions • Artificial social networks are more similar to natural ones in presence of uncertainty, gossip and memory does not seem to have an impact on this

30. Acknowledgement • John Lazarus • Gilbert Roberts