Uncertainty, cooperation, communication complexity, and social network structure Peter Andras

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

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

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

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

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

7 Simulation of uncertainty Usual game matrix Usual game matrix Game matrix with uncertainty Game matrix with uncertainty P=N(p,  ), Q=N(q,  ), R=N(r,  ), S=N(s,  ) P=N(p,  ), Q=N(q,  ), R=N(r,  ), S=N(s,  ) Player 1 Player 2 CpDf Cpp,pr,q Dfq,rs,s Player 1 Player 2 CpDf CpP,PR,Q DfQ,RS,S

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

9 Uncertainty and cooperation more uncertainty  more 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 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 Representation: variance of resources

11 Objective uncertainty Suppose the environment is described in terms of resources Suppose the environment is described in terms of resources Objective uncertainty is the variance of the resource distribution 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 The observable range of resources is different from the natural range of them E.g., resource amounts too little to be worth exploring 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 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. 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 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 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 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 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 – I coop Intention of cooperation – I coop 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’) = I coop P(h|y,y’) = I coop (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 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 High uncertainty may lead to lower ambiguity of the language army army surgical theatre surgical theatre West-African languages West-African languages Ambiguity ~ lexical complexity Ambiguity ~ lexical complexity

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

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

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? 23

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

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

Results Kolmogorov-Smirnov test (Matlab) was used to check the match between measured and expected distributions 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. 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. 26

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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 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 The presence of uncertainty is critical for the generation of interaction networks with scale- free connectedness distribution 28

29 Summary More uncertain environments induce more cooperation More uncertain environments induce more cooperation Uncertainty: objective, subjective effective uncertainty; Objective  2 < Subjective  2, Effective  2 < Subjective  2 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 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 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 John Lazarus Gilbert Roberts Gilbert Roberts