globals [ number_of_regions ;; main outcome variable regions_list ;; list of region identifyers x_of_active ;; these are the coordinates of the selected agent y_of_active overlap ;; overlap among the features of the selected agent and its neighbour. It corresponds to the porbability of trait adoption chosen-feature ;; feature selected to be copied by the selected agent new-trait ;; trait (feature value) adopted by the selected agent from its neighbour my_neighbors ;; these are auxiliar variables used along the code found loop-step ] patches-own [ ;; define here the characteristics of the agents (because agents do not move, these are patches) feature ;; list of cultural features of each agent (patch) color1 ;; this is the color of the first feature (the only one we present at the interface) region_id ;; this is the 'opinion region' to wich the agent belongs ] to setup clear-all ask patches ;; the following commands are executed by all the agents (in a sequential way) when 'setup' botton is pressed [ ;; basically, they initialized the system set feature (list random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits random number_of_traits) if report_CC = true [print feature] recolor-patch ] make-regions-list ;; calculates the number of regions end ;;to setup to go ;; the following commands are executed iteratively in an infinite loop while 'run' botton is pressed ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;; Mutation (not Axelrod) ;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; if random-float (1.0) < mutation_rate [ ask patch random (max-pxcor + 1) random (max-pycor + 1) [set feature replace-item random (number_of_Features) feature random (number_of_traits)]] ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;1st: choose agent to be updated ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; set x_of_active random (max-pxcor + 1) set y_of_active random (max-pycor + 1) if report_CC = true [print (word "chosen agent is "(list x_of_active y_of_active)) ] ; this message is shown only if 'report_CC' in the interface is ON ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;2nd: select interaction partner ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ask patch x_of_active y_of_active [ ifelse range_of_interaction = 3 [set my_neighbors other ( patches in-radius 2 )][ifelse range_of_interaction = 2 [set my_neighbors neighbors][set my_neighbors neighbors4]] ;; defines the neighborhood ;;ask my_neighbors [set pcolor (green)] if report_CC = true [print my_neighbors ] let feature_neigh [feature] of one-of my_neighbors ;; copies the features of the interaction partner to the focal agent ;;print feature_neigh ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;3rd: calculate the cultural similarity ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; calc-overlap feature_neigh if report_CC = true [print feature] if report_CC = true [print feature_neigh] set overlap overlap / number_of_Features ;;print overlap ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;4th: social influence ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; if (overlap < 1) and ((overlap > random-float 1) or (Random_interaction > (random 100) + 1)) [ ;; Notice that (Random_interaction > (random 100) + 1) correspond to the noise, which is not included in Axelrod's model ;;print Random_interaction point-dissimilar feature_neigh set new-trait item chosen-feature feature_neigh set feature replace-item chosen-feature feature new-trait if report_CC = true [print overlap] ;; these parameter's values are shown only if 'report_CC' in the interface is ON if report_CC = true [print chosen-feature] if report_CC = true [print feature] if report_CC = true [print feature_neigh] recolor-patch ] ] ;;ask patch x_of_active y_of_active tick make-regions-list end ;;to go ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;; Some procedures called from 'go' ;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to point-dissimilar [b] ;; determines the feature value to be copied by the selected agent from its neighbour set found false loop [ set chosen-feature random number_of_Features if item chosen-feature feature != item chosen-feature b [set found true] if found [stop] ] end ;;to point-dissimilar to calc-overlap [b] ;; calculates the similarity set loop-step 0 set overlap 0 loop [ ;;print loop-step if item loop-step feature = item loop-step b [set overlap overlap + 1] set loop-step loop-step + 1 if loop-step = number_of_Features [stop] ;;print overlap ] end ;;to calc-overlap to recolor-patch set pcolor (item 0 feature) end ;;to recolor-patch to make-regions-list ;; calculates the number of regions set regions_list [] ask patches[ calc-region-id ;;print region_id set regions_list fput region_id regions_list ] ;;print regions_list set regions_list remove-duplicates regions_list ;;print regions_list set number_of_regions length regions_list ;;print number_of_regions do-plot end ;; to make-regions-list to calc-region-id ;; determines the region to which an agent belongs set region_id item 0 feature set loop-step 1 loop[ set region_id region_id + (10 ^ loop-step)*(item loop-step feature) set loop-step loop-step + 1 if loop-step = number_of_Features [stop] ] end ;; to calc-region-id to do-plot ;; updates the plot set-current-plot "Number of Regions" plot number_of_regions end ; This model was developed by Michael Maes (M.Maes@rug.nl) and Sergi Lozano (slozano@ethz.ch) ; Zurich, October 2008 @#$#@#$#@ GRAPHICS-WINDOW 232 14 517 320 -1 -1 25.0 0 10 1 1 1 0 0 0 1 0 10 0 10 1 1 1 ticks CC-WINDOW 5 648 526 743 Command Center 0 BUTTON 7 13 70 46 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL SLIDER 7 101 179 134 number_of_Features number_of_Features 1 20 5 1 1 NIL HORIZONTAL SLIDER 7 141 179 174 number_of_traits number_of_traits 1 20 10 1 1 NIL HORIZONTAL SLIDER 7 181 179 214 range_of_interaction range_of_interaction 1 3 1 1 1 NIL HORIZONTAL BUTTON 95 13 158 46 run go T 1 T OBSERVER NIL NIL NIL NIL SWITCH 12 601 125 634 report_CC report_CC 1 1 -1000 PLOT 8 371 208 521 Number of Regions Time (ticks) Number of Regions 0.0 100.0 0.0 10.0 true false PENS "default" 1.0 0 -16777216 true MONITOR 76 525 208 570 Number of Regions number_of_regions 17 1 11 SLIDER 8 309 182 342 Random_interaction Random_interaction 0 100 0 1 1 % HORIZONTAL SLIDER 8 267 182 300 mutation_rate mutation_rate 0.0 0.01 0 0.0005 1 NIL HORIZONTAL TEXTBOX 30 78 180 96 Axelrod's parametres 14 0.0 1 TEXTBOX 31 245 181 263 Extension parametres 14 0.0 1 @#$#@#$#@ WHAT IS IT? ----------- This is Axelrod's model of cultural dissemination. It models a population of actors that hold a number of cultural attributes (called features) and interact with their neighbors. Dynamics are based on two main mechanisms. First, agents tend to chose culturally similar neighbors as interaction partners (homophily). Second, during interaction agents influence each other in a way that they become more similar. The interplay of these mechanisms either leads to cultural homogeneity (all agents are perfectly similar) or the development of culturally distinct regions. The model allows studying to which degree the likelihood of these two outcomes depends on the size of the population, the number of features the agents hold, the number of traits (values) each feature can adopt and the neighborhood size (interaction range). We furthermore implemented cultural mutation and random interaction. HOW IT WORKS ------------ Each patch of the grid represents an agent. Agents hold a number of features. Each feature is a nominal variable that can adopt a certain number of values (called traits). Initially, agents adopt randomly chosen traits. During each tick, the computer randomly selects a patch as the focal agent. Then, one of the focal agent's neighbors is selected at random and the cultural overlap between these two agents is computed. The cultural overlap is equal to the percentage of similar features. With probability similar to the overlap, the two agents interact. Otherwise, the program continues with the next tick. An interaction consists of selecting at random one of the features on which the two agents differ and changing the focal agent's feature to the interaction partner's trait. Note that if the overlap is zero, interaction is not possible and the respective agents refuse to influence each other. HOW TO USE IT ------------- First, you should choose the population size. Use the black arrows in the grid window to manipulate the size of the grid. Second, click on SETUP to initialize the population. You can influence, how many features the agents hold by using the 'NUMBER_OF_FEATURES' slider. How many traits each feature can adopt can be changed with the 'NUMBER_OF_TRAITS' slider. Furthermore, you can vary the size of the neighborhood. Here, 1 means that each agent has 4 neighbors. 2 corresponds to 8 neighbors and 3 to 12 neighbors. In the grid, each patch (agent) adopts a color which represents the agent’s trait on the first feature. If two patches adopt the same color, they are similar on the first feature. Click on RUN and the simulation starts. You can follow the changes of the first feature in the grid. Furthermore, there is a graph reporting the number of cultural regions in the population. A region is a set of agents that are similar on all features We included two crucial extensions of Axelrod's model. First, you can implement cultural mutation, meaning that sometimes the computer changes a randomly chosen feature of a randomly chosen agent to a randomly chosen trait. The probability of such changes can be influenced using the 'MUTATION_RATE' slider. Secondly, we allowed for interaction between dissimilar neighbors. In the original model, agents do not interact when the overlap is zero. It has been shown (see references below) that relaxing this assumption changes the outcomes of the model significantly. We implemented that as follows. If two agents that are dissimilar on all features are selected for interaction, then the probability that social influence occurs is similar to the value chosen with the 'RANDOM_INTERACTION' slider. THINGS TO NOTICE ---------------- Note that the model does not stop 'ticking' when equilibrium is reached. When there are no changes in the grid and the number of regions is stable over a reasonable long time, you should click on the RUN button to stop the process. Note furthermore that for the assessment of the number of regions, the model only counts the number of distinct attribute vectors in the population. The program does not check if two sets of agents that hold similar features are connected or not. It could thus happen that you see for instance three regions in the grid but the number of regions is only 2. You can use the 'REPORT_CC' switch to follow the steps of the simulation and for debugging. Note that this makes the program slower. THINGS TO TRY ------------- Vary the population size, the number of features, the number of traits and the range of interactions. Conduct experiments to find out under which conditions the model predicts cultural differences. You will find quite some counter intuitive effects. Axelrod’s paper (see below) provides you with explanations for these effects. In addition, you could change grid to a torus (a world that looks like a donut) by activating 'World wraps horizontally' and 'World wraps vertically' in the Settings menu. Why do the model's implications change? Experiment with a very small mutation rate. What happens? Why? Try also high mutation rates. Allow for random interaction. To start with, you could run a simulation without random interaction until stable regions have developed and then put the 'RANDOM_INTERACTION' slider to 5% and click on run again. EXTENDING THE MODEL ------------------- Many extensions of this model have been proposed (see e.g. references below). One of the most interesting is certainly the inclusion of metric features. Interestingly, it has been shown that this makes the persistence of different cultural regions very unlikely. Try to think of ways to make cultural diversity possible again. Incorporate social networks into this model. Currently, agents interact only with their neighbors and all agents (except those at the borders) have the same number of neighbors. Both could be changed. NETLOGO FEATURES ---------------- Note that the agents (patches) hold several features. We used lists to implement that. The model allows varying the size of the neighborhoods. RELATED MODELS -------------- Flache, Andreas, and Michael Mäs. 2008. "How to get the timing right? A computational model of how demographic faultlines undermine team performance and how the right timing of contacts can solve the problem." Computational and Mathematical Organization Theory 14:23-51. Hegselmann, Rainer, and Ulrich Krause. 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis, and Simulation." Journal of Artificial Societies and Social Simulation 5. CREDITS AND REFERENCES ---------------------- This model has been developed by Robert Axelrod. It was implemented by Sergi Lozano (slozano@ethz.ch) and Michael Maes (m.maes@rug.nl). This is the paper where Axelrod presented the model: Axelrod, R. 1997. "The dissemination of culture - A model with local convergence and global polarization." Journal of Conflict Resolution 41:203-226. Extensions can be found at: Flache, A., and M. Macy. 2006. "What sustains cultural diversity and what undermines it? Axelrod and beyond." arXiv:physics/0604201v1 [physics.soc-ph]. Flache, A., and M. Macy. 2007. "Local Convergence and Global Diversity: The Robustness of Cultural Homophily." arXiv:physics/0701333v1 [physics.soc-ph]. Klemm, K., V. M. Eguiluz, R. Toral, and M. S. Miguel. 2003a. "Global culture: A noise-induced transition in finite systems." Physical Review E 67:-. Klemm, K., V. M. Eguiluz, R. Toral, and M. San Miguel. 2003b. "Nonequilibrium transitions in complex networks: A model of social interaction." Physical Review E 67 Copyright 2008 by Sergi Lozano (slozano@ethz.ch) and Michael Maes (m.maes@rug.nl). 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