; to describe the breakthrough of the product use the threshold value and the network ; ie once firms are able to satisfy to a user, both fitness and network effects. ; since the effect of diffusion on itself is positive it is capturing the appropriateness of the product breed [consumers consumer] breed [firm1bits firm1bit] breed [firm2bits firm2bit] breed [basics basic] basics-own [ initbits ] firm1bits-own [ bits fitness ] firm2bits-own [ bits fitness ] consumers-own [ adoptweight1 adoptweight2 adoptweight3 adoptscore choiceweight network networkeffect selection welfare ] globals [ counter maturity previousmaturity industrygrowth best1 best2 diffusion hdistance mylist cov fitranks pop Ashare Bshare adversecases networkcases hindex socialwelfare effranking ] to setup clear-all set counter 0 create-basics population-size [ set initbits n-values designlength [one-of [0 1]] hide-turtle ] create-firm1bits population-size create-firm2bits population-size repeat population-size [ ask firm1bit (counter + population-size) [ set bits [initbits] of basic counter hide-turtle calculate-fitness ] ask firm2bit (counter + (population-size * 2)) [ set bits [initbits] of basic counter hide-turtle calculate-fitness ] set counter counter + 1 ] ask basics [die] set best1 max [fitness] of firm1bits set best2 max [fitness] of firm2bits set maturity (( (best1 + best2) / 2 ) / designlength) create-consumers consumer-population [ setxy random-xcor random-ycor set color red set adoptweight1 random-float 1 set adoptweight2 1 - adoptweight1 set adoptweight3 random-float 1 set network consumers in-radius networksize set welfare 0 ] set industrygrowth 0 set hdistance 1 set mylist [ 0 ] set mylist lput maturity mylist set cov 1 set adversecases 0 set networkcases 0 set hindex 0.5 set socialwelfare 0 set effranking sort-by > list (max[fitness] of firm1bits) (max[fitness] of firm2bits) reset-ticks end to go create-next-generation set best1 max [fitness] of firm1bits set best2 max [fitness] of firm2bits set maturity (( (best1 + best2) / 2 ) / designlength) set industrygrowth (maturity - previousmaturity ) set previousmaturity maturity set diffusion (count consumers with [color = white]) / (count consumers) diversity adoption set mylist lput maturity mylist set cov (standard-deviation mylist) / (mean mylist) set effranking sort-by > list (max[fitness] of firm1bits) (max[fitness] of firm2bits) ifelse max [fitness] of firm1bits >= max [fitness] of firm2bits [set fitranks "A"] [set fitranks "B"] ask consumers with [color = red] [ ifelse empty? modes [selection] of network with [color = white] [ set pop fitranks ] [set pop item 0 modes [selection] of network with [color = white]] ] calculateshares tick end to adoption ask consumers with [color = red] [ set adoptscore ((adoptweight1 * maturity) + (adoptweight2 * (-1 * cov)) + (diffusion * adoptweight3 * (count network with [color = white] / count network))) / (adoptweight1 + adoptweight2 + ( adoptweight3 * diffusion)) if random-float 1 < adoptscore [choice] ] end ;;;;FITNESS MEASUREMENT;;;; to calculate-fitness set fitness length (remove 0 bits) end ;;;;GENETIC ALGORITHM ;;;; to create-next-generation let old-generation1 firm1bits with [true] let old-generation2 firm2bits with [true] let crossover-count (floor (population-size * crossover-rate / 100 / 2)) repeat crossover-count [ let parent1firm1 max-one-of (n-of 3 old-generation1) [fitness] let parent2firm1 max-one-of (n-of 3 old-generation1) [fitness] ; let parent1firm2 max-one-of (n-of 3 old-generation2) [fitness] let parent2firm2 max-one-of (n-of 3 old-generation2) [fitness] ; let child-bits1 crossover ([bits] of parent1firm1) ([bits] of parent2firm1) let child-bits2 crossover ([bits] of parent1firm2) ([bits] of parent2firm2) ; ask parent1firm1 [ hatch 1 [ set bits item 0 child-bits1 ] ] ask parent2firm1 [ hatch 1 [ set bits item 1 child-bits1 ] ] ask parent1firm2 [ hatch 1 [ set bits item 0 child-bits2 ] ] ask parent2firm2 [ hatch 1 [ set bits item 1 child-bits2 ] ] ; ] repeat (population-size - crossover-count * 2) [ ask max-one-of (n-of 3 old-generation1) [fitness] [ hatch 1 ] ask max-one-of (n-of 3 old-generation2) [fitness] [ hatch 2 ] ] ask old-generation1 [die] ask old-generation2 [die] ; ask firm1bits [ mutate calculate-fitness ] ask firm2bits [ mutate calculate-fitness ] end to mutate ;; turtle procedure set bits map [ifelse-value (random-float 100.0 < mutation-rate) [1 - ?] [?]] bits end to-report crossover [bits1 bits2] let split-point 1 + random (length bits1 - 1) report list (sentence (sublist bits1 0 split-point) (sublist bits2 split-point length bits2)) (sentence (sublist bits2 0 split-point) (sublist bits1 split-point length bits1)) end to-report hamming-distance [bits1 bits2] report (length remove true (map [?1 = ?2] bits1 bits2)) / designlength end to diversity set hdistance hamming-distance ([bits] of max-one-of firm1bits [fitness])([bits] of max-one-of firm2bits [fitness]) end to choice ;ifelse ((adoptweight1 * maturity) + (adoptweight2 * (-1 * cov)) > (diffusion * adoptweight3 * (count network with [color = white] / count network))) ifelse hdistance > (count network with [color = white] / count network ) [;if random-float 1 < hdistance set selection fitranks set welfare (item 0 effranking) - (item 1 effranking) set socialwelfare socialwelfare + welfare set color white ] [ set selection pop set color white if selection != fitranks [ set adversecases adversecases + 1 set welfare (item 1 effranking) - (item 0 effranking) set socialwelfare socialwelfare + welfare ] set networkcases networkcases + 1 ] if selection = 0 [set color red] end to calculateshares set Ashare count consumers with [selection = "A" and color = white ] / count consumers set Bshare count consumers with [selection = "B" and color = white ] / count consumers if count consumers with [color = white] > 0 [ let SA count consumers with [selection = "A" and color = white ] / count consumers with [color = white ] let SB count consumers with [selection = "B" and color = white ] / count consumers with [color = white ] set hindex (SA ^ 2) + (SB ^ 2) ] end @#$#@#$#@ GRAPHICS-WINDOW 6 10 323 167 -1 -1 3.0732 1 10 1 1 1 0 0 0 1 0 99 0 40 0 0 1 ticks 30.0 BUTTON 10 186 76 219 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 88 187 151 220 go go\nif ticks = 100 [stop]\nif diffusion = 1 [stop] T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 9 237 329 270 population-size population-size 0 40 25 1 1 NIL HORIZONTAL SLIDER 10 280 329 313 crossover-rate crossover-rate 0 100 70 1 1 NIL HORIZONTAL SLIDER 9 325 329 358 mutation-rate mutation-rate 0 2 0.5 0.05 1 NIL HORIZONTAL PLOT 681 226 984 602 Fitness Plots Simulated Time Raw Fitness 0.0 50.0 0.0 100.0 true true "" "" PENS "Firm A" 1.0 0 -5298144 true "" "plot max [fitness] of firm1bits" "Firm B" 1.0 0 -10899396 true "" "plot max [fitness] of firm2bits" SLIDER 366 185 668 218 consumer-population consumer-population 0 10000 8000 50 1 NIL HORIZONTAL SLIDER 10 367 330 400 designlength designlength 100 1000 100 50 1 NIL HORIZONTAL PLOT 364 10 666 175 Industrial Maturity and Product Differentiation Simulated Time Maturity Rate 0.0 50.0 0.0 1.0 true true "" "" PENS "Maturity" 1.0 0 -16777216 true "" "if plot-all? [plot maturity]" "Diversity" 1.0 0 -8630108 true "" "if plot-all? [plot hdistance]" PLOT 366 273 671 483 Diffusion Rate Simulated Time Diffusion 0.0 50.0 0.0 100.0 true false "" "" PENS "default" 1.0 0 -16777216 true "" "if plot-all? [plot (diffusion * 100)]" SLIDER 364 231 668 264 networksize networksize 0 10 4 1 1 NIL HORIZONTAL PLOT 678 10 1050 166 Variance in Industrial Improvement (coeff of variation) NIL NIL 0.0 50.0 -0.1 0.1 true true "" "" PENS "CoV" 1.0 0 -13791810 true "" "plot cov" "Zero" 1.0 0 -16777216 true "" "plot 0" TEXTBOX 12 414 162 489 Simulated Behavior of adopters in the face of Technological Innovation: Recombination and Diffusion 12 0.0 1 TEXTBOX 369 486 663 583 The diffusion curve is not simply logistic. The initial concavity reflects the slow diffusion based on techonlogy features. Adopters are most likely to make a choice once the variance in industrial improvement slows down 11 0.0 1 TEXTBOX 683 604 979 716 The longer the diffusion process goes on the more chance firms have to improve their product. Thus a switch between the best practice technology is most likely due in long drawn out processes. \n 11 0.0 1 PLOT 1050 10 1304 233 Market Shares of Firms NIL NIL 0.0 100.0 0.0 100.0 true true "" "" PENS "Firm A " 1.0 0 -2674135 true "" "if plot-all? [plot Ashare * 100]" "Firm B" 1.0 0 -10899396 true "" "if plot-all? [plot Bshare * 100]" "H - Index" 1.0 0 -8020277 true "" "if plot-all? [plot hindex * 100]" PLOT 999 235 1311 385 # of Adverse Selection Cases NIL NIL 0.0 100.0 0.0 3000.0 true true "" "" PENS "Adverse Selection" 1.0 0 -10141563 true "" "if plot-all? [plot adversecases]" "Network Good" 1.0 0 -16777216 true "" "if plot-all? [plot networkcases]" SWITCH 228 412 331 445 plot-all? plot-all? 0 1 -1000 PLOT 1002 451 1313 601 Welfare gains/losses during adoption NIL NIL 0.0 100.0 -5000.0 5000.0 true false "" "" PENS "default" 1.0 0 -16777216 true "" "plot socialwelfare" TEXTBOX 735 170 1050 240 H - Index is the hirfhindahl index of the market, denoting the concentration as well as monopolistic tendencies of the market. \n 11 0.0 1 TEXTBOX 1002 388 1298 486 Network Good is a count of adoption due to the network. Adverse Selection is a subset of the Network Good count, where the adopter ended up with the less efficient product. 11 0.0 1 TEXTBOX 1002 608 1292 664 Welfare gains/losses is the sum of each adopter's indvidual gains/losses from adoption. 11 0.0 1 TEXTBOX 162 172 312 228 Due to computational needs, keep the speed slider closer to fastest at before pressing go. 11 0.0 1 @#$#@#$#@ ## WHAT IS IT? A model of innovation and its subsequent diffusion, in a rigid-network population of user/adopters. The idea is to show the evolution of variants of an innovation, while also addressing how users time their adoption decisions. The end-result is an analysis of market structures such as "dynamic" lock ins or best practice diffusions, as well as network deadweight losses. ## HOW IT WORKS Two firms are given the same initial set of solution bit-strings. This represents a technological bottleneck and each firm runs a genetic algorithm on this string to get 'fitter' technologies. In this case the 'all ones' solution is the fittest solution. ie the fitness of any string is measured by the total number of ones in the string. Potential Adopters (the red dots in the display) evaluate the technology based: 1) Industrial Maturity: The mean fitness during a time period, of competing firms' product fitness. This shows the adopter how well the 'problem solvers' are doing in solving the bottleneck. Consider for eg how functionally mature new variants of personal computers are, to a potential adopter. 2) Volatility in Technological maturity: In the face of a high rate of technological change, adopters want to time their decisions appropriately. Thus they give a negative weight to the coefficient of variation in the industrial maturity. 3) Network Effects: Adopters are involved in a rigid local network. Consider for example different parts of a supply chain. Therefore at the microfoundational level, each adopter evaluates their local network to see if the new technology is being adopted. The weight on this factor increases as the overall rate of diffusion increases. The decision to adopt is set as a probability, positively dependent on the product score as per the evaluation criteria described above. Once a user decides to adopt (transformation into a white dot on the display), they decide which variant or standard to go with. In this case there's a tradeoff between the most commonly occurring product in their local network versus the properties of the product itself. For any adopter, if the percentage variation between the alternatives is higher than the level of adoption in their network (in percentage terms) they go for the 'fitter' product. Else they go for the most commonly occurring standard in their network. Finally, at the point of adoption a welfare measure is introduced to measure a 'network deadweight loss.' The welfare gain/loss is given by the difference between the competing products' fitness. If the user made a choice based on the actual product, they have chosen the better product thus their welfare gain is positive. If the user made a choice based on their network imperative but the network was locked into the worse product, the user has a negative welfare gain (ie a welfare loss). ## HOW TO USE IT Press the SETUP button to create an initial random population of solutions as well as initialize a population of potential adopters. Press the GO button to start the innovation-diffusion process. The process runs for 100 steps. The best solution found in each generation is displayed in the VIEW. Each white column represents a "1"-bit and each black column represents a "0"-bit. === Parameters === The POPULATION-SIZE slider controls the number of solutions that are present in each generation. The CROSSOVER-RATE slider controls what percent of each new generation is created through reproduction (recombination or crossover between two parents' genetic material), and what percent (100 - CROSSOVER-RATE) is created through cloning of one parent's genetic material. The MUTATION-RATE slider controls the percent chance of mutation. This chance applies to each position in the string of bits of a new individual. For instance, if the string is 100 bits long, and the mutation-rate is set at 1%, then on average one bit will be changed during the creation of each new individual. The DESIGNLENGTH slider controls the size of the bit strings used in the genetic algorithm The CONSUMER-POPULATION slider controls the number of potential adopters. The NETWORK-SIZE slider sets a geographic network for each potential adopter. ie for a value of X, the potential adopter is networked with every agent within a radius of X (each distance measure is from the center of each patch), of themselves. The "Fitness Plot" is used to show the best fitness values of the solutions at each generation, for each firm. ## THINGS TO NOTICE Notice that initial dynamics tend to have a long lasting memory in terms of market outcomes. The adverse selection plot shows how many consumers chose the less efficient option, due to their network based selection. The welfare plot is also interesting in giving a picture of the social outcomes due to efficient/inefficient selection. ## CREDITS AND REFERENCES * Stonedahl, F. and Wilensky, U. (2008). NetLogo Simple Genetic Algorithm model. http://ccl.northwestern.edu/netlogo/models/SimpleGeneticAlgorithm. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. * Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. 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