;Lee, Lee & Rho (2002), Model replication in Netlogo ;v0.6 - 14 feb 2020 - Andrea Gallucci globals [ S ; threshold for strategic interactions Alpha ; parameter related to sigma-rivalry tournament-size ; stochastic component for the selection operator ] turtles-own [ x ; product-quality (the strategic choice of the firm) age ; parameter used to determine whether the firm is an incumbent or ; a new-entrant r ; random uniform number to assign payoff, ; to be drawn again every generation p ; probability to get the high payoff if the high-end segment pay ; single firm's last payoff wr ; working register ] to setup clear-all reset-ticks set S 10 set alpha 0.5 set tournament-size 5 crt firms [ set x random-float 0.5 ; firms start operating in the low-end segment (x < 0.5) set r random-float 1 set age 0 ] end to go if ticks > 2000 [stop] ask turtles[ set r random-float 1 update-p ifelse x < 0.5 [set pay payoff x] ; following Lee et al's assumptions, the payoff ; in the low-end segment is always safe [ifelse r <= p ; instead, the payoff in the high-end is risky can lead ; to a payoff equal to 0 [set pay payoff x] [set pay 0] ] ; the following lines of code are the ; operationalization of the sharing function let neigh turtles with [abs (x - [x] of myself) < sigma-rivalry] let mx x ask neigh [set wr 1 - (abs (x - mx) / sigma-rivalry) ^ alpha] let m sum [wr] of neigh set pay pay / m ifelse x >= 0.5 [set age age + 1] [set age 0] ; the age of the firms in the high-end segment ; is increased by one each generation. In this ; way, the difference between incumbents and ; new-entrants can be kept set ycor age ] selection tick end to update-p let n count turtles with [x >= 0.5] ; number of firms in the high end if age = 0 and n < S [set p mb] if age = 0 and n >= S [set p mb - psi] ; psi represents the preemptive effect ; of strategic interactions if age > 0 [set p dc] let si mb - psi end to selection let survived max-n-of 45 turtles [pay] let dead min-n-of 5 turtles [pay] ; each generation, 5 firms have ; the possibility to reshuffle their ; strategic choice ask dead [die] repeat 5 [ let t1 max-one-of (n-of tournament-size turtles) [pay] let t2 max-one-of (n-of tournament-size turtles) [pay] let lambda random-float 1 crt 1 [ set x lambda * ([x] of t1) + (1 - lambda) * [x] of t2 set age 0 set x x + random-normal 0 0.2 if x > 1 [set x 1] if x < 0 [set x 0] ] ] ; 5 new firms with new strategies ; replace the old ones. ; the population is kept unaltered (50) end ; this procedure replicates and operationalize selection to-report payoff [number] let y number * 180 / pi report sin (3 * pi * y) + 3 * number end to-report average [a b] report (a + b) / 2 end @#$#@#$#@ GRAPHICS-WINDOW 210 10 647 448 -1 -1 13.0 1 10 1 1 1 0 1 1 1 -16 16 -16 16 0 0 1 ticks 30.0 SLIDER 24 12 196 45 sigma-rivalry sigma-rivalry 0 1 0.5 0.05 1 NIL HORIZONTAL SLIDER 25 61 197 94 mb mb 0 1 0.01 0.01 1 NIL HORIZONTAL SLIDER 26 151 198 184 dc dc 0 1 0.96 0.05 1 NIL HORIZONTAL SLIDER 25 201 197 234 firms firms 10 200 50.0 5 1 NIL HORIZONTAL PLOT 5 273 205 423 plot 1 NIL NIL 0.0 1.0 0.0 1.0 true false "" "" PENS "default" 1.0 0 -16777216 true "" "plot count turtles with [x > 0.5] / firms" BUTTON 678 21 742 54 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 679 62 742 95 go go T 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 669 133 869 283 plot 2 NIL NIL 0.0 1.0 0.0 0.5 true false "" "" PENS "default" 1.0 1 -16777216 true "" "plot mean [pay] of turtles with [x < 0.5]" "pen-1" 1.0 0 -2674135 true "" "plot mean [pay] of turtles with [x > 0.5]" PLOT 673 308 873 458 plot 3 NIL NIL 0.0 1.1 0.0 50.0 true false "set-histogram-num-bars 15" "" PENS "default" 1.0 1 -16777216 true "" "histogram [x] of turtles" MONITOR 81 444 153 489 High-end count turtles with [x > 0.5] / firms 17 1 11 SLIDER 26 105 198 138 psi psi 0 mb 0.05 0.01 1 NIL HORIZONTAL @#$#@#$#@ ## Introduction The present model replicates Lee, J, Lee, K & Rho, S 2002, An evolutionary perspective on strategic group emergence: A genetic algorithm-based model. Strategic Management Journal, 23 (8): 727-747. It describes the dynamics of interactions between firms and it makes it possible to observe the phenomenon of strategic group emergence. ## Description of the model Replicating Lee et al.’s model using Netlogo serves the purpose of testing the consistency of the aforementioned theoretical assumptions and observing the similarities and discussing the differences with the current model. Replicating successfully a model is an important theoretical achievement, since it provides great validity to the findings. The way in which the features of Lee’s model have been translated in Netlogo will be shortly analyzed. The first attribute of the turtles (the firms in this case) is the product quality , which has been defined as the variable x linked to the following payoff function: y = sine (3πx) + 3x The product quality of the first generation of agents is randomly generated. It is assumed, as Lee et al. does, that all the firms start operating in the low-end segment (x < 0.5). Therefore, the value related to the product quality of the first generation of firms is a random number between 0 and 0.49. In addition to that, each firm owns a probability (p), which represents the probability to either enter or maintain the competitive positioning in the high-end segment, depending on the case: p = MB if age = 0 and n < S p = SI if age = 0 and n ≥ S p = DC if age > 0 As in Lee et al., if the firm is a potential new entrant in the high-end, then the success probability is either going to be provided by the mobility barriers (MB), if the number of incumbents is less than S (a threshold value for strategic interactions), or by the strategic interactions (SI) otherwise. Dynamic Capabilities (DC) are going to apply just for incumbents. It is possible to distinguish incumbents by new entrants in Netlogo by introducing another feature characterizing the firms: their age. For every generation in which a firm manages to survive in the high-end segment, the age value is increased by one. Therefore, each firm with an age higher than 0 is going to be incumbent, while new entrants’ age is going to be 0. In addition to p, the turtles own r, a random number from 0 to 1, drawn at the beginning of each new period. This number is necessary to randomly determine whether the firm is going to be successful or not in joining the high-end segment, according to the related probability. In fact, as seen in the previous chapter: y = sine (3πx)+ 3x if 0 ≤x<0.5 y = sine (3πx)+ 3x if 0.5 ≤x≤1 and r≤p y = 0 if 0.5 ≤x≤1 and r>p By substituting p respectively with MB, SI and DC, depending on the case, Lee et al.’s payoff function is exactly replicated. The sharing function is similarly replicated by dividing the payoff y by m, a parameter that takes into account the neighboring firms to share the payoff with. To summarize, the firms (“turtles”) own the following characteristics: - Product quality (x). It represents a number from 0 to 1, related to the determination of the payoff (y) - Payoff (y). It represents the profits/revenues related to a determined choice in product quality. The final payoff is affected by the presence of neighboring firms (m) - p. It represents the probability for a firm to be successful in joining the high-end segment. It is described alternatively by the mobility barriers, strategic interactions or dynamic capabilities, depending on the case. - r. It represents a random number drawn each turn for each firm. It determines whether the firm is going to be successful (r ≤ p) or not (r > p) - age. It represents the age of a firm, conceived as the number of consecutive generations in the high-end segment. It distinguishes incumbents and potential new entrants (in the high-end segment) To function in Netlogo, some changes to the original model had to be done. An important modification pertains the way the numbers representing the product quality have been encoded. In fact, as mentioned above, Lee et al. conceived a number as a 10-bit string representative of a value between 0 and 1 (with 6 decimals) for modeling purposes (Lee, Lee & Rho 2002, p. 736). To perform the crossover, the offspring string was composed by one bit coming alternatively from parent 1 and one bit from parent 2, until the tenth and last bit of the string. Mutation was translated in the model language by setting a determined likelihood for each bit to change, as thoroughly described in the previous chapter. Encoding a real number as a binary string was really popular some decades ago, because of the limited technical possibilities available. Nowadays, thanks to innovation in the computer systems and softwares, it is possible to instruct the model using a simple real encoding. For the present model, a simple real number from 0 to 1 has been employed to describe x. Crossover is just a weighted average of the two parents’ product quality: xab = λ xa + (1 – λ) xb λ is generated randomly each generation. xa and xb represent respectively the product quality of parent 1 and parent 2. In this way, it is possible to determine in a much easier way the offspring product quality by calculating the weighted average between the selected parents. In addition to that, the fact that λ floats between a random value range (from 0 to 1) adds a stochastic component which makes crossover more dynamic. Mutation is operationalized similarly by adding a random value, which is a normally distributed floating-point number (z). The mean (μ) of the related distribution is 0 and the standard deviation (σ) is 0.2. x1= x0 + z In Lee’s model, only the 5 new firms mutate each period. This assumption has been kept unaltered also in our model in order to be the closest to the original. The selection operator requires to be further discussed as well. In fact, in the original model the potential parent candidates’ payoff was positively correlated with their chances to be selected for reproduction. Lee et al. does not specifically mention the function determining the relation between probability to be selected and the performance. In order to translate the selection process in our model, the following mechanism was employed. Five parent candidates are selected at random. Among them, the top performer is selected to be the first parent. The same operation is repeated to select the second one. In this way, both a stochastic and a performance-based way for capturing natural selection in the model is granted. ## CREDITS AND REFERENCES Andrea Gallucci, Complexity and Management, Rethinking strategic algorithms through genetic algorithms @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle 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turtles setup go count turtles with [x > 0.5] / firms @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 0 @#$#@#$#@