;Edoardo Campanella, Daniele Destefanis, Alessandro Manello ;Modello di simuazione sull'oligopolio alla Bertrand turtles-own [high-demand-consumer? low-demand-consumer? ;; this variables identify two kinds of consumers, according to their willingness to pay willingness-to-pay? ;; this is consumers' maximum price:above this price, they won't buy any additional unit of the good happy? ] ;; identifies those who are satisfied because they buy the good, since their willingness to pay is bigger than market price globals [firm-sites ;; those patches which represent firms distance-firms rounds ;; this is the number of interaction number-happy ;; this is the number of happy consumers number-unhappy ;; this is the number of unhappy consumers average-market-price ;; this is the average of the prices at which firms sell their goods to consumers colluded-average-market-price] ;; this is the average of the prices at which firms sell their goods to consumers in case of collusion patches-own [high-demand-consumer ;; these are the two different types of consumers low-demand-consumer people quantity-demanded ;; this is the initial price of a firm: Q market-price ;; the price at whom a firm sells its product: P= Q*0,8 own-marginal-cost ;; marginal cost of a single firm in the case of marginal cost differentiation colluded-market-price ;; the price at whom a firm sells its product in case of collusion, equal to the maximum price on the market * 1.5 ] to setup ca set firm-sites patches with [firm-site?] ;; this creates a group of patches which represent the firms set-default-shape turtles "person" set distance-firms floor (screen-size-x / num-firms) ;; disposes the firms on the screen ask turtles[ set ycor 0 set xcor random screen-size-x ] ;; this command puts the turtles on the x-axis ask turtles [move-into-firm] ;; this makes the turtles go where the firms are setup-turtles setup-patches setup-plots set rounds 0 update-labels spread-consumers update-happy-plot update-price-plot end to setup-turtles crt num-consumers ask turtles [set size 0.8] ;; this command modifies turtles dimension ask turtles[ ifelse (random 2 = 0) [set high-demand-consumer? true set low-demand-consumer? false] [set high-demand-consumer? false set low-demand-consumer? true] ;; this randomly create consumers of the two different groups ] ask turtles [ ifelse consumer-differentiation? ;; if the user wants the consumers to be different one from each other, this assigns different degrees of willingness to pay [ifelse high-demand-consumer? [set willingness-to-pay? (minimum-willingness-to-pay * 2)] [set willingness-to-pay? (minimum-willingness-to-pay * 1 )] ] [set willingness-to-pay? (minimum-willingness-to-pay)] ;; else the willingness to pay of every consumer will be the one decided by the user ] ask turtles [ ifelse (random 2 = 0) [set heading 90] [set heading 270] ;; this command randomly turns the turtles on the right or on the left ] ask turtles [fd random screen-edge-x] ask turtles [ move-into-firm] ;; this moves forward every turtle until it finds the closest group of firms end to setup-patches ask firm-sites [ set high-demand-consumer 0 set low-demand-consumer 0 set people 0] ask turtles [ if high-demand-consumer? [set high-demand-consumer (high-demand-consumer + 1)] if low-demand-consumer? [set low-demand-consumer (low-demand-consumer + 1)]] ask firm-sites [ set people (high-demand-consumer + low-demand-consumer)] ;; these commands allow the patches to count the two different kinds of consumers ask firm-sites [ ifelse different-marginal-cost? [set own-marginal-cost (marginal-cost * (random-float 2))] [set own-marginal-cost (marginal-cost)]] ;; if the user decides to have marginal cost differetation, ;; patches are asked to calculate their own marginal cost as a product of the one decided by the user and a floating number, randomly chosen ask firm-sites [ set quantity-demanded (count turtles-here)* 5] ask firm-sites [ set market-price (quantity-demanded)* 0.5 ;; market price is the result of the equation: P= 0.8*Q ] ask firm-sites [ if market-price < own-marginal-cost [set market-price (own-marginal-cost)] ] ;; price must be at least equal to marginal costs update-consumer-happiness calculate-average-market-price end to update-labels ask firm-sites [ set plabel count turtles-here ] end to-report firm-site? ;; this is a turtle or patch procedure and checks the coordinates of a firm or a patch ;; which is located where a group is supposed to be located; it checks the right arrangement ;; of groups on the screen, according to the number of groups decided by the user let firm-interval floor (screen-size-x / num-firms) report (pycor = 0) and (((screen-edge-x - pxcor) mod firm-interval) = 0) and (floor ((screen-edge-x - pxcor) / firm-interval) < num-firms) end to move-into-firm if not firm-site? [ fd 1 ;; this command ask the turtles to move to the nearest firm site if limit-speed? [ wait 0.2 ] ;; it slows it down in order to make it easier for the user to observe what happens move-into-firm ] end to spread-consumers ;; this command spreads consumers out vertically according to their willingness to pay ask turtles [ifelse high-demand-consumer? [set heading 0 fd 2] [set heading 180 fd 2] jump count other-turtles-here] end to go if (number-happy = num-consumers) ;; if everyone is happy, it stops the simulation [stop ] group-people update-consumer-happiness update-market-price move-consumers update-quantity-demanded update-consumer-happiness calculate-average-market-price update-labels spread-consumers set rounds (rounds + 1) update-happy-plot update-price-plot if limit-speed? [ wait 0.4 ] end to group-people ;; this groups the consumers on the x-axis ask turtles [set ycor 0] end to update-consumer-happiness ;; this update consumers happiness: they are happy if they can buy a good, so if their willingness to pay is higher or equal to market price ask firm-sites [ set people (high-demand-consumer + low-demand-consumer)] ask turtles [ ifelse (willingness-to-pay? >= market-price) [set happy? true set color blue] [set happy? false set color red] set number-happy count turtles with [happy?] set number-unhappy count turtles with [not happy?] ] ;; these count the number of happy and unhappy people and pass the data to the monitors end to move-consumers ask turtles [ ;; if a consumer is not happy, if (not happy?) [ifelse high-demand-consumer? [set high-demand-consumer high-demand-consumer - 1] ;; the command decreases the count in his old group, [set low-demand-consumer low-demand-consumer - 1] ifelse (random 2 = 0) [set heading 90] [set heading 270] ;; it askes the turtle to turn, randomly, on the right or on the left fd 1 ;; and to leave its old group move-into-firm ifelse high-demand-consumer? [set high-demand-consumer high-demand-consumer + 1] [set low-demand-consumer low-demand-consumer + 1]]] ;; the command increases the count in consumer's new group end to update-quantity-demanded ask firm-sites [ set quantity-demanded (count turtles-here)* 5] end to update-market-price ask firm-sites [ set market-price (quantity-demanded)* 0.8 ;; this update the market price of a firm according to the new number of customers using the same equation as before: P= 0.8*Q ] ask firm-sites [ if number-unhappy > count turtles-here * 0.20 [set market-price (market-price - market-price * 0.50)] ;; if 20% of consumers on a firm-site are unhappy, the firm reduces its price by 50% if number-unhappy = count turtles-here [set market-price (market-price - market-price * 0.80)] ;; if all the consumers on a firm-site are unhappy, the firm reduces its price by 80% ] ask firm-sites [ ;; price must be at least equal to marginal costs if market-price < own-marginal-cost [set market-price (own-marginal-cost)] ] end to calculate-average-market-price ;; this calculates an average market price for the plot of the simulation set average-market-price (mean values-from firm-sites [market-price]) end to setup-plots set-current-plot "number happy consumers" set-plot-y-range 0 num-consumers end to update-happy-plot set-current-plot "number happy consumers" set-current-plot-pen "happy consumers" plot (count turtles with [happy?]) end to update-price-plot set-current-plot "average market price" set-current-plot-pen "average market price" plot average-market-price end to collude ;; now it's possible that firms collude ask firm-sites [ ifelse plabel-color = white [set colluded-market-price ((max values-from patches [market-price]) * 1.5)] ;; this is the rule to fix collusion price [set colluded-market-price (market-price)] ] group-people update-consumer-happiness-with-collusion move-consumers update-colluded-market-price update-consumer-happiness-with-collusion calculate-average-market-price calculate-colluded-average-market-price update-labels spread-consumers set rounds (rounds + 1) update-happy-plot update-colluded-price-plot if limit-speed? [ wait 0.4 ] if (number-happy = num-consumers) ;; if everyone is happy, it stops the simulation [stop ] end to update-consumer-happiness-with-collusion ;; this updates consumers happiness: they are happy if they can buy a good, so if their willingness to pay is higher than market price ask firm-sites [ set people (high-demand-consumer + low-demand-consumer)] ask turtles [ ifelse (willingness-to-pay? >= colluded-market-price) [set happy? true set color blue] [set happy? false set color red] set number-happy count turtles with [happy?] set number-unhappy count turtles with [not happy?] ] ;; these count the number of happy and unhappy people and pass the data to the monitors of the simulation end to update-colluded-market-price ask firm-sites [ set quantity-demanded (count turtles-here)* 5] ask firm-sites [ set market-price (quantity-demanded)* 0.8 ;; this update market price of a firm according to the new number of customers using the same equation as before: P= 0.8*Q ] ask firm-sites [ if number-unhappy > count turtles-here * 0.20 [set market-price (market-price - market-price * 0.50)] ;; if 20% of consumers on a firm-site are unhappy, the firms reduce its price by 50% if number-unhappy = count turtles-here [set market-price (market-price - market-price * 0.80)] ;; if all consumers on a firm-site are unhappy, the firm reduce its price by 80% ] ask firm-sites [ ;; it's impossible that price is less than marginal cost if market-price < own-marginal-cost [set market-price (own-marginal-cost)] ] ask firm-sites [ ifelse plabel-color = white [set colluded-market-price ((max values-from patches [market-price]) * 1.5)] [set colluded-market-price (market-price)] ] if collusion-breaking? ;; if the firm breaks the collusion, after 5 rounds, color becomes green [ask firm-sites [if (rounds > 5) and (market-price < colluded-market-price * 0.60) [set colluded-market-price (market-price) set plabel-color green] ]] end to calculate-colluded-average-market-price ;; this calculates an average market price with collusion for the plot of the simulation set colluded-average-market-price (mean values-from firm-sites [colluded-market-price]) end to update-colluded-price-plot set-current-plot "average market price" set-current-plot-pen "average market price" plot average-market-price set-current-plot "average market price" set-current-plot-pen "colluded average market price" plot colluded-average-market-price end ;; References ; Wilensky, U. (1997). NetLogo Party model. ; http://ccl.northwestern.edu/netlogo/models/Party. ; Center for Connected Learning and Computer-Based Modeling, ; Northwestern University, Evanston, IL. @#$#@#$#@ GRAPHICS-WINDOW 303 10 733 461 17 17 12.0 1 10 1 1 1 0 1 1 1 CC-WINDOW 5 543 1195 638 Command Center 0 BUTTON 54 23 125 62 NIL setup NIL 1 T OBSERVER T NIL SLIDER 49 199 223 232 num-firms num-firms 2 15 2 1 1 NIL SWITCH 49 394 169 427 limit-speed? limit-speed? 1 1 -1000 SLIDER 50 149 223 182 num-consumers num-consumers 1 100 50 1 1 NIL SLIDER 51 249 223 282 marginal-cost marginal-cost 10 50 20 1 1 NIL BUTTON 177 26 253 67 NIL go T 1 T OBSERVER T NIL MONITOR 800 417 886 466 NIL number-happy 0 1 MONITOR 858 480 941 529 NIL rounds 0 1 MONITOR 916 415 1007 464 NIL number-unhappy 0 1 SWITCH 48 349 211 382 different-marginal-cost? different-marginal-cost? 1 1 -1000 PLOT 804 13 1185 195 number happy consumers rounds number-happy 0.0 10.0 0.0 10.0 true false PENS "happy consumers" 1.0 0 -16777216 true PLOT 805 212 1186 393 average market price rounds average market price 0.0 10.0 0.0 10.0 true false PENS "average market price" 1.0 0 -16777216 true "colluded average market price" 1.0 0 -2674135 true SLIDER 49 296 224 329 minimum-willingness-to-pay minimum-willingness-to-pay 10 50 20 1 1 NIL SWITCH 47 445 223 478 consumer-differentiation? consumer-differentiation? 1 1 -1000 BUTTON 109 89 185 126 NIL collude T 1 T OBSERVER T NIL SWITCH 49 490 208 523 collusion-breaking? collusion-breaking? 0 1 -1000 @#$#@#$#@ WHAT IS IT? ----------- This program is a simulation of a little market, where operate only two classes of agents: firms, represented by patches, and consumers, represented by turtles. In this market only one product is available. Consumers can be satisfated or not according to their willingness to pay and to the price at which the firm where they are is selling its product. If they are satisfied, they buy and stop walking. If they aren't, they don't buy and walk around looking for a lower price. The simulation stop when all persons are happy. HOW IT WORKS ------------ The rules are simple. Every consumer has a willigness to pay: if product price is lower than it, he is happy and he buys (his colour become blue); but if product price is higher tahn his willingness to pay, he is unhappy and he starts walking looking for a cheaper firm (his colour became red). Every firm has a marginal cost and fixs a product price, which is function of its own demand. Firms cut prices if many of their customers are unhappy. HOW TO USE IT ------------- Start the simulation by clicking setup. Then, after clicking go, persons start moving and searching lower prices. Not always every consumer becomes happy: in this case, the market is not in equilibrium. By clicking collude, persons start moving, but all the firms fix an hight homogeneous price, that is 50% higher than the maximum price which would be fixed in a competitive context. Buttons: Setup resets everything and creates a variable number of turtles that are randomly located Buttons: Go if clicked, the simulation begins and the turtles start moving. Buttons: Collude if clicked, the turtles start moving, but firm behaviour is not the same. They make a trust and fix an higher price. Sliders: On the left of the screen, below setup, go and collude buttons, there are four sliders. They allow the user to manipulate certain parameters. Switches: On the left of the screen, below buttons and sliders, there are four switches. taht allow the user to choose four conditions that modify the simulation. Monitors: On the left of the screen there are three monitors. They monitor and shw certain counters and variables. Plots: On the left of the screen there are two graphs that show the trend of two variables (three in the case of collusion) TO MANIPULATE ------------- Slider num-consumers: you can choose how many turtles populate the market. Slider num-firms: this program simulate an oligopoly, the number of firms (pathes) on the marker is not large, and varies from 2 to 15. Slider marginal-cost: we assume that fixed cost are inesistent. You can modify the value and establish it below, above or equal to consumers' willigness to pay. Slider minimum-willigness-to-pay: you can choose this value. If it is under the marginal cost there is no equilibrium, because there are always unhappy consumers. Switch different-marginal-cost: if this switch is on the "on", there are firms with different marginal costs which are obtained by multiplying the value of the marginal cost choosed by the user by a random float number from 0 to 2 Swich limit-speed: if it is on, the speed of the agents's interaction is slowed down to make it easier for the user to observe the simulation. Swich consumer-differentation: if on the "on", consumers are shared in two types, one with a high willigness to pay (double of the value choosed by the homonymous slider), the other with a low willigness to pay (the same value choosed by the slider). Switch collusion-breaking: if on the "on", after 5 rounds each firm can break the collusion trust. A firm breaks collusion if its market price is smaller than 60% of colluded market price price. THINGS TO TRY ------------- You can run the model with the following settings: a) Bertrand duopoly: num-consumer=50 num-firm=2 marginal-cost=20 willigness-to-pay=20 different-marginal-cost OFF different-willigness-to-pay OFF Clicking on GO after only one round the sistem go to equilibrium. b) Oligopoly: num-consumer=50 num-firm=5 marginal-cost=20 willigness-to-pay=20 different-marginal-cost OFF different-willigness-to-pay OFF Clicking on GO after a little number of round the sistem goes to equilibrium; if the number of firms rises, the simulation goes to equilibrium more quickly. If the number of consumers rises, the equilibrium is more difficult to be reached. If the switches are on "On", all is more dependent on the casual distribution of consumers. c) Collusion: num-consumer=50 num-firm=5 marginal-cost=20 willigness-to-pay=20 different-marginal-cost OFF different-willigness-to-pay OFF collusion-breaking OFF Clicking on COLLUDE firms choose an high price, and often all the consumers became unhappy. If the collusion-breaking is on "ON", after 5 rounds prices decrease and the number of happy consumers increases. EXTENDING THE MODEL ---------------- It's possible to make the collusion rules more complicated. In this program every firm chooses a collusion price that is the 150% of the highest price on the market. If the collusion rules become more complicated, also results could become more real. CREDITS AND REFERENCES ---------------------- Wilensky, U. (1997). NetLogo Party model. http://ccl.northwestern.edu/netlogo/models/Party. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. @#$#@#$#@ 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 -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 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Line -7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 3.0 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@