globals [ cigRation boxWidthChocs boxHeightCigs ; patches initialPatch patchChoc patchCigs maxUCaptPatch maxUSgtPatch maxTotalUPatch maxTotalUtility maxTotalUCapt maxTotalUSgt initialTotalUtility captInitialUtility sgtInitialUtility captInitialMRS sgtInitialMRS price ; to calcuate demand and supply curves and market clearing price priceChocs minExcessDemand captDemand sgtSupply excessDemand market-clearing-price ; feasible optima maxFeasibleUCapt maxFeasibleUSgt maxFeasibleTotalUtility captInitialUtilityas%Max sgtInitialUtilityas%Max totalInitialUtilityas%Max tradePriceatCaptMaxU tradePriceatSgtMaxU tradePriceatMaxTotalU ; deal deal dealChocs dealCigs ; latest position latestPatch latestTotalUtility captLatestUtility sgtLatestUtility changeInCaptUtility% changeInSgtUtility% changeInTotalUtility% captLatestUtulityas%Max sgtLatestUtulityas%Max totalLatestUtulityas%Max captLatestMRS sgtLatestMRS ; counter tradeRound ] patches-own [ captsChocs captsCigs sgtsChocs sgtsCigs utilityCapt utilitySgt totalUtility mrsCapt mrsSgt tradeChocs tradeCigs tradePrice ] breed [agents agent] agents-own [ agentType initialUtility initialMRS latestUtility latestMRS ; demand and supply tempBudget optimalChocs demand supply ; for trade chocs cigs mrs budget optimal offer newChocs newCigs ] ;____________________________________________________________________________________________________________________________________ to setup clear-all ; defines box size and sets colour of patches in box to black ask patches [set pcolor white ] set cigRation ( 100 - chocRation ) set boxWidthChocs chocRation * 2 set boxHeightCigs cigRation * 2 resize-world 0 boxWidthChocs 0 boxHeightCigs set-patch-utilities ; defines agents and locates them according to the initial allocation set-default-shape agents "person" create-agents 2 [ set size 5 set color white setxy chocRation cigRation ] set initialPatch [ patch-here ] of agent 0 ask agent 0 [ set agentType "Capt" pen-down ] ask agent 1 [ set agentType "Sgt" ] ask agents [ set chocs chocRation set cigs cigRation ] set-utility ask agents [ set initialUtility latestUtility ] ask agents [ set initialMRS latestMRS ] set captInitialUtility [ initialUtility ] of agent 0 set sgtInitialUtility [ initialUtility ] of agent 1 set initialTotalUtility ( captInitialUtility + sgtInitialUtility ) set captInitialMRS [ initialMRS ] of agent 0 set sgtInitialMRS [ initialMRS ] of agent 1 set tradeRound 0 colour-box find-feasible-maxima define-core draw-demand-and-supply-curves reset-ticks end ;__________________________________________________________________ to go trade stop end ;___________________________________________________________________________________________________________________ ; PROCEDURES ;___________________________________________________________________________________________________________________ to set-patch-utilities set patchCigs 1 repeat ( boxHeightCigs - 1) [ set patchChoc 1 repeat ( boxWidthChocs - 1) [ calculate-patch-utilities ] set patchCigs patchCigs + 1 ] end ;;------------------- to calculate-patch-utilities ; use *Ration here as does not change ask patch patchChoc patchCigs [ set captsChocs patchChoc set captsCigs patchCigs set sgtsChocs ( boxWidthChocs - patchChoc ) set sgtsCigs ( boxHeightCigs - patchCigs ) set utilityCapt precision ( ( captsChocs ^ alphaCapt ) * ( captsCigs ^ ( 1 - alphaCapt ) ) ) 2 set utilitySgt precision ( ( sgtsChocs ^ alphaSgt ) * (sgtsCigs ^ (1 - alphaSgt ) ) ) 2 set totalUtility ( utilityCapt + utilitySgt ) set mrsCapt ( alphaCapt * captsCigs ) / ( ( 1 - alphaCapt ) * captsChocs ) set mrsSgt ( alphaSgt * sgtsCigs ) / ( ( 1 - alphaSgt ) * sgtsChocs ) set tradeChocs ( pxcor - chocRation ) set tradeCigs ( cigRation - pycor ) ifelse tradeChocs > 0 [ set tradePrice precision (tradeCigs / tradeChocs ) 2 ] [ set tradePrice 0 ] if tradePrice <= 0 [ set tradePrice "na" ] set patchChoc patchChoc + 1 ] end ;--------------------------- to set-utility ask agent 0 [ set latestUtility [ utilityCapt ] of patch-here set latestMRS [ mrsCapt ] of patch-here ] ask agent 1 [ set latestUtility [ utilitySgt ] of patch-here set latestMRS [ mrsSgt ] of patch-here ] end ;------------------------ to colour-box ; zero values not allowed ask patches with [ pxcor = 0 or pycor = 0 or pxcor = boxWidthChocs or pycor = boxHeightCigs ] [ set pcolor white ] ; compares agents' utilities with patch utilities and colours box ; defines the core that offers both agents greater utility ask patches with [ pxcor > 0 and pxcor < boxWidthChocs and pycor > 0 and pycor < boxHeightCigs ] [ set pcolor black ] ; the core is left coloured black after the rest have been given different colours ; blue area is blocked by agent 0 ask patches with [ pcolor = black and utilityCapt < captInitialUtility ] [ set pcolor blue ] ; red area is blocked by agent 1 ask patches with [ pcolor = black and utilitySgt < sgtInitialUtility ] [ set pcolor red ] ; magenta is blocked by both ask patches with [ pcolor = blue or pcolor = red and utilityCapt < captInitialUtility and utilitySgt < sgtInitialUtility ] [ set pcolor magenta ] ; light blue is better for both ask patches with [ pcolor = black and utilityCapt >= captInitialUtility and utilitySgt >= sgtInitialUtility ] [ set pcolor sky + 2 ] ; changed colour ; sets initial allocation yellow - done last to avoid being overwritten ask patches with [ pxcor = chocRation and pycor = ( 100 - chocRation ) ] [ set pcolor yellow ] end ;---------------------------- to find-feasible-maxima ; before the core is defined, all unblocked (feasible) points are coloured light blue ('sky') ; finds highest feasible utility for each agent ; 'max-one-of' reports the agent in the agentset that has the highest value for the given reporter set maxUCaptPatch max-one-of patches with [ pcolor = sky + 2 ] [ utilityCapt ] if maxUCaptPatch != nobody [ set maxFeasibleUCapt [ utilityCapt ] of maxUCaptPatch set tradePriceatCaptMaxU [ tradePrice ] of maxUCaptPatch set captInitialUtilityas%Max ( captInitialUtility / maxFeasibleUCapt ) * 100] set maxUSgtPatch max-one-of patches with [ pcolor = sky + 2 ] [ utilitySgt ] if maxUSgtPatch != nobody [ set maxFeasibleUSgt [ utilitySgt ] of maxUSgtPatch set tradePriceatSgtMaxU [ tradePrice ] of maxUSgtPatch set sgtInitialUtilityas%Max ( sgtInitialUtility / maxFeasibleUSgt ) * 100 ] set maxTotalUPatch max-one-of patches with [ pcolor = sky + 2 ] [ totalUtility ] if maxTotalUPatch != nobody [ set maxFeasibleTotalUtility [ totalUtility ] of maxTotalUPatch set tradePriceatMaxTotalU [ tradePrice ] of maxTotalUPatch set totalInitialUtilityas%Max ( initialTotalUtility / maxFeasibleTotalUtility ) * 100 ] if maxTotalUPatch != nobody [ ask patches with [ pxcor = [ pxcor ] of maxTotalUPatch and pycor = [ pycor ] of maxTotalUPatch ] [ set pcolor green ] ] end ;--------------------------- to define-core ; defines core i.e. the part of the contract curvre that is not blocked: points where the MRSs are equal ; The curve is found using the idea that the patch where the line should be drawn will ; be surrounded by at least one patch where the MRS for the Cpt exceeds the ; MRS for the Sgt, and at least one patch where the reverse is true - ; in other words, the difference between the MRSs passes through zero within the ; patch ask patches with [ pcolor = sky ] [ ; only look at the area where both wuld be better off if (any? neighbors4 with [ mrsCapt > mrsSgt ] and any? neighbors4 with [ mrsCapt < mrsSgt ]) [ set pcolor black ] ] end ;------------------------------------------------------------------------------------------------------ to draw-demand-and-supply-curves ; excess demand i.e. how much will trade set priceChocs 0.1 set minExcessDemand boxWidthChocs ; to set an inital max repeat 200 [ ; calculates budget ask agents [ set tempBudget ( chocs * priceChocs ) + cigs ] ; calculates optimal chocolate and calculates excess demand/supply i.e. allowing for how much the agent has already ; ensures values are not negative or exceed total available ask agent 0 ; Capt [ set optimalChocs round ( tempBudget * alphaCapt / priceChocs ) if optimalChocs < 1 [ set optimalChocs 1 ] set demand ( optimalChocs - chocs ) if demand < 0 [ set demand 0 ] if demand > ( chocs - 1 ) [ set demand ( chocs - 1 ) ] ] set captDemand [demand ] of agent 0 ask agent 1 ; Sgt [ set optimalChocs round ( tempBudget * alphaSgt / priceChocs ) if optimalChocs < 1 [ set optimalChocs 1 ] set supply ( chocs - optimalChocs ) if supply < 0 [ set supply 0 ] if supply > ( chocs - 1 ) [ set supply ( chocs - 1 ) ] ] set sgtSupply [ supply ] of agent 1 ; ensure values are not negative or exceed total available set excessDemand captDemand - sgtSupply ; if tradeRound > 0 [ clear-plot plot-demand-and-supply ] plot-demand-and-supply if abs excessDemand < minExcessDemand [ set minExcessDemand abs excessDemand set market-clearing-price precision priceChocs 2 ] set priceChocs priceChocs + 0.1 ] end ;--------------------------------------------------------------------------------------------------- to trade ; clear previous trade data ask agents [ set optimal 0 set offer 0 set deal 0 set price 0 ] if tradeRound > 0 [ ask agents [ set chocs newChocs set cigs newCigs] clear-output ] if priceMechanism = "Market clearing" [ set price market-clearing-price set yourChoice 0] if priceMechanism = "Captain's favour" [ set price tradePriceatCaptMaxU set yourChoice 0] if priceMechanism = "Sergeant's favour" [ set price tradePriceatSgtMaxU set yourChoice 0] if priceMechanism = "Random" [ set-random-price ] if priceMechanism = "Geometric mean" [ set price sqrt ( ( [ latestMRS ] of agent 0 * [ latestMRS ] of agent 1 ) ) ] if priceMechanism = "Your choice" [ set price yourChoice ] ; agent 0 - Capt - determines how much to buy at negotiated price ; "floor" ensures number rounded DOWN to nearest integer to avoid possible reduction in utility ask agent 0 [ if price > 0 [ set budget ( chocs * price ) + cigs set optimal round ( budget * alphaCapt / price ) set offer floor ( optimal - chocs ) ] ] ask agent 1 [ if price > 0 [ set chocs ( boxWidthChocs - [ pxcor ] of patch-here ) set cigs ( boxHeightCigs - [ pycor ] of patch-here ) set budget ( chocs * price ) + cigRation set optimal round ( budget * alphaSgt / price ) set offer floor ( chocs - optimal ) ] ] ; check offers valid ; to ensure offer does not exceed rations, but each agent always has 1! ask agents [ if offer > chocs [ set offer ( chocs - 1 ) ] ] ; to ensure offers are positive ask agents [ set offer abs offer ] ; to ensure only whole numbers traded eg if offer = 32 and 3 chocs traded for 1 cig, then offer has to be 10. ask agents with [ offer > 0 and price < 1 ] [ let offerUnits floor ( offer * price ) set offer offerUnits / price ] ask agents with [ offer < 0 ] [ set offer 0 ] if [ offer ] of agent 0 = 0 [output-type (word "No deal: Capt won't trade" ) ] if [ offer ] of agent 1 = 0 [output-type (word "No deal: Sgt won't trade" ) ] ; set deal set deal min list ( [ offer ] of agent 0 ) ( [ offer ] of agent 1 ) ; check if deal valid let newX [ chocs] of agent 0 + deal let newY [ cigs ] of agent 0 - ( deal * price ) if newX < 0 or newY < 0 [ set deal 0 output-type (word "No deal: outside Box" ) ] if newX > boxWidthChocs or newY > boxHeightCigs [ set deal 0 output-type (word "No deal: outside Box" ) ] if ( deal > 0 and [ pcolor ] of patch newX newY = red ) [ set deal 0 output-type (word "No deal: Sgt worse off" )] if ( deal > 0 and [ pcolor ] of patch newX newY = blue ) [ set deal 0 output-type (word "No deal: Capt worse off") ] if ( deal > 0 and [ pcolor ] of patch newX newY = white ) [ set deal 0 output-type (word "No deal: zero holdings" )] if ( deal > 0 and [ pcolor ] of patch newX newY = magenta ) [ set deal 0 output-type (word "No deal: both worse off" )] if deal > 0 [ output-type (word "Deal done!" )] ; do deal ; buyer (agent 0) gains chocs = deal but loses cigs = deal * price; opposite for seller set dealChocs deal set dealCigs deal * price ; Capt ask agent 0 [ if deal > 0 [ set newChocs ( chocs + ( dealChocs ) ) set newCigs ( cigs - ( dealCigs ) ) stamp setxy newChocs newCigs ] ] ; Sgt ask agent 1 [ if deal > 0 [ set newChocs ( chocs - ( dealChocs ) ) set newCigs ( cigs + ( dealCigs ) ) setxy ( boxWidthChocs - newChocs ) ( boxHeightCigs - newCigs ) ] ] ask agents [ set-utility ] if deal > 0 [ set latestPatch [ patch-here ] of agent 0 set latestTotalUtility [ totalUtility ] of latestPatch set captLatestUtility [ latestUtility ] of agent 0 set sgtLatestUtility [ latestUtility ] of agent 1 set changeInCaptUtility% (( captLatestUtility - captInitialUtility ) / captInitialUtility ) * 100 set changeInSgtUtility% (( sgtLatestUtility - sgtInitialUtility ) / sgtInitialUtility ) * 100 set changeInTotalUtility% (( latestTotalUtility - initialTotalUtility ) / initialTotalUtility ) * 100 set captLatestUtulityas%Max ( captLatestUtility / maxFeasibleUCapt ) * 100 set sgtLatestUtulityas%Max ( sgtLatestUtility / maxFeasibleUSgt ) * 100 set totalLatestUtulityas%Max ( latestTotalUtility / maxFeasibleTotalUtility ) * 100 set captLatestMRS [ latestMRS ] of agent 0 set sgtLatestMRS [ latestMRS ] of agent 1 set tradeRound tradeRound + 1 plot-utility-%increase plot-trades draw-demand-and-supply-curves ] end ;--------------------------------- to set-random-price let minMRS min [ latestMRS ] of agents let maxMRS max [ latestMRS ] of agents set price minMRS + ( random ( 100 * ( maxMRS - minMRS ) ) / 100 ) end ;_________________________________________________________________________________________________________________________ ; PLOTS ;_________________________________________________________________________________________________________________________ to plot-demand-and-supply set-current-plot "Excess Demand & Supply" set-plot-x-range 0 200 set-plot-y-range 0 20 if tradeRound > 0 and priceChocs = 0.1 [ plot-pen-reset ] set-current-plot-pen "Capt" plotxy captDemand priceChocs if tradeRound > 0 and priceChocs = 0.1 [ plot-pen-reset ] set-current-plot-pen "Sgt" plotxy sgtSupply priceChocs end to plot-utility-%increase set-current-plot "% increase in utility" set-current-plot-pen "Capt" plotxy tradeRound changeInCaptUtility% set-current-plot-pen "Sgt" plotxy tradeRound changeInSgtUtility% set-current-plot-pen "Total" plotxy tradeRound changeInTotalUtility% end to plot-trades set-current-plot "Trades" set-current-plot-pen "Chocs" plotxy tradeRound deal set-current-plot-pen "Cigs" plotxy tradeRound dealCigs set-current-plot-pen "Price" plotxy tradeRound price end ;_____________________________________________________________________________________________________________________________ ;_____________________________________________________________________________________________________________________________ @#$#@#$#@ GRAPHICS-WINDOW 20 145 405 551 -1 -1 3.7143 1 10 1 1 1 0 0 0 1 0 100 0 100 0 0 0 ticks 30.0 BUTTON 510 10 574 43 Setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 805 100 875 145 Go Go T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 510 50 650 83 chocRation chocRation 25 75 50 5 1 NIL HORIZONTAL SLIDER 655 10 765 43 alphaCapt alphaCapt 0.6 0.9 0.9 0.1 1 NIL HORIZONTAL SLIDER 770 10 900 43 alphaSgt alphaSgt 0.1 0.5 0.1 0.1 1 NIL HORIZONTAL MONITOR 670 50 739 95 NIL cigRation 0 1 11 TEXTBOX 30 585 515 721 YELLOW - initial allocation\nBLUE - blocked by Captain RED - blocked by Sergeant PURPLE - blocked by both\nLIGHT BLUE - allocations offering both agents greater utility than the initial allocation but are not in the core. \nBLACK - core GREEN - maximum total utility\nBecause the two agents move together, only one is visible: to see both, use \"inspect\". Agent 0 is the Capt; Agent 1, the Sgt. 12 0.0 1 MONITOR 545 520 695 565 Capt's initial utility captInitialUtility 2 1 11 MONITOR 705 520 845 565 Sgt's initial utility sgtInitialUtility 2 1 11 MONITOR 415 715 505 760 NIL boxWidthChocs 0 1 11 MONITOR 325 715 415 760 NIL boxHeightCigs 0 1 11 TEXTBOX 755 50 920 91 Total items per agent = 100 \neg if chocs = 30, cigs = 70 12 0.0 1 MONITOR 730 260 805 305 Capt's offer [ offer ] of agent 0 0 1 11 MONITOR 805 260 880 305 Sgt's offer [ offer ] of agent 1 0 1 11 MONITOR 705 385 770 430 NIL dealChocs 0 1 11 MONITOR 505 375 595 420 NIL captInitialMRS 2 1 11 MONITOR 595 375 685 420 NIL sgtInitialMRS 2 1 11 TEXTBOX 540 205 905 261 If price < 1, then 1 cig is worth more than 1 choc e.g price = 0.25 => 4 chocs for 1 cig. \nIf price > 1, then that is the number of cigs traded for 1 choc. 12 0.0 1 MONITOR 535 670 685 715 % Change in Capt's utility changeInCaptUtility% 1 1 11 MONITOR 695 670 835 715 % Change in Sgt's utility changeInSgtUtility% 1 1 11 MONITOR 825 385 915 430 New Position latestPatch 1 1 11 MONITOR 845 625 990 670 NIL latestTotalUtility 1 1 11 MONITOR 535 625 685 670 Capt's latest utility captLatestUtility 1 1 11 MONITOR 695 625 835 670 Sgt's latest utility sgtLatestUtility 1 1 11 MONITOR 855 520 1000 565 NIL initialTotalUtility 2 1 11 MONITOR 505 420 597 465 NIL captLatestMRS 2 1 11 MONITOR 595 420 685 465 NIL sgtLatestMRS 2 1 11 MONITOR 845 670 990 715 % Change in total utility changeInTotalUtility% 1 1 11 OUTPUT 650 315 925 365 12 PLOT 930 10 1225 265 Excess Demand & Supply Quantity of chocolate Price 0.0 200.0 0.0 5.0 true true "" "" PENS "Capt" 1.0 0 -13345367 true "" "" "Sgt" 1.0 0 -2674135 true "" "" MONITOR 767 385 827 430 NIL dealCigs 0 1 11 MONITOR 715 150 792 195 NIL tradeRound 0 1 11 PLOT 930 275 1225 465 Trades Trade Round Deals 0.0 10.0 0.0 10.0 true true "" "" PENS "Chocs" 1.0 0 -13345367 true "" "" "Cigs" 1.0 0 -2674135 true "" "" "Price" 1.0 0 -16777216 true "" "" PLOT 1010 485 1210 755 % increase in utility Trade Round % increase in utility 0.0 10.0 0.0 50.0 true true "" "" PENS "Capt" 1.0 0 -13345367 true "" "" "Sgt" 1.0 0 -2674135 true "" "" "Total" 1.0 0 -16777216 true "" "" MONITOR 855 475 1000 520 NIL maxFeasibleTotalUtility 1 1 11 MONITOR 545 475 697 520 Capt's max feasible utility maxFeasibleUCapt 1 1 11 MONITOR 705 475 847 520 Sgt's max feasible utility maxFeasibleUSgt 1 1 11 CHOOSER 510 90 667 135 priceMechanism priceMechanism "Market clearing" "Captain's favour" "Sargeant's favour" "Random" "Geometric mean" "Your choice" 3 MONITOR 715 100 790 145 NIL price 2 1 11 INPUTBOX 610 140 690 200 yourChoice 0 1 0 Number MONITOR 535 715 685 760 Capt's latest utility as % max captLatestUtulityas%Max 1 1 11 MONITOR 690 715 835 760 Sgt's latest utility as % max sgtLatestUtulityas%Max 1 1 11 MONITOR 845 715 990 760 Total latest utulity as % max totalLatestUtulityas%Max 1 1 11 TEXTBOX 25 10 505 145 INSTRUCTIONS\nSet the alphas for the two agents - the higher the number, the stronger the preference for choclate - and the initial endowment of chocolate. \nChoose the price mechanism. If YourChoice selected, enter a figure in \"yourPrice\".\nPress SETUP and GO\nChoose another price mechanism if you wish to change, and press GO again.\nThe aim is to move the agents as close as possible to the green patch.\nTo start again, press SETUP. 12 0.0 1 MONITOR 545 565 695 610 Capt's initial utility as % max captInitialUtilityas%Max 1 1 11 MONITOR 705 565 845 610 Sgt's initial utility as % max sgtInitialUtilityas%Max 1 1 11 MONITOR 855 565 1000 610 Total initial utility as % max totalInitialUtilityas%Max 1 1 11 @#$#@#$#@ ## WHAT IS IT? The model presents the Edgeworth Box as a game. The aim is to select prices at which the agents can trade to move them as close as possible to their maximum utility ## HOW IT WORKS There are two agents - the Captain and the Sergeant - and two goods - chocolate and cigarettes. Each agent is each given the same allocation of cigarettes and chocolate. But they have different tastes: the Captain prefers chocolate to cigarettes and the Sergeant prefers cigarettes to chocolate. The further the Captain is from the bottom left-hand corner, the higher is his utility. The further the Sergeant is from the top right-hand corner, the higher is his utility. Their utility is represented by Cobb-Douglas utility functions, with alpha lying bteween 0 and 1, with the alphas represent the strength of preference for chocolate. The higher the alpha, the stronger the preference.) So the marginal rate of substitution (MRS) is ( alpha * goodB ) / ( 1 - alpha) * goodA). This means that alphas cannot be 1 because the MRS would then be undefined. The model starts by colouring in the Edgeworth box as follows: - white which not feasible as it involves zero quantities - yellow indicates the initial allocation - dark blue where the Captain would be worse off - red where the Sergeant would be worse off - violet where both would be worse off - light blue where both would be better off. Within this area, the core is shown in black i.e. the segment of the contract curve that is not blocked. - the green indicates the feasible point where total utility is maximised. Unless the initial allocations happen to co-incide with their preferences, the agents can increase their utility by trading. There are four ways of setting the prices: - based on the market-clearing price i.e. the price at which the demand and supply curves intersect - "Captain's favour": the price that would maximise the Captain's utility but the Sergeant will be reluctant to trade - "Sergeant's favour": the price that would maximise the Sergeant's utility but the Captain will be reluctant to trade - "Random": but between the MRSs of the two agents and in such as way that there is a 50/50 chance of the price being greater or less than 1. - a price chosen by the modeller. The proces can be repeated. Each time a deal is done, the demand and supply curves are redrawn. There are no stochastic processes involved. Because the two agents move together, only one is visible: but both can be seen using "inspect". ## HOW TO USE IT Set the alphas for the two agents: - for the Captain this is between 0.6 and 0.9 - for the Sergeant this is between 0.1 and 0.5 Set the initial endowment of chocolate: this can be between 25 and 75. (To keep the size of the box within reasonable limits.) Choose the price mechanism. If YourChoice selected, enter a figure in "yourPrice". Press SETUP Press GO Choose another price mechanism if you wish to change, and press GO again. ## CREDITS AND REFERENCES Runs on NetLogo 5.2. For more information, see Hamill, L. & Gilbert, N. (2016) Agent-based Modelling in Economics. Wiley: Chapter 5. To refer to this model: Hamill, L. & Gilbert, N. (2016) Edgeworth Box Game model. @#$#@#$#@ 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 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240 Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163 Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165 Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225 Circle -16777216 true false 135 90 30 Line -16777216 false 150 105 195 60 Line -16777216 false 150 105 105 60 car false 0 Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180 Circle -16777216 true false 180 180 90 Circle -16777216 true false 30 180 90 Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89 Circle -7500403 true true 47 195 58 Circle -7500403 true true 195 195 58 circle false 0 Circle -7500403 true true 0 0 300 circle 2 false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 cow false 0 Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167 Polygon -7500403 true true 73 210 86 251 62 249 48 208 Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123 cylinder false 0 Circle -7500403 true true 0 0 300 dot false 0 Circle -7500403 true true 90 90 120 face happy false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 true 75 45 90 45 flower false 0 Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135 Circle -7500403 true true 85 132 38 Circle -7500403 true true 130 147 38 Circle -7500403 true true 192 85 38 Circle -7500403 true true 85 40 38 Circle -7500403 true true 177 40 38 Circle -7500403 true true 177 132 38 Circle -7500403 true true 70 85 38 Circle -7500403 true true 130 25 38 Circle -7500403 true true 96 51 108 Circle -16777216 true false 113 68 74 Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218 Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240 house false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 leaf false 0 Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 sheep false 0 Rectangle -7500403 true true 151 225 180 285 Rectangle -7500403 true true 47 225 75 285 Rectangle -7500403 true true 15 75 210 225 Circle -7500403 true true 135 75 150 Circle -16777216 true false 165 76 116 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 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 5.2.0 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ setup go count turtles @#$#@#$#@ @#$#@#$#@ 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 @#$#@#$#@ 1 @#$#@#$#@