turtles-own [ individual-strategy-list ;; list of strategies per agent individual-choices-list ;; list of choices per agent active-predictor ;; reference of the used strategy forecast ;; forecast of each agent choice ;; choice according to the forecast strategies-scores ;; list of scores of each strategy position-min-score ;; position of the most accurate strategy agent-score ;; each agent's score step ;; loop tool ] globals [count-list ;; list of agents attending the bar count-list-go ;; list of agents forecasting the bar is closed history ;; list of opening of the bar (1 if opened, 0 if not) strategies ;; list of available strategies open-level ;; level of opening of the bar (60 in the standard version) value ;; loop tool ] ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;; Setting Up ;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup setting-up ;; preparing the simulation patches-setup ;; set up the patches turtles-setup ;; set up the turtles strategy-setting ;; create the strategy list distribute-strategies ;; distribute the strategies to the agents end to setting-up ca set-default-shape turtles "person" set count-list [] set count-list-go [] end to patches-setup ask patches [set pcolor blue - 3] ask random-n-of Number-of-Agents patches [ sprout 1 [ set open-level (round (0.6 * count turtles)) set agent-score 0.5 ifelse (random-int-or-float 1.0 < .5) [set choice 1] [set choice 0] ] ] end to turtles-setup ask turtles [ifelse choice = 1 [set color pink] [set color white]] set count-list lput count turtles with [choice = 1] count-list set count-list-go lput ((count turtles with [active-predictor > open-level]) * 100 / count turtles) count-list-go ifelse (last count-list > open-level) [set history 0] [set history 1] end to strategy-setting set strategies n-values Strategy-Space [?] repeat ((length strategies) - Strategy-Space)[ set strategies remove-item (random (length strategies)) strategies] set value (Memory - 1) repeat (20 - Memory) [set strategies remove-item value strategies set strategies remove-item ((2 * value) - 1) strategies set strategies remove-item ((3 * value) - 2) strategies set strategies remove-item ((4 * value) - 3) strategies set strategies remove-item ((5 * value) - 4) strategies set strategies remove-item ((6 * value) - 5) strategies set strategies remove-item ((7 * value) - 6) strategies set strategies remove-item ((8 * value) - 7) strategies set strategies remove-item ((9 * value) - 8) strategies ] end to distribute-strategies ask turtles [ set strategies-scores n-values Strategies-per-agent [0] set individual-strategy-list [] while [length (remove-duplicates individual-strategy-list) < strategies-per-agent ] [set individual-strategy-list lput (random-one-of strategies) individual-strategy-list set individual-strategy-list remove-duplicates individual-strategy-list] ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;; Go !!!!!!! ;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to go ;;according to last weeks attendence, each strategy determines a new choice update-individual-choices ask turtles [;;each agent chooses the his active-predictor, the most "accurate" ;; ie : the lowest aggregate error or score out of the vailable strategies mapping-score-strategy ;;each agent selects an action (to go or not) select-action] turtles-setup update-agent-score update-scores-agent-list do-plot end to update-individual-choices ask turtles [ set individual-choices-list n-values Strategies-per-agent [0] set step 0 repeat (strategies-per-agent) [forecasts]] end to forecasts if item step individual-strategy-list <= 19 [TitForTat set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 19 and item step individual-strategy-list <= 39 [Mirror set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 39 and item step individual-strategy-list <= 59 [Fixed set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 69 and item step individual-strategy-list <= 89 [Trend set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 89 and item step individual-strategy-list <= 99 [OppositeTrend set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 99 and item step individual-strategy-list <= 119 [Trend2 set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 119 and item step individual-strategy-list <= 139 [MovingAverage set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 139 and item step individual-strategy-list <= 159 [OppositeMovingAverage set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 159 and item step individual-strategy-list <= 179 [Trend3 set individual-choices-list (replace-item step individual-choices-list forecast)] if item step individual-strategy-list > 179 and item step individual-strategy-list <= 199 [OppositeTrend3 set individual-choices-list (replace-item step individual-choices-list forecast)] set step (step + 1) end to mapping-score-strategy set position-min-score position (min strategies-scores) strategies-scores set active-predictor item position-min-score individual-choices-list end to select-action ifelse (active-predictor <= open-level) [set choice 1] [set choice 0] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;; Scores ;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to update-agent-score ask turtles [ if (choice = 1 and history = 0) [set agent-score agent-score + 0.4] if (choice = 0) [set agent-score agent-score + 0.5] if (choice = 1 and history = 1) [set agent-score agent-score + 0.6] ] end to update-scores-agent-list ask turtles [ set step 0 repeat (strategies-per-agent)[ set strategies-scores replace-item step strategies-scores ((Lambda * (item step strategies-scores)) + ((1 - Lambda) * (abs (last count-list - (item step individual-choices-list))))) set step (step + 1)] ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;; Strategies ;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to TitForTat ;The same as N (up to 20) weeks ago ifelse (length count-list < (item step individual-strategy-list) + 1) [set forecast (random count turtles)] [set forecast (item ((length count-list) - (item step individual-strategy-list) - 1) count-list)] end to Mirror ;A mirror image around 50% of N (up to 20) weeks ago ifelse (length count-list < (item step individual-strategy-list) + 1 - 20) [set forecast (random count turtles)] [set forecast (count turtles - (item ((length count-list) - (item step individual-strategy-list) - 1 + 20) count-list))] end to Fixed ;Allways choose the same attendence (5%, 10%, 15%, 20%, 25% ... or 100%) set forecast (round ((((item step individual-strategy-list) - 40 + 1) * 5 / 100) * count turtles)) end to Trend ;A N (up to 20 weeks ago) dated 2 day trend applied to the last attendence ifelse (length count-list < (item step individual-strategy-list) + 2 - 60) [set forecast (random count turtles)] [set forecast (last count-list + (item ((length count-list) - (item step individual-strategy-list) - 1 + 60) count-list) - (item ((length count-list) - (item step individual-strategy-list) - 2 + 60) count-list)) if forecast > count turtles [set forecast count turtles] if forecast < 0 [set forecast 0]] end to OppositeTrend ;A N (up to 20 weeks ago) dated 2 day opposite trend applied to the last attendence ifelse (length count-list < (item step individual-strategy-list) + 2 - 80) [set forecast (random count turtles)] [set forecast (last count-list - (item ((length count-list) - (item step individual-strategy-list) - 1 + 80) count-list) + (item ((length count-list) - (item step individual-strategy-list) - 2 + 80) count-list)) if forecast > count turtles [set forecast count turtles] if forecast < 0 [set forecast 0]] end to Trend2 ;A N (up to 20 weeks ago) dated 2 day (3 day spaced) trend applied to the last attendence ifelse (length count-list < (item step individual-strategy-list) + 4 - 100) [set forecast (random count turtles)] [set forecast (last count-list + (item ((length count-list) - (item step individual-strategy-list) - 1 + 100) count-list) - (item ((length count-list) - (item step individual-strategy-list) - 4 + 100) count-list)) if forecast > count turtles [set forecast count turtles] if forecast < 0 [set forecast 0]] end to MovingAverage ;A N (up to 20 weeks ago) 5 day Moving average ifelse (length count-list < (item step individual-strategy-list) + 5 - 120) [set forecast (random count turtles)] [set forecast (round ( 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 1 + 120) count-list) + 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 2 + 120) count-list) + 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 3 + 120) count-list) + 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 4 + 120) count-list) + 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 5 + 120) count-list) ))] end to OppositeMovingAverage ;A N (up to 20 weeks ago) opposite 5 day Moving average ifelse (length count-list < (item step individual-strategy-list) + 5 - 140) [set forecast (random count turtles)] [set forecast (Count turtles - round ( 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 1 + 140) count-list) + 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 2 + 140) count-list) + 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 3 + 140) count-list) + 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 4 + 140) count-list) + 0.2 * (item ((length count-list) - (item step individual-strategy-list) - 5 + 140) count-list) ))] end to Trend3 ;A N (up to 20 weeks ago) dated 2 day relative trend applied to the last attendence ifelse (length count-list < (item step individual-strategy-list) + 2 - 160) [set forecast (random count turtles)] [set forecast (last count-list + (((item ((length count-list) - (item step individual-strategy-list) - 1 + 160) count-list) - (item ((length count-list) - (item step individual-strategy-list) - 2 + 160) count-list)) / last count-list) * 100) set forecast round (forecast) if forecast > count turtles [set forecast count turtles] if forecast < 0 [set forecast 0]] end to OppositeTrend3 ;A N (up to 20 weeks ago) dated 2 day relative trend applied to the last attendence ifelse (length count-list < (item step individual-strategy-list) + 2 - 160) [set forecast (random count turtles)] [set forecast (last count-list - (((item ((length count-list) - (item step individual-strategy-list) - 1 + 160) count-list) - (item ((length count-list) - (item step individual-strategy-list) - 2 + 160) count-list)) / last count-list) * 100) set forecast round (forecast) if forecast > count turtles [set forecast count turtles] if forecast < 0 [set forecast 0]] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;; Plotting ;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to do-plot locals [Gone Averag min-score max-score avg-score ] set Gone count turtles with [Choice = 1] set-current-plot "People going to El Farol" set-plot-y-range 0 count turtles set-current-plot-pen "Present" set-plot-y-range 0 count turtles plot (Gone) set Averag mean count-list set-current-plot-pen "Mean" plot (Averag) set-current-plot "Attendance-Histogram" set-plot-pen-mode 1 set-plot-x-range 0 count turtles auto-plot-on histogram-list count-list set min-score min values-from turtles [agent-score] set max-score max values-from turtles [agent-score] set avg-score mean values-from turtles [agent-score] set-current-plot "Agent's scores" set-current-plot-pen "min-score" plot (min-score / (length count-list)) set-current-plot-pen "max-score" plot (max-score / (length count-list)) set-current-plot-pen "avg-score" plot (avg-score / (length count-list)) end @#$#@#$#@ GRAPHICS-WINDOW 209 10 414 206 6 5 15.0 1 10 1 1 1 0 CC-WINDOW 2 606 749 722 Command Center SLIDER 7 128 203 161 Strategies-per-agent Strategies-per-agent 3 12 6 1 1 NIL BUTTON 140 10 202 43 Go Go T 1 T OBSERVER T NIL PLOT 419 10 719 186 People going to El Farol Week Attendence 0.0 100.0 0.0 100.0 true false PENS "Present" 1.0 0 -16776961 true "Mean" 1.0 0 -65281 true MONITOR 8 262 64 311 Present count turtles with [choice = 1] 0 1 MONITOR 65 262 120 311 Mean mean count-list 0 1 MONITOR 8 211 176 260 History (list item ((length count-list) - 8) count-list\n item ((length count-list) - 7) count-list\n item ((length count-list) - 6) count-list\n item ((length count-list) - 5) count-list\n item ((length count-list) - 4) count-list\n item ((length count-list) - 3) count-list\n item ((length count-list) - 2) count-list\n item ((length count-list) - 1) count-list) 3 1 MONITOR 121 262 176 311 St Dev standard-deviation count-list 2 1 BUTTON 6 10 68 43 NIL Setup NIL 1 T OBSERVER T NIL SLIDER 7 93 203 126 Strategy-Space Strategy-Space 6 200 200 1 1 NIL BUTTON 71 10 136 43 Go Once Go NIL 1 T OBSERVER T NIL SLIDER 110 163 203 196 Lambda Lambda 0 0.9 0.5 0.1 1 NIL MONITOR 65 314 120 363 <= 60% 100 - mean count-list-go 0 1 SLIDER 7 59 203 92 Number-of-Agents Number-of-Agents 0 143 100 1 1 NIL PLOT 419 188 719 364 Agent's scores Week Scores 0.0 100.0 0.45 0.55 true false PENS "min-score" 1.0 0 -16776961 true "avg-score" 1.0 0 -11352576 true "max-score" 1.0 0 -65536 true PLOT 210 210 413 363 Attendance-Histogram Present Turtles 0.0 100.0 0.0 100.0 true false SLIDER 7 163 99 196 Memory Memory 5 20 20 1 1 NIL MONITOR 8 314 63 363 > 60% 100 - mean count-list-go 0 1 @#$#@#$#@ WHAT IS IT? ----------- El Farol is a bar in Santa Fe, New Mexico, at which a band plays Irish music on Thursday evenings. The bar is enjoyable only if it is not too crowded (say more than 60% of the agents). Trying to decide whether or not to go to El Farol on Thursday nights is what Arthur's, 1994, "El Farol bar problem" is about. Each agent (out of "Number-of-Agents") has to decide whether they should go or not by making an independent decision. In other words, each agent enjoys going to El Farol to listen to the music, but not if the bar is going to be too crowded. In order to optimise ones utility, each agent has to try and predict what everybody else will do. However, the problem is set up so that any model of the problem that is shared by most of the agents is what Schelling refers to as a self-negating prophecy: "If all believe few will go, all will go and vice versa". HOW IT WORKS ------------ Arthur modelled this situation by randomly giving each agent "Strategies-per-agent" potentially suitable predictors, given past data (e.g. the past "D" weeks attendance figures, called "Memory"). For example, the number of people turning up over the past 10 weeks might be: 15, 67, 84, 34, 45, 76, 40, 56, 23 and 35. Each person then independently employs a prediction procedure to estimate how many people will appear at the bar in the coming week. Typical predictors might be for example: -the same number as last week (35), -a mirror image around 50% of last week's attendance, -a (rounded) average of attendances over the past four weeks (39). -the same as 2 weeks ago (2-period cycle predictor), -etc. ... Each week each agent evaluates these models against the past data and chooses the one that was the best predictor on this data and then uses this to predict the number who will go this time (the active predictor). It will go if this prediction is less than 60% and not if it is more than 60%. Because agents have "Strategies-per-agent" different suitable predictors in their sets, some will turn up at the bar, while others will not. A new attendance figure is available and everyone updates the accuracies of all their predictors. HOW TO USE IT ------------- 1 - The Sliders --------------- The "Number-of-Agents" slider is straight-forward. It determines the number of agents in the game (set at 100 in the standard game). The "Strategy-Space" slider will determine the size "S" of possible strategies (S = 6 to 200, set at 200). The "Strategies-per-agent" slider will distribute randomly the strategy soups (3, 4, ..., or 12 out of S pre-designed ones, set at 6) to each agent. The "Memory" slider will determine the length of the past data the agents use (5 to 20, set at 20). The "Lambda" slider is used to compute the performance of each strategy. A low "Lambda" uses gives more importance to current performance while a high "Lambda" uses the past. (0 to 0.9). 2 - Buttons ----------- Two buttons, "SETUP" and "GO", control execution of the model. The "SETUP" button resets the system, preparing the model to be run. The number of strategies per agent is determined by the slider. The "GO" button, a forever button, will then run the model. The "GO ONCE" button is the same as GO except the agents only take one step. 3 - Plot -------- People Going to El Farol - The total attendance at the bar and the average vs. time. Agent's scores - The best, worst and average score vs. time. Attendance-Histogram - Histogram of the attendance at the bar. **The agents have a binary choice, to go or to stay, respectively coloured in pink and white. STRATEGIES ---------- The strategies used in this simulation are the following. TitForTat: This family of strategies predicts next week's attendance by using the same as N weeks ago, with N from 0 to "Memory" (20 possibilities). It could be for example N = 0 for last weeks attendance or N = 4 for 5 weeks ago's one. Mirror: This is a family of strategies using a mirror image around 50% of N (up to 20) weeks ago as prediction. Fixed: The "Fixed" strategy always chooses the same attendance (5%, 10%, 15%, 20%, 25% ... or 100%). Trend: A N (up to 20) dated 2 day trend applied to the last attendance. OppositeTrend: A N (up to 20) dated 2 day opposite trend applied to the last attendance. Trend2: A N (up to 20) dated 2 day (3 day spaced) trend applied to the last attendance. MovingAverage: A N (up to 20) 5 day Moving average. OppositeMovingAverage: A N (up to 20) opposite 5 day Moving average. Trend3: A N (up to 20) dated 2 day relative trend applied to the last attendance. OppositeTrend3: A N (up to 20) dated 2 day relative trend applied to the last attendance. THINGS TO NOTICE ---------------- In the case of absence of collusion or prior communication between agents, this model, of limited resources, shows how unstable behaviour is yielded in this repeated game, and two interesting patterns are revealed. First, the number of people who attend the bar fluctuates around an average level of 60%, with on average 60% predicting not to go and 40% to go, which constitutes the Nash Equilibria, which is selected through the computer simulations. It is learning that allows the bounded-rational agents to select this equilibrium strategy. Second, the dynamics seem random, despite that no random component determines the dynamics of how many people go. In fact, although at a microscopic level each agent is applying a different predictor at any one time, with varying degrees of success, when viewed globally, they seem pretty indistinguishable. The only random part of Arthur's model is the setting-up. Therefore once the game is set the output is completely deterministic since the rule update is stable. CREDITS AND REFERENCES ---------------------- This model was based upon Brian Arthur's article: Arthur, Brian, (1994), "Inductive Reasoning and Bounded Rationality: The El Farol Bar Problem", American Economic Review, 84(2), pp.406-411. Information can be found on the web at: http://www.santafe.edu/arthur/Papers/El_Farol.html AUTHOR ------ The Author, Mark Garofalo, may be contacted by Email at: mark_garofalo@hotmail.com http://www.markgarofalo.com/ January 2004. @#$#@#$#@ default true 0 Polygon -7566196 true true 150 5 40 250 150 205 260 250 ant true 0 Polygon -7566196 true true 136 61 129 46 144 30 119 45 124 60 114 82 97 37 132 10 93 36 111 84 127 105 172 105 189 84 208 35 171 11 202 35 204 37 186 82 177 60 180 44 159 32 170 44 165 60 Polygon -7566196 true true 150 95 135 103 139 117 125 149 137 180 135 196 150 204 166 195 161 180 174 150 158 116 164 102 Polygon -7566196 true true 149 186 128 197 114 232 134 270 149 282 166 270 185 232 171 195 149 186 Polygon -7566196 true true 225 66 230 107 159 122 161 127 234 111 236 106 Polygon -7566196 true true 78 58 99 116 139 123 137 128 95 119 Polygon -7566196 true true 48 103 90 147 129 147 130 151 86 151 Polygon -7566196 true true 65 224 92 171 134 160 135 164 95 175 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