Generic 3x3 evolutionary game

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WHAT IS IT?

This model is a multiplayer version of the iterated prisoner's dilemma. It is intended to explore the strategic implications that emerge when the world consists entirely of prisoner's dilemma like interactions. If you are unfamiliar with the basic concepts of the prisoner's dilemma or the iterated prisoner's dilemma, please refer to the PD BASIC and PD TWO PERSON ITERATED models found in the PRISONER'S DILEMMA suite.

HOW IT WORKS

The PD TWO PERSON ITERATED model demonstrates an interesting concept: When interacting with someone over time in a prisoner's dilemma scenario, it is possible to tune your strategy to do well with theirs. Each possible strategy has unique strengths and weaknesses that appear through the course of the game. For instance, always defect does best of any against the random strategy, but poorly against itself. Tit-for-tat does poorly with the random strategy, but well with itself.

This makes it difficult to determine a single "best" strategy. One such approach to doing this is to create a world with multiple agents playing a variety of strategies in repeated prisoner's dilemma situations. This model does just that. The turtles with different strategies wander around randomly until they find another turtle to play with. (Note that each turtle remembers their last interaction with each other turtle. While some strategies don't make use of this information, other strategies do.)

Payoffs

When two turtles interact, they display their respective payoffs as labels.

Each turtle's payoff for each round will determined as follows:

             | Partner's Action
  Turtle's   |
   Action    |   C       D
 ------------|-----------------
       C     |   3       0
 ------------|-----------------
       D     |   5       1
 ------------|-----------------
  (C = Cooperate, D = Defect)

(Note: This way of determining payoff is the opposite of how it was done in the PD BASIC model. In PD BASIC, you were awarded something bad- jail time. In this model, something good is awarded- money.)

HOW TO USE IT

Buttons

SETUP: Setup the world to begin playing the multi-person iterated prisoner's dilemma. The number of turtles and their strategies are determined by the slider values.

GO: Have the turtles walk around the world and interact.

GO ONCE: Same as GO except the turtles only take one step.

Sliders

N-STRATEGY: Multiple sliders exist with the prefix N- then a strategy name (e.g., n-cooperate). Each of these determines how many turtles will be created that use the STRATEGY. Strategy descriptions are found below:

Strategies

RANDOM - randomly cooperate or defect

COOPERATE - always cooperate

DEFECT - always defect

TIT-FOR-TAT - If an opponent cooperates on this interaction cooperate on the next interaction with them. If an opponent defects on this interaction, defect on the next interaction with them. Initially cooperate.

UNFORGIVING - Cooperate until an opponent defects once, then always defect in each interaction with them.

UNKNOWN - This strategy is included to help you try your own strategies. It currently defaults to Tit-for-Tat.

Plots

AVERAGE-PAYOFF - The average payoff of each strategy in an interaction vs. the number of iterations. This is a good indicator of how well a strategy is doing relative to the maximum possible average of 5 points per interaction.

THINGS TO NOTICE

Set all the number of player for each strategy to be equal in distribution. For which strategy does the average-payoff seem to be highest? Do you think this strategy is always the best to use or will there be situations where other strategy will yield a higher average-payoff?

Set the number of n-cooperate to be high, n-defects to be equivalent to that of n-cooperate, and all other players to be 0. Which strategy will yield the higher average-payoff?

Set the number of n-tit-for-tat to be high, n-defects to be equivalent to that of n-tit-for-tat, and all other playerst to be 0. Which strategy will yield the higher average-payoff? What do you notice about the average-payoff for tit-for-tat players and defect players as the iterations increase? Why do you suppose this change occurs?

Set the number n-tit-for-tat to be equal to the number of n-cooperate. Set all other players to be 0. Which strategy will yield the higher average-payoff? Why do you suppose that one strategy will lead to higher or equal payoff?

THINGS TO TRY

Observe the results of running the model with a variety of populations and population sizes. For example, can you get cooperate's average payoff to be higher than defect's? Can you get Tit-for-Tat's average payoff higher than cooperate's? What do these experiments suggest about an optimal strategy?
Currently the UNKNOWN strategy defaults to TIT-FOR-TAT. Modify the UNKOWN and UNKNOWN-HISTORY-UPDATE procedures to execute a strategy of your own creation. Test it in a variety of populations. Analyze its strengths and weaknesses. Keep trying to improve it.
Relate your observations from this model to real life events. Where might you find yourself in a similar situation? How might the knowledge obtained from the model influence your actions in such a situation? Why?

EXTENDING THE MODEL

Relative payoff table - Create a table which displays the average payoff of each strategy when interacting with each of the other strategies.

Complex strategies using lists of lists - The strategies defined here are relatively simple, some would even say naive. Create a strategy that uses the PARTNER-HISTORY variable to store a list of history information pertaining to past interactions with each turtle.

Evolution - Create a version of this model that rewards successful strategies by allowing them to reproduce and punishes unsuccessful strategies by allowing them to die off.

Noise - Add noise that changes the action perceived from a partner with some probability, causing misperception.

Spatial Relations - Allow turtles to choose not to interact with a partner. Allow turtles to choose to stay with a partner.

Environmental resources - include an environmental (patch) resource and incorporate it into the interactions.

NETLOGO FEATURES

Note the use of the to-report keyword in the calc-score procedure to report a number.

Note the use of lists and turtle ID's to keep a running history of interactions in the partner-history turtle variable.

Note how agentsets that will be used repeatedly are stored when created and reused to increase speed.

RELATED MODELS

PD Basic, PD Two Person Iterated, PD Basic Evolutionary

HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

Wilensky, U. (2002). NetLogo PD N-Person Iterated model. http://ccl.northwestern.edu/netlogo/models/PDN-PersonIterated. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

COPYRIGHT AND LICENSE

CC BY-NC-SA 3.0

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.

Comments and Questions

Ann Randrup

Strategies in 'Generic 3x3 evolutionary game'

Hi, I would like to try this nice simulation, but I can't find the place to choose a strategy. There is no slider (?) Thank you Ann

Posted almost 3 years ago

Click to Run Model

globals [
  ;;number of turtles with each strategy
  num-X
  num-Y
  num-Z
  num-X-rep
  num-Y-rep
  num-Z-rep

  ;;number of interactions by each strategy
  num-random-games
  num-cooperate-games
  num-defect-games
  num-tit-for-tat-games
  num-unforgiving-games
  num-unknown-games

  ;;total score of all turtles playing each strategy
  X-score
  Y-score
  Z-score
]

turtles-own [
  score
  strategy
  partner-strategy
  partnered?        ;;am I partnered?
  partner-X?
  playX?
  partner           ;;WHO of my partner (nobody if not partnered)
]


;;;;;;;;;;;;;;;;;;;;;;
;;;Setup Procedures;;;
;;;;;;;;;;;;;;;;;;;;;;

to setup
  clear-all
  store-initial-turtle-counts ;;record the number of turtles created for each strategy
  setup-turtles ;;setup the turtles and distribute them randomly
  reset-ticks
end 

;;record the number of turtles created for each strategy
;;The number of turtles of each strategy is used when calculating average payoffs.
;;Slider values might change over time, so we need to record their settings.
;;Counting the turtles would also work, but slows the model.

to store-initial-turtle-counts
  set num-X n-X
  set num-Y n-Y
  set num-Z n-Z
end 

;;setup the turtles and distribute them randomly

to setup-turtles
  make-turtles ;;create the appropriate number of turtles playing each strategy
  setup-common-variables ;;sets the variables that all turtles share
end 

;;create the appropriate number of turtles playing each strategy

to make-turtles
  crt num-X [ set strategy "X" set color green - 1 set playX? true]
  crt num-Y [ set strategy "Y" set color red set playX? false]
  crt num-z [ set strategy "Z" set color yellow set playX? false]
end 

;;set the variables that all turtles share

to setup-common-variables
  ask turtles [
    set score 8
    set partnered? false
    set partner nobody
    setxy random-xcor random-ycor
  ]
end 




;;;;;;;;;;;;;;;;;;;;;;;;
;;;Runtime Procedures;;;
;;;;;;;;;;;;;;;;;;;;;;;;

to go
  clear-last-round
  ask turtles [ partner-up ]                        ;;have turtles try to find a partner
  let partnered-turtles turtles with [ partnered? ]
  ask partnered-turtles [ get-payoff ]
  do-scoring
  reproduce-X
  reproduce-Y
  reproduce-Z
  let p1 random-float 100
  if p1 < random-mutationX [reproduce-X1]
  let p2 random-float 100
  if p2 < random-mutationY [reproduce-Y1]
  let p3 random-float 100
  if p3 < random-mutationZ [reproduce-Z1]
  ask turtles [ set score (score - cost-of-living) ]
  ask turtles with [score > rep-score] [set score score - 4]
  ask turtles with [score < death-score] [die]
;;  ask turtles [set label score]
  do-scoring
  if count turtles > rescale-after [rescale]
  tick
end 

to clear-last-round
  let partnered-turtles turtles with [ partnered? ]
  ask partnered-turtles [ release-partners ]
end 

;;release partner and turn around to leave

to release-partners
  set partnered? false
  set partner nobody
  rt 180
  set label ""
end 

;;have turtles try to find a partner
;;Since other turtles that have already executed partner-up may have
;;caused the turtle executing partner-up to be partnered,
;;a check is needed to make sure the calling turtle isn't partnered.

to partner-up ;;turtle procedure
  if (not partnered?) [              ;;make sure still not partnered
    rt (random-float 90 - random-float 90) fd 1     ;;move around randomly
    set partner one-of (turtles-at -1 0) with [ not partnered? ]
    if partner != nobody [              ;;if successful grabbing a partner, partner up
      set partnered? true
;;      set shape "turtle"
      set heading 270                   ;;face partner
      ask partner [
        set partnered? true
        set partner myself
;;        set shape "turtle"
        set heading 90
      ]
    ]
  ]
end 

;;calculate the payoff for this round and
;;display a label with that payoff.

to get-payoff
  set partner-strategy [strategy] of partner
  if partner-strategy = "X" [
    ifelse strategy = "X" [
      set score (score + A)
    ] [
      ifelse strategy = "Y" [
        set score (score + D)
      ] [
        set score (score + G)
      ]
    ]
  ]
  if partner-strategy = "Y" [
    ifelse strategy = "X" [
      set score (score + B)
    ] [
      ifelse strategy = "Y" [
        set score (score + EE)
      ] [
        set score (score + H)
      ]
    ]
  ]
  if partner-strategy = "Z" [
    ifelse strategy = "X" [
      set score (score + C)
    ] [
      ifelse strategy = "Y" [
        set score (score + F)
      ] [
        set score (score + I)
      ]
    ]
  ]
end 

to reproduce-X
  crt num-X-rep [
    set strategy "X"
    set color green - 1
    set score 5
    set partnered? false
    set partner nobody
    set playX? true
    setxy random-xcor random-ycor
  ]
end 

to reproduce-Y
  crt num-Y-rep [
    set strategy "Y"
    set color red
    set score 5
    set partnered? false
    set partner nobody
    set playX? false
    setxy random-xcor random-ycor
  ]
end 

to reproduce-Z
  crt num-Z-rep [
    set strategy "Z"
    set color yellow
    set score 5
    set partnered? false
    set partner nobody
    set playX? false
    setxy random-xcor random-ycor
  ]
end 

to reproduce-X1
  crt random-mutationX [
    set strategy "X"
    set color green - 1
    set score 4
    set partnered? false
    set partner nobody
    set playX? true
    setxy random-xcor random-ycor
  ]
end 

to reproduce-Y1
  crt random-mutationY [
    set strategy "Y"
    set color red
    set score 4
    set partnered? false
    set partner nobody
    set playX? false
    setxy random-xcor random-ycor
  ]
end 

to reproduce-Z1
  crt random-mutationZ [
    set strategy "Z"
    set color yellow
    set score 4
    set partnered? false
    set partner nobody
    set playX? false
    setxy random-xcor random-ycor
  ]
end 

to rescale
  let K count turtles
    if count turtles with [strategy = "Y"] > 2 [
  ask n-of (num-Y - (rescale-after * ((num-Y) / K) )) turtles with [ strategy = "Y" ] [ die ]
  ]
  if count turtles with [strategy = "X"] > 2 [
  ask n-of (num-X - (rescale-after * ((num-X) / K) )) turtles with [ strategy = "X" ] [ die ]
  ]
  if count turtles with [strategy = "Z"] > 2 [
  ask n-of (num-Z - (rescale-after * ((num-Z) / K) )) turtles with [ strategy = "Z" ] [ die ]
  ]
end 

;;;;;;;;;;;;;;;;;;;;;;;;;
;;;Plotting Procedures;;;
;;;;;;;;;;;;;;;;;;;;;;;;;

;;calculate the total scores of each strategy

to do-scoring
  set num-X count turtles with [strategy = "X"]
  set num-Y count turtles with [strategy = "Y"]
  set num-Z count turtles with [strategy = "Z"]
  set X-score  (calc-score "X" num-X)
  set Y-score  (calc-score "Y" num-Y)
  set Z-score  (calc-score "Z" num-Z)
  set num-X-rep count turtles with [(strategy = "X") and (score > rep-score)]
  set num-Y-rep count turtles with [(strategy = "Y") and (score > rep-score)]
  set num-Z-rep count turtles with [(strategy = "Z") and (score > rep-score)]
end 

;; returns the total score for a strategy if any turtles exist that are playing it

to-report calc-score [strategy-type num-with-strategy]
  ifelse num-with-strategy > 0 [
    report (sum [ score ] of (turtles with [ strategy = strategy-type ]))
  ] [
    report 0
  ]
end 


; Copyright 2002 Uri Wilensky.
; See Info tab for full copyright and license.

There is only one version of this model, created over 4 years ago by Adam Galambos.

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Generic 3x3 evolutionary game v1.1

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