NetLogo加权有向图观念扩散模型：动态效用函数设计与p值更新实现求助

Let's break down how to implement the dynamic mechanism you want—where agents' p values update based on incoming influences from red vs. gray agents—while refining your model's core logic.

Key Changes to Implement #

1. Adjust Initial p Values to Continuous Range #

Your original assign-p sets p to either 0 or 1, which is too rigid for dynamic updates. Let's switch to a continuous 0-1 range (since p represents a probability):

to assign-p ;assign probability to agents (0 to 1, continuous)
  ask group [set p random-float 1]
end

2. Add a Dynamic p Update Procedure #

Create a new procedure that calculates each agent's net influence from incoming links, then adjusts their p value. We'll clamp p between 0 and 1 to keep it valid as a probability:

to update-p
  ask group [
    ; Calculate total weight from red sending agents (incoming links where end1 is red)
    let red-influence sum [weight] of influences with [end1 = myself and end1.color = red]
    ; Calculate total weight from gray sending agents
    let gray-influence sum [weight] of influences with [end1 = myself and end1.color = gray]
    ; Update p: add red influence, subtract gray influence
    set p p + red-influence - gray-influence
    ; Clamp p to 0-1 to prevent invalid values
    set p max (list 0 (min (list 1 p)))
  ]
end

Note: We use myself here to target incoming links where the current agent is the recipient (end2 of the link). This aligns with your goal of agents receiving influence from others via directed links.

3. Refine the behavior Procedure #

Your original behavior loop directly sets color based on static p values. Now we'll first update p dynamically, then set color based on the updated p (we use 0.5 as your original trigger, but you can adjust this threshold):

to behavior
  ; First, update all agents' p values based on incoming influences
  update-p
  
  ; Update agent colors based on their new p values
  ask group [
    if p > 0.5 [
      set color red
      ; Optional: Mark outgoing links from red agents to visualize influence flow
      ask my-out-links [set color red]
    ] [
      set color gray
      ask my-out-links [set color gray]
    ]
  ]
  
  tick
end

This ensures color reflects the agent's current state after receiving influence, rather than a static initial p value.

4. Optimize the Utility Function #

Your original static utility function can be modified to run dynamically each tick, reflecting the current state of the network. Here's an updated version that calculates weighted diffusion effectiveness in real-time:

to plot-utility
  let total-red-p sum [p] of group with [color = red]
  let total-p sum [p] of group
  let total-red-weight sum [weight] of influences with [color = red and weight > 0.5]
  let total-weight sum [weight] of influences with [weight > 0.5]
  
  ; Avoid division by zero if there are no valid links or agents
  let utility ifelse-value (total-p = 0 or total-weight = 0) [
    0
  ] [
    (total-red-p * total-red-weight) / (total-p * total-weight)
  ]
  
  plot utility
end

You can call this procedure in your behavior loop (after update-p) to plot the dynamic utility over time.

Full Modified Code #

Here's the complete code with all changes integrated:

extensions [nw] ;network extension
breed [group g] ;turtles are called group
directed-link-breed [influences inf] ;directed link are called influences
links-own [weight] ;weight of directed link, related to links only
group-own [p] ;probability to take or not red idea, related to turtles only

; SETUP
to setup-pa ;generate preferential-attachment network
  ca
  nw:generate-preferential-attachment group influences members 1
  [ set color grey
    setxy random-xcor random-ycor
    set shape "person"
    set size 2]
  assign-weight
  assign-p
  reset-ticks
end

to setup-small-world ;generate small-world network
  ca
  nw:generate-watts-strogatz group influences members 1 1
  [ set color grey
    setxy random-xcor random-ycor
    set shape "person"
    set size 2]
  assign-weight
  assign-p
  reset-ticks
end

to setup-random ;generate random network
  ca
  nw:generate-random group influences members 1
  [ set color grey
    setxy random-xcor random-ycor
    set shape "person"
    set size 2]
  assign-weight
  assign-p
  reset-ticks
end

to assign-weight ;assign random-float weight to links in a range from 0 to 1
  ask influences [set weight random-float 1 ]
end

to assign-p ;assign probability to agents (0 to 1, continuous)
  ask group [set p random-float 1]
end

; EXPERIMENT
to update-p
  ask group [
    let red-influence sum [weight] of influences with [end1 = myself and end1.color = red]
    let gray-influence sum [weight] of influences with [end1 = myself and end1.color = gray]
    set p p + red-influence - gray-influence
    set p max (list 0 (min (list 1 p)))
  ]
end

to behavior
  update-p
  
  ask group [
    if p > 0.5 [
      set color red
      ask my-out-links [set color red]
    ] [
      set color gray
      ask my-out-links [set color gray]
    ]
  ]
  
  ; Uncomment the line below to plot the dynamic utility each tick
  ; plot-utility
  
  tick
end

to plot-utility
  let total-red-p sum [p] of group with [color = red]
  let total-p sum [p] of group
  let total-red-weight sum [weight] of influences with [color = red and weight > 0.5]
  let total-weight sum [weight] of influences with [weight > 0.5]
  
  let utility ifelse-value (total-p = 0 or total-weight = 0) [
    0
  ] [
    (total-red-p * total-red-weight) / (total-p * total-weight)
  ]
  
  plot utility
end

Additional Notes #

• Link Color Visualization: The code marks outgoing links with the agent's color to help you visualize how influence spreads through the directed network. You can remove this if it's not needed.
• Threshold Adjustment: If you want a different threshold for agents turning red, just change the p > 0.5 condition in the behavior procedure.
• Rate of Change: If you want slower or faster updates to p, multiply the influence difference by a scaling factor (e.g., set p p + 0.3 * (red-influence - gray-influence)).

内容的提问来源于stack exchange，提问作者Alice