Heterogeneous Network Games

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;;; Global variables ;;;
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globals
[
  tie_counter         ;; when adding random ties, this varibale monitors the number of random ties already added
  random_agent_1      ;; used when one or more agents are randomly selected
  random_agent_2      ;; used when one or more agents are randomly selected
  links_in_network    ;; sets the number of links in the network
  iteration           ;; sets the number of iterations to a maximum (in case of falling into a cycle).
  nash_network        ;; used when the action profile of all agents is and equilibrium best response
]

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;;; Types of agents ;;;
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breed [bops bop]      ;; bop agents prefer A=0
breed [bips bip]      ;; bip agents prefer A=1

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;;; Turtle variables ;;;
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turtles-own
[
  action                  ;; agent's choice (1 or 0)
  threshold_high          ;; agent's threshold to choose their disliked_action, as a function of their number of connections
  threshold_low           ;; agent's threshold to choose their liked_action, as a function of their number of connections
  alpha                   ;; payoff earned for coordinating in the liked_action
  beta                    ;; payoff earned for coordinating in the disliked_action 
  tie_check               ;; auxiliary variable that is needed to check whether two agents maintain a link
  set_ties                ;; indicates the set of links an agent maintains
  total_ties              ;; indicates the cardinality of the set of links an agent maintains: agent's degree
  set_A1                  ;; set of agents who choose A=1
  set_A0                  ;; set of agents who choose A=0 
  A0_neighbors            ;; set of neighbors who choose A=1, for the focal agent
  A1_neighbors            ;; set of neighbors who choose A=1, for the focal agent
  total_A0_neighbors      ;; cardinality of the set of neighbors A_0
  total_A1_neighbors      ;; cardinality of the set of neighbors A_1
  liked_action            ;; this is the choice that gives higher payoffs to the focal agent
  disliked_action         ;; this is the choice that gives lower payoffs to the focal agent
  prob_like_first         ;; probability of liking the first choice
  happy                   ;; variable that shows if an agent's choice == liked_choice
  nash                    ;; variable that shows if an agent's choice is stable when fixing the choices of all her neighbors
  set_nash                ;; this is the set of agents that don't want to change their choice
  total_set_nash          ;; this is the cardinality of the nash set
]

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;;; Setting up the world ;;;
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to setup
  clear-all               ;; clears the world   
  reset-ticks             ;; ticks start from 0 after every setup
  setup-link_number       ;; calculates the number of links in the network
  setup-bops              ;; creates the bops
  setup_bips              ;; creates the bips
  make_network            ;; sets the random formation prior to the coordination game
  setup-liked_action      ;; sets the value of the favorite action for each breed
  setup-disliked_action   ;; sets the value of the non-favorite action for each breed
  setup-first_choice      ;; sets the random initial choice agents make
  set iteration 0         ;; sets the iteration counter: relevant for the length of run
  set nash_network 0      ;; sets the nash network variable
  setup_color             ;; sets the initial color of the turtles
end 

to setup-link_number  
  set links_in_network ((proportion-links * ((number_nodes * (number_nodes - 1)) / 2 )) / 100)
end 
;; The initial number of links is given by the input of the proportion-links slider

to setup-bops
  set-default-shape bops "circle"
  create-bops (number_nodes)
  [
  set size 1
  ]
end 
;; All nodes created are initially bops

to setup_bips
  if number_nodes = 0 [stop]   
  if number_bips > number_nodes [stop] 
  set-default-shape bips "triangle"
  loop [                       
  if (number_bips > 0) [      
    ask one-of turtles [ set breed bips]
  ]
  if (count bips = number_bips) [stop] 
  ]
end 
;; if there are no nodes in the network there can be no bips
;; if the number of bips to be created is greater than the number of nodes, all nodes will remain as bops
;; the loop process randomly chooses a node to change her breed from bop to bip
;; the loop process starts only if at least one bip is to be created, as given by the input from the number_bips slider
;; the process stops when the number of bips is the one selected in the setup

to make_network
  repeat links_in_network [ layout-spring turtles links 0.4 6 1]  
  set tie_counter 0            
  while [tie_counter < links_in_network] 
  [
    set random_agent_1 0 
    set random_agent_2 0
    ask turtle random_agent_1 [ask link-neighbors [set tie_check 1]]
    while [(random_agent_1 = random_agent_2) or ([tie_check] of turtle random_agent_2 = 1)] 
    [                                                                                       
      ask turtle random_agent_1 [ask link-neighbors [set tie_check 0]] 
      set random_agent_1 random number_nodes    
      set random_agent_2 random number_nodes
      ask turtle random_agent_1 [ask link-neighbors [set tie_check 1]] 
    ]
    ask turtle random_agent_1 [create-link-with turtle random_agent_2]
    set tie_counter tie_counter + 1  
  ]
  if (links_in_network = 0) [layout-circle (sort turtles) max-pxcor - 2  ] 
  ask turtles [set set_ties link-neighbors]      
  ask turtles [set total_ties count set_ties]
  ask turtles [
    set alpha 3       
    set beta 2      
  ]
end 
;; the spring-out layout arranges the setup given the links, it is ignored if layout-circle is set
;; the tie_counter = 0 sets that initially there are no links in the network
;; the process of link creatiion is repeated as long as there are less than the proportion of links chosen in the setup
;; there are two random agents chosen to create a link between them. The two random agents are initially agent 0
;; if there is a link between two agents the tie_check gives value 1
;; if either both random_agents are the same or are already linked, they are skipped from the formation process
;; for each agent the count of links (link-neighbors) starts in 0 
;; Pairs of agents are randomly selected from the entire population (number_nodes) and if they are not connected an undirected link is formed
;; and the tie_counter of links is updated, by adding a new link into it. 
;; The update will stop when the total number of links counted is the one setup
;;
;; If there are no links to be formed, the layout-circle locates all agents on a circle
;;
;; The set_ties is the set of neighbors for an agent
;; The total_ties is the cardinality of the neighborhood
;; Alpha is set to 3 and beta is set to 2

to setup-liked_action  
  ask turtles [
  ifelse breed = bops
  [set liked_action 0] 
  [set liked_action 1]
  ]
end 
;; this is the parameter for liked actions given an agents breed
;; bops like action 0 and bips like action 1

to setup-disliked_action 
  ask turtles [
  ifelse breed = bops
  [set disliked_action 1]  
  [set disliked_action 0]
  ]
end 
;; this is the parameter for disliked actions given an agents breed
;; bops dislike action 1 and bips dislikeaction 0

to setup-first_choice    
  ask turtles [
    set prob_like_first random 100   
    ifelse prob_like_first < I_like_first_choice 
    [set action liked_action]
    [set action disliked_action]
    ]                        
end 
;; this setups the choice agents start with (prior to "go")
;; First, it sets a random number between 0 and 100 as the probability to like the first choice
;; if the probability set is lower than the probability set as an input in the I_like_first_choice slider, 
;; an the focal agent starts choosing the action she likes. This is repeated for all agents
;; OJO: given the inequality/equality in 0 or 100% there is still a chance for liked/disliked action????

to setup_color
  ask bops [
    ifelse action = liked_action
    [set color pink]  
    [set color cyan]  
  ]
  ask bips [
    ifelse action = liked_action
    [set color cyan]
    [set color pink]
  ]
end 
;; this sets the initial color of the agents given their initial choice
;; action 0 is assigned color pink (independently of who is choosing it)
;; action 1 is assigned color cyan (independently of who is choosing it)


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;;; Here starts GO ;;;
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to go
  if not any? turtles [stop]            ;; if there are no nodes in the network the model stops
  if ticks >= max_iterations [stop]     ;; if the maximum_iterations is reached the model stops
    set_threshold_high                  ;; sets the threshold_high for every agent
    set_threshold_low                   ;; sets the threshold_low for every agent
    set_A1_choice                       ;; makes a set of turtles choosing action 1
    set_A0_choice                       ;; makes a set of turtles choosing action 0
    set_happy                           ;; makes a set of turtles choosing the action they like
    set_A0_neighbors                    ;; makes a set of neighbors choosing action 0, for the focal agent
    set_A1_neighbors                    ;; makes a set of neighbors choosing action 1, for the focal agent
    check_nash                          ;; sets if an agent's choice is stable (nash)
    set_nash_set                        ;; makes a set of agents whose choice is nash
    report_nash                         ;; displays a label 1 if an agent is nash, and 0 otherwise
    check_nash_network                  ;; checks wether all agents are in the nash set (1) or not (0)
  if nash_network = 1 [stop]            ;; if all agents are in the nash set the model stops
    choose_action                       ;; agents that are not in nash change their action
    set_color                           ;; the color is set of all agents given their choice
  tick                                  ;; a new tick (period of time) runs
end 

to set_threshold_high
  ask turtles [
    ifelse links_in_network = 0
    [set threshold_high 0 ]
    [ifelse total_ties = 0
      [set threshold_high 0]
    [set threshold_high (((total_ties * alpha) + alpha - beta ) / (alpha + beta ))]
    ]
  ]
end 
;; The threshold_high is a function of an agents connections. It determines the tipping point to choose the disliked action.

to set_threshold_low
  ask turtles [
    ifelse links_in_network = 0
    [set threshold_low 0 ]
    [ifelse total_ties = 0
      [set threshold_low 0]
    [set threshold_low (((total_ties * beta) - alpha + beta ) / (alpha + beta ))]
    ]
  ]
end 
;; The threshold_low is a function of an agents connections. It determines the tipping point to choose the liked action.

to set_A1_choice
  ask bops [
    ifelse action = liked_action
    [set set_A1 0]
    [set set_A1 1]
  ]
  ask bips [
  ifelse action = liked_action
  [set set_A1 1]
  [set set_A1 0]
]
end 
;; The set_A1 is composed by all agents choosing action 1. It is defined given the agents' breed and liked/disliked actions

to set_A0_choice
  ask bops [
    ifelse action = liked_action
    [set set_A0 1]
    [set set_A0 0]
  ]
  ask bips [
  ifelse action = liked_action
  [set set_A1 1]
  [set set_A1 0]
]
end 
;; The set_A0 is composed by all agents choosing action 0. It is defined given the agents' breed and liked/disliked actions

to set_happy
  ask turtles [
    ifelse action = liked_action
    [set happy 1]
    [set happy 0]
  ]
end 
;; The happy is composed by all agents choosing the action they like

to set_A0_neighbors
  ask turtles [
    set A0_neighbors link-neighbors with [set_A0 = 1]
    set total_A0_neighbors count A0_neighbors
  ]
end 
;; The set_A0_neighbors is composed by all neighbors of the focal agents choosing action 0. Its cardinality is total_A0_neighbors

to set_A1_neighbors
  ask turtles [
    set A1_neighbors link-neighbors with [set_A1 = 1]
    set total_A1_neighbors count A1_neighbors
  ]
end 
;; The set_A1_neighbors is composed by all neighbors of the focal agents choosing action 1. Its cardinality is total_A1_neighbors

to check_nash
  ask turtles[
  ifelse complements?
  [
  ask bops[
    ifelse action = liked_action  
    [ifelse total_A0_neighbors >= threshold_low
      [set nash 1]
      [set nash 0]
    ]
    [ifelse total_A1_neighbors > threshold_high
      [set nash 1]
      [set nash 0]
    ]
  ]
  ask bips[
    ifelse action = liked_action  
    [ifelse total_A1_neighbors >= threshold_low
      [set nash 1]
      [set nash 0]
    ]
    [ifelse total_A0_neighbors > threshold_high
      [set nash 1]
      [set nash 0]
    ]
  ]
  ]
   [
  ask bops[
    ifelse action = liked_action  
    [ifelse total_A1_neighbors >= threshold_low
      [set nash 1]
      [set nash 0]
    ]
    [ifelse total_A0_neighbors > threshold_high
      [set nash 1]
      [set nash 0]
    ]
  ]
  ask bips[
    ifelse action = liked_action  
    [ifelse total_A0_neighbors >= threshold_low
      [set nash 1]
      [set nash 0]
    ]
    [ifelse total_A1_neighbors > threshold_high
      [set nash 1]
      [set nash 0]
    ]
  ]
  ]
  ]
end 
;; An agent is nash depending on the relation between her neighbors' choices and the thresholds.

to set_nash_set
  ask turtles [ 
    set set_nash turtles with [nash = 1]
    set total_set_nash count set_nash
  ]
end 
;; All agents that are nash are part of the nash set. The cardinality of the set is total_set_nash

to report_nash
  ask turtles[set label nash]
end 
;; This displays a label (1) on top if every agent when nash, and 0 otherwise

to check_nash_network
   ask turtles [
   ifelse total_set_nash = number_nodes
   [set nash_network 1]
   [set nash_network 0]
   ]
end   
;; The nash_network takes value 1 if all agents are part of the nash set. If at least one agent is not nash, it takes value 0 

to choose_action
  ask turtles[
    ifelse action = liked_action
    [ifelse nash = 1
      [set action liked_action]
      [set action disliked_action]
    ]
    [ifelse nash = 1
      [set action disliked_action]
      [set action liked_action]
    ]
  ]
end 
;; Agents that are not in the nash set change their action. Agents in the nash set keep their same choice as in the previous period.

to set_color
  ask bops [
    ifelse action = liked_action
    [set color pink]
    [set color cyan]
  ]
  ask bips [
    ifelse action = liked_action
    [set color cyan]
    [set color pink]
  ]
end 
;; If an agent changed her action her color is updated, otherwise her color is kept the same.

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;;; End of the model ;;;
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