sim_doctors <- function(num.doctors,num.meetings,starting_adopters, prob) {
  # vector to keep track of which doctors have adopted
  has_adopted <- rep(FALSE, num.doctors)
  # Set some to have adopted initially
  has_adopted[1:round(starting_adopters*num.doctors)] <- TRUE
  # matrix to keep track of adoptions over time
  adoptions_vs_time <- matrix(FALSE,nrow=num.doctors,ncol=num.meetings)
  for (meeting in 1:num.meetings) {
    # select 2 doctors at random
    meeting_pair <- sample(1:num.doctors,size=2,replace=FALSE)
    # check whether exactly one selected doctor has adopted
    if(has_adopted[meeting_pair[1]] != has_adopted[meeting_pair[2]]) {
      # With probability prob., update the vector of adopters
      if(rbinom(n=1,size=1,prob=prob)) { has_adopted[meeting_pair] <- TRUE }
    }
    # update adoptions_vs_time matrix
    adoptions_vs_time[,meeting] <- has_adopted    
  }
  return(adoptions_vs_time)
}

sim1 <- sim_doctors(num.doctors=10,num.meetings=10,starting_adopters=0.1,prob=1.0)