Trying to reproduce Yuji Ijiri's 1964 paper about business firm growth and size

industry.cpp

#include <iostream>
#include <fstream>
#include <cstdlib>
#include <algorithm>
#include <vector>

static const int SESSIONS = 10000;
static const double ALPHA = 0.25;
static const double BETA = 0.95;



void seed() {
	int seed;
	std::cout << "Enter seed number : ";
	std::cin >> seed;
	srand(seed);
}

double sample() {
	return (double)rand() / RAND_MAX;
}


struct Firm {
	int size;
	double weight;

	Firm(int size, double weight) : size(size), weight(weight) {}
};

struct Industry {
	std::vector<Firm> firms;
	int total_size = 0;
	double total_weight = 0;

	void add(Firm firm) {
		firms.push_back(firm);

		total_weight += firm.weight;
		total_size += firm.size;
	}

	void step() {
		// calculates values at step t based on the values at step t-1

		// initial state:
		//  firm.size - size of each firm at t - 1: x(t-1)
		//  firm.weight - weights to select the firm to grow at this step: sum(tau = 1...t-1, x(tau) * beta ^ tau)

		// result:
		//  firm.size - size of each firm at t: x(t)
		//  firm.weight - weights to select the firm to grow at the next step: sum(tau = 1...t, x(tau) * beta ^ tau)

		// stage 1
		if (sample() < ALPHA) {
			firms.push_back(Firm(1, 1));
			total_size++;
		} else {
			// stage 2
			double r = sample();
			double sum = 0;

			auto growing = firms.begin();

			for (auto firm = firms.begin(); firm != firms.end(); firm++) {
				sum += firm->weight;

				if (sum > r * total_weight) {
					// this way growing will point to the firm with the largest index which satisfies the condition
					break;
				}

				growing = firm;
			}

			// the firm size grows by 1
			growing->size++;
			total_size++;

			// the weight gets incremented by 1, and then decays 
			growing->weight += 1.0;
		}

		// decaying
		double sum = 0;
		for (Firm &firm : firms) {
			firm.weight *= BETA;
			sum += firm.weight;
		}
		total_weight = sum;
	}

	void sort() {
		// sort so that firms with larger size comes first
		std::sort(firms.begin(), firms.end(), [](Firm a, Firm b) { return a.size > b.size; });
	}

	void print(std::string file) {
		std::ofstream output(file);
		if (!output) {
			std::cerr << "Could not open output file!" << std::endl;
			return;
		}

		output << "Rank" << "," << "Firm Size" << "," << "Number of Firms" << "," << "Weight" << "," << "Cumulative Weight" << "," << "Cumulative Percent of Total Assets" << std::endl;

		int sum_size = 0;
		double sum_weight = 0;
		int rank = 0;

		for (auto firm = firms.begin(); firm != firms.end();) {
			int count = 1;
			double weight = firm->weight;
			int size = firm->size;

			while (true) {
				firm++;

				if (firm == firms.end() || firm->size != size) break;

				count++;
				weight += firm->weight;
			}

			rank += count;
			sum_size += count * size;
			sum_weight += weight;

			output << rank << "," << size << "," << count << "," << weight / total_weight << "," << sum_weight / total_weight << "," << (double)sum_size / total_size << std::endl;
		}

		std::cout << "Output Complete!" << std::endl;
	}
};


int main(int argc, char **argv) {
	seed();

	Industry industry;
	industry.add(Firm(5, 1.0));
	industry.add(Firm(3, 1.0));
	industry.add(Firm(1, 1.0));

	for (int i = 0; i < SESSIONS; i++) {
		industry.step();
	}

	industry.sort();
	industry.print("output.csv");

	return 0;
}