War, Wealth and the Formation of States

Abstract

Employing agent-based modelling techniques, the authors examine the evolution of a world with sovereign states that maximize power. They show that: (1) the size (number) of states increases (decreases) as war technologies become capital-intensive; (2) the number of states declines with development and population expansion; (3) capital-rich (capital-poor) economies lead to smaller (larger) economies (mainly because war is less frequent if capital is mobile); (4) world government may become possible in the future (given the evolution of military technology) yet only with a very low probability (given the distribution of economic activities throughout the globe); (5) the possibility of secession leads to a permanent increase in the number of countries if all effects when the countries involved in the split are democratic. These stylized findings fit well the historical evolution of Europe and most of the territorial dynamics of state formation over time, at least until the nineteenth century. The last point accommodates the explosion of the number of countries we have witnessed in the twentieth century.

Appendix

In the model, the parameters (that can be specified individually for each country) are: initial population density; rate of population increase; tax rate (from 0 to 1); a parameter indicating which percentage of error one country can incur when evaluating if it is convenient to attack another country; technology; and mobility (measuring how much of one country’s belongings are transferred to another country in case the first one is attacked and defeated).

1.1 Initial Moment

At the beginning of the simulation population is assigned to each region according to the density parameter. If the region is “hills” the density is decreased by 25% and if it is “mountains” it is decreased by 75%.

Given a certain initial density and the type of territory (plain, hill, mountain), the initial population is calculated as:

Population_t = (density * number of plain cells) + (density * number of hilly cells * 0.75) + (density * number of mountainous cells * 0.25).

[In turn, savings of each state are calculated as:

Savings_t = (population * technology * taxation).]

1.2 Evolution of Parameters

Parameters evolve at each step according to following structure.

Population

The population of each unit region is incremented by a factor (1 + PopInc/1,000).

Population_t+1 = Population_t * (1 + (Population increase/1,000) − in peace times. (Population increase is set by the simulator).

Military costs

Military costs are of two types: fixed costs K and variable costs M * D^S, where D is the distance of the cell from the capital of the country.

The parameters K, M, and S may depend on the current time step of the simulation. (See above for how to set them.)

Military costs can be manipulated to be of two types:

• 1. MC or Own Territory’s Military Costs = K + m * D^S;

  where K is a fixed cost, m is a multiplier, D is the distance from the region to the capital. S approximates a function that modifies the cost of distance. The total military cost is computed by adding the military costs for each of its regions m * D^S.

• 2. MCplus or Military Costs of Controlling Other Territories: m * D^S * z;

  where z is a parameter (equal to or larger than 1) denoting how much harder it is to conquer and control the territory of other countries.

Income

Income_t+1 = Population_t * Technology * Taxation [Taxation ≤ Mobility Parameter).

[The parameters Tech and Taxes can remain as they were originally set in the country even after it has been conquered. Or they can change to take the values of the conquering country.]

Net revenues

Net Revenues_t+1 = Income_t+1 − MC_t+1

Savings

Savings_t+1 = Savings_t + Net Revenues_t

1.3 Simulation: War

Decision to attack

A country evaluates the possibility to attack a neighbor randomly, about every ten steps, unless there are already two ongoing attacks.

In this environment, any country A decides to attack D if the following conditions take place:

The attack lasts a random number of steps (between 10 and 30 steps).

Duration of war

An attack lasts a random number of steps (between 10 and 30).

Formula to evaluate strength or relative power ratio of countries

Relative power ratio (PR) = (S_A − S_D) * random perturbation/S_A

Consequences of war

Both countries involved suffer a loss of 10% of population and accumulated wealth

If PR ≤ 1.05, war ends in a tie with no winner. (The attacker does not conquer anything. The defender does not gain any territory.)

If 1.20 ≤ PR < 1.05, partial conquest of D by A (unless the annexed territory of D includes its capital, in which case there is total annexation).

If PR > 1.20 or if the partial annexation involves the loser’s capital, the winner absorbs completely the loser’s country.

Depending on the mobility parameter, a fraction of the loser’s accumulated wealth is transferred to the winner or it is lost.

If the attacking country has mistakenly evaluated the strength of its victim, the roles are reversed.

Depending on whether the parameters are “country-based” or not, the conquered regions either acquire the winner’s default parameters or maintain their current values.

1.4 Rules of Secession

Seminal secession

1. With some probability p, any cell decides to secede. Probability p is a function of (a) distance to capital and (b) of some parameter z. The distance to capital has a concave effect on probability to secede: it declines as cell is closer to capital and also closer to border of existing country. The parameter z is a time-declining parameter starting at 1 when the cell first belongs to the current country.

2. The seceding cell is the capital of the new country.

3. The political regime of the seceding cell is determined in the following way. If the cell belonged to a different country than the current one and has some ‘memory’ of that past, it will chose the regime in the past country. If it has no such memory (either it did not belong to any other country in the past or the ‘memory’ of belonging has decline to 0), then the seceding cell mirrors the political regime of the country it wants to secede from.

4. The seceding cell defines the potential space of secession as follows: all those (contiguous) cells whose net contribution (income – military costs) is positive.

5. After having identified the potential secession space, the seceding cell (which, again, acts as capital of the potential seceding space) determines whether that space can survive vis-à-vis its neighbors.

(The possibility of survival is calculated by looking both at the military strength and the probability of attack of neighbors. This means that there will be more secessions in areas that are contiguous to peace-prone countries.)

Secession under democracy

6. If both the seceding area and the existing country are democratic, the secession process works according to the following procedure:

• a. If the ‘seceding space’ is of no interest to the existing country, the seceding space becomes a new country automatically. After a given number of rounds, the new country behaves as a ‘normal’ country and all rules (on war decisions etc.) apply to it with no exceptions. ‘No interest’ means that the seceding space does not generate net revenue for the old country (MC are larger than generated taxable income).

• b. If the ‘seceding cells’ are equally valuable (i.e. generate net contributions) for the old country, they are allocated according to the following rule: a (weighted) formula determines under which capital the cell under dispute is better off; the formula takes into account the tax rate they pay and the distance from each capital (the higher the distance the worse the quantity/quality of goods received from the corresponding capital and therefore the higher the incentive to join the closer capital; but this is conditional on the tax effort the cell would make to each side).

Example:

[Note: To set the tax of the new territory, tax t * random error. The tax t is the tax of the existing country if the seceding cell has always belonged to that country. Or the tax of the old country to which it belonged in the past.]

Secession under authoritarian regime

7. If any of the two countries is authoritarian, the secession process works according to the following procedure:

• a. If there are no common valuable cells, the old country lets the country secede (since the seceding space is just generating net losses).

• b. If there valuable cells to both parties, settlement comes through war.

At the end of the war is determined by looking at the military power of the old and the new countries:

MPOC (Military Power Old Country) = Income of all cells with positive contribution − MC of defending them.

MPNC (Military Power New Country) = Income of all cells with positive contribution − MC of defending them.

If MPOC > MPNC, the secession fails. Otherwise, the new countries becomes independent and obtains up to ½ of all the cells that are valuable to both countries. (Upper bound of ½ is arbitrary).

1.5 Alliances

• 1. Alliances can only be defensive.

• 2. Alliances are only organized against potential aggressors.

• 3. At some random intervals, some countries estimate the strength of their neighbors. (This can occur at the same time those countries scan potential victims.)

• 4. If the scanning country W finds a stronger neighbor PA – with a strength defined over a given threshold (that the neighbor is two times stronger than the scanning unit or S_PA > 2 * S_W), the scanning country:

  • a. Lists the neighbors of PA (for ‘potential aggressor’), ranking them by strength.

  • b. Offers an alliance to them – following the order of the list – up to the point where their accumulated strength surpasses the strength of PA.

• 5. The countries R that receive an alliance offer join it provided they meet the following conditions:

  • i. If W and R are neighbors:

    • a. Their relationship to PA in terms of strength is identical, that is, S_PA > 2 * S_W and S_PA > 2 * S_R.

    • b. W and R strengths are such that S_c > 1.2 * S_W. Otherwise W may prefer to avoid the alliance and have the opportunity to fight and conquer W.

  • ii. If W and R are not neighbors:

    • a. Their relationship to PA in terms of strength is identical, that is, S_PA > 2 * S_W and S_PA > 2 * S_R. (former condition b does not apply here.)

• 6. Countries that are allies do not fight with each other.

• 7. Alliances remain in place for a fixed number of steps (25 as the default) unless the conditions in #5 above change.

• 8. Alliances are public knowledge.

• 9. Alliance only work to defend allied countries against the PA (potential aggressor) that has triggered the alliance to start with.

• 10. When looking at any country in an alliance against PA, PA assesses the strength of the alliance:

  • i. As the sum of the strengths of the countries in the alliance.

  • ii. Discounted by a factor that depends on the number of allies: 0.95 for a 2-state alliance, 0.9 for a three-state alliance, 0.85 for a four-state alliance, and 0.8 if there are 5 or more countries.

• 11. The losses or gains of allies are distributed according to a proportionality rule – that is, according to their contribution to total strength.