Multicomponent Attrition Game

In Game theory, a Multicomponent Attrition Game is a model of conflict using limited resources with varying properties. It takes the form of an iterated game in which two parties compete using a finite series of resources which each have properties that counter one or more of their opponent's resources, and are countered by one or more of their opponent's resources, similar to the game rock, paper, scissors. This model can be used in many situations, but is often referenced in strategic warfare, logistics, politics, and other situations where losses result in a loss of options and resources on a scale above the tactical scale.

The game is similar to and often confused with the games War of Attrition, Rock, Paper, Scissors, and Colonel Blotto. The distinctive difference is the combination of itereration, the asymetric value of resources against particular opposing resources, and the asymetry of resources between the two players. In a sense, the Multicomponent attrition game is a fusion of the three aformentioned games, combining the "risk or concede" aspect of War of Attrition; the semi-blind chosing of options from Rock, Paper, Scissors, in which the right choice depends on your opponent's choice; and the asymetric combat resources of Colonel Blotto, in which the player with fewer resources can, through strategy or chance, be victorious.

Examining the Game

The game is most easily understood with concrete examples, so the matrix here will use simplified versions of various types of military forces as the resources represented. The resources represented can range, however, from animals to political entities.

The key attributes which the resources must possess for the game to qualify as a Multicomponent Attrition Game are:

No one resource is superior in every situation. A single resource may be stronger against any number of the opponent's resources, but not all.
Resources which are used but not lost are able to be used on subsequent rounds of the game.

The example used here is extremely simplifed for clarity's sake, so as to give simple win/lose scenarios.

**Muticomponent Attrition Game**
	Knights (3)	Footsoldiers (3)
Pikemen (3)	Pikemen Survive Knights Lost	Pikemen Lost Footsoldiers Survive
Bowmen (3)	Bowmen Lost Knights survive	Bowmen Survive Footsoldiers Lost

This example depicts a simplified medival combat scenario. Pikemen are intended to be used against knights on horseback, but pikes are unweildy and thus ineffective against footsoldiers, giving the footsoldier a clear advantage. Against bowmen, relativly slow-moving footsoldiers are easy targets, but the armored and fast mounted knights can easily flank archers. The number in parenthesis will represent the number of this type of soldier remaining. In this scenario, each player has three of each of their two respective types of soldier at the beginning of the game, and as the rounds of the game continue, the numbers will be updated to reflect this.