Attrition warfare

Attrition warfare is a military strategy in which a belligerent attempts to win a war by wearing down the enemy to the point of collapse through continuous losses in personnel and material. The war will usually be won by the side with greater such resources. The word attrition comes from the Latin root atterere to rub against, similar to the "grinding down" of the opponent's forces in attrition warfare.

Strategic considerations

Military theorists and strategists like Sun Tzu have viewed attrition warfare as something to be avoided. In the sense that attrition warfare represents an attempt to grind down an opponent through superior numbers, it represents the opposite of the usual principles of war in which one attempts to achieve decisive victories by using minimal necessary resources and in minimal amount of time, through maneuver, concentration of force, surprise, and the like.

On the other hand, a side that perceives itself to be at a marked disadvantage in maneuver warfare or unit tactics may deliberately seek out attrition warfare to neutralize its opponent's advantages. If the sides are nearly evenly matched, the outcome of a war of attrition is likely to be a Pyrrhic victory.

War of attrition (game)

In game theory, the war of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while constantly accumulating costs over the time t that the contest lasts. The model was originally formulated by John Maynard Smith; a mixed evolutionarily stable strategy (ESS) was determined by Bishop & Cannings. Strategically, the game is an auction, in which the prize goes to the player with the highest bid and each player pays the loser's low bid (making it an all-pay sealed-bid second-price auction). In Combat sports, an all-out brawl between the two competitors is often called a War of Attrition.

Examining the game

The war of attrition cannot be properly solved using the payoff matrix. The players' available resources are the only limit to the maximum value of bids; bids can be any number if available resources are ignored, meaning that for any value of α, there is a value β that is greater. Attempting to put all possible bids onto the matrix, however, will result in an ∞×∞ matrix. One can, however, use a pseudo-matrix form of war of attrition to understand the basic workings of the game, and analyze some of the problems in representing the game in this manner.

War of Attrition

The War of Attrition (Arabic: حرب الاستنزاف‎ Ḥarb al-Istinzāf, Hebrew: מלחמת ההתשה‎ Milhemet haHatashah) involved fighting between Israel and Egypt, Jordan, PLO and their allies from 1967 to 1970.

Following the 1967 Six-Day War, no serious diplomatic efforts tried to resolve the issues at the heart of the Arab–Israeli conflict. In September 1967, the Arab states formulated the "three nos" policy, barring peace, recognition or negotiations with Israel. Egyptian President Gamal Abdel Nasser believed that only military initiative would compel Israel or the international community to facilitate a full Israeli withdrawal from Sinai, and hostilities soon resumed along the Suez Canal.

These initially took the form of limited artillery duels and small-scale incursions into Sinai, but by 1969 the Egyptian Army judged itself prepared for larger-scale operations. On March 8, 1969, Nasser proclaimed the official launch of the War of Attrition, characterized by large-scale shelling along the Suez Canal, extensive aerial warfare and commando raids. Hostilities continued until August 1970 and ended with a ceasefire, the frontiers remaining the same as when the war began, with no real commitment to serious peace negotiations.