My source is Steven Pinker's Better Angels of our Nature. A few of the sources he highlights on the subject:
1] War of Attrition game: Maynard Smith, 1982, 1988; see also Dawkins, 1976/1989.
2] Loss aversion: Kahneman & Renshon, 2007; Kahneman & Tversky, 1979, 1984; Tversky & Kahneman, 1981. Sunk costs in nature: Dawkins & Brockmann, 1980.
3] More lethal wars last longer: Richardson, 1960, p. 130; Wilkinson, 1980, pp. 20–30.
4] Weber’s Law for perceived deaths: Richardson, 1960, p. 11.
And a couple of relevant quotes:
> In these simulations, the destructiveness of a war depends mainly on the territorial size of the combatants and their alliances. But in the real world, variations in destructiveness also depend on the resolve of the two parties to keep a war going, with each hoping that the other will collapse first. Some of the bloodiest conflicts in modern history, such as the American Civil War, World War I, the Vietnam War, and the Iran-Iraq War, were wars of attrition, where both sides kept shoveling men and matériel into the maw of the war machine hoping that the other side would exhaust itself first.
...
> I already mentioned some evidence from Richardson’s dataset which suggests that combatants do fight longer when a war is more lethal: small wars show a higher probability of coming to an end with each succeeding year than do large wars. The magnitude numbers in the Correlates of War Dataset also show signs of escalating commitment: wars that are longer in duration are not just costlier in fatalities; they are costlier than one would expect from their durations alone. If we pop back from the statistics of war to the conduct of actual wars, we can see the mechanism at work. Many of the bloodiest wars in history owe their destructiveness to leaders on one or both sides pursuing a blatantly irrational loss-aversion strategy. Hitler fought the last months of World War II with a maniacal fury well past the point when defeat was all but certain, as did Japan. Lyndon Johnson’s repeated escalations of the Vietnam War inspired a protest song that has served as a summary of people’s understanding of that destructive war: “We were waist-deep in the Big Muddy; The big fool said to push on.”