A War of Attrition with Experimenting Players*

Since the end of the war itself, research on the German economy during the Second World War has focused – explicitly or implicitly – on the search for an explanation of the disparities in armaments and output between the first and second halves of the war. In the first half of the war, up until the winter of 1941–2, the development of armaments production was characterised by more or less stable levels of output against the background of the series of swift and successful military campaigns in Poland and in the West. This stands in stark contrast to the second half, which witnessed a radical increase in aggregate armaments output which lasted well into the summer of 1944, and which saw tank production reach 589 per cent of the level at which it had stood in January 1942, weapons production reach 382 per cent of its January 1942 level, and aircraft production 367 per cent of its January 1942 level over the same period, to name some of the most obvious successes. These increases were all the more astonishing for the fact that they were achieved against the background of a massive war of attrition on the Eastern Front which placed demands on German resources and drew male labour from German factories into the Wehrmacht on a scale out of all proportion to that experienced in the first half of the war.

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A dynamic programming approach to evolutionarily stable strategy theory

Advances in Applied Probability ◽

10.2307/1426480 ◽

1980 ◽

Vol 12 (1) ◽

pp. 3-5 ◽

Cited By ~ 2

Author(s):

C. Cannings ◽

D. Gardiner

Keyword(s):

Dynamic Programming ◽

Density Function ◽

Evolutionarily Stable Strategy ◽

Programming Approach ◽

Stable Strategy ◽

War Of Attrition ◽

Dynamic Programming Approach ◽

The Individual ◽

Image Position ◽

Evolutionarily Stable

In the war of attrition (wa), introduced by Maynard Smith (1974), two contestants play values from [0, ∞), the individual playing the longer value winning a fixed prize V, and both incurring a loss equal to the lesser of the two values. Thus the payoff, E(x, y) to an animal playing x against one playing y, is A more general form (Bishop and Cannings (1978)) has and it was demonstrated that with and there exists a unique evolutionarily stable strategy (ess), which is to choose a random value from a specified density function on [0, ∞). Results were also obtained for strategy spaces [0, s] and [0, s).

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