It's seems weird that for example during the crisis of the third century so many in the roman elites tried to become an emperor despite the high odds of being dead next year. I mean one would think that, assuming possible pretenders behave rationally, a lot of emperors dying on the job would greatly decreases the atractivity of a coup. What explains this behavior? Was this something special to roman/byzantine history or do you find this in other cultures as well? And are there any papers about the probability of rulers dying violently as determent to seizing power?
I think your basic assumption that " many in the roman elites tried to become an emperor despite the high odds of being dead next year ." Is based on two fallacies; that there was perfect information about what was happening in relatively fractured roman world on the mid third century and secondly that, teleogically speaking, they knew that they knew that "they would be dead in the next year." It was not like everyone and their dog was being declared imperiator, but rather those that saw the opportunity to gain some degree of power (locally/regionally) , and did so without complete information and a lot of rumor. Compare that to the "revolt" of Cassius against Marcus Aurelius, based on the belief that he had died.