I understand your analysis using game theory, but I think it comes down to a much simpler calculus. Hamas is like any "gang".

In order to maintain control over its territory, it must suppress opposition/competition within its territory through intimidation and murder and justify its existence (in this instance, by attacking Jews.

Don't confuse Hamas with freedom fighters do so assuming that Hamas intends to win. It does not. Nor can it. And if by accident it did win, it would have no choice but to start another war.

No doubt, that other organizations "benefit" from gang activity. Including those who derive their funding and support combatting the violence that these "global" gangs must inflict to preserve their right to exist.

Palestinians and Israelis both have justifiable claims over the land of Israel. And those claims may in fact be irreconcilable at this time. But Hamas existence while dependent on this conflict is not about restoring the claims of Palestinians who feel wronged... it is about power and wealth and if pretending to embrace the grievances of Palestinians offers them an opportunity to gain power and wealth, then they will pretend to embrace them.

But have no doubt, that if within the Palestinians a new group emerges intent on representing the Palestinians, Hamas will attack them with equal intensity. Since as i said, Hamas is about wealth and power and not about winning.