In what ways does the history of Israel influence the identity of the people today?
The above answer ignores the history which the people of Israel fervently believe, and that is that the land which they occupy was promised to their ancestor Abraham and was given to them as the "promised land."
In the Bible, in Genesis 12:1 Abraham is told to move into the land which would be his people's inheritance:
The Lord had said to Abram, “Leave your country, your people and your father’s household and go to the land I will show you. I will make you into a great nation and I will bless you; I will make your name great, and you will be a blessing. I will bless those who bless you, and whoever curses you I will curse; and all peoples on earth will be blessed through you.
In fact, the name Israel was the name given to Jacob, Abraham's grandson after an encounter with an angel. This is told in Genesis 35:10
God appeared to him again and blessed him. God said to him, “Your name is Jacob, but you will no longer be called Jacob; your name will be Israel." So he named him Israel
The early ancestors of today's Israeli people referred to themselves as the "children of Israel." According to tradition, the people lived in the land for some time, but because of great famine moved to Egypt where they lived and multiplied for over four hundred years. They were ultimately led away from slavery and Egypt by Moses, their great prophet who returned them to the land God had promised them. God restated his promise to Moses, even though Moses was not allowed to enter the land. The story is told in Deuteronomy 34:4
Then the Lord said to him, “This is the land I promised on oath to Abraham, Isaac and Jacob when I said, ‘I will give it to your descendants.’ I have let you see it with your eyes, but you will not cross over into it.
The people of Israel ultimately lost the land several times, once to the Babylonians and later to the Romans which led to the great Diaspora. However, with the re-creation of the state of Israel in 1948. Jews the world over saw this as simply the restoration of the promise which had been made to Abraham thousands of years before. Hedonistic hardly seems to be the appropriate adjective to describe the people; yet they are certainly tough minded because in their heart of hearts, they are defending the land which God promised to them.
First of all, please note that there can be no objective answer to this sort of question because we cannot prove exactly what the nature of a people's identity is or where it came from.
That said, it seems likely that Israel's history as a refuge from anti-Semitism and as a country with hostile neighbors has affected the identity of its people. Israel's whole history has been one in which it has seemed like a haven in the midst of danger. This is likely to have helped contribute to the mix of hedonism and toughness that has been said to characterize Israelis. They are tough because they are in danger and hedonistic (at least in the past) because of the feeling that life could be short.
This may be changing, though. Israel is coming to be dominated more and more by very religious Jews whose identity is tied more to the Bible and who certainly do not share the hedonistic attitudes mentioned above.