Combat in EVE Online is conducted on the basis of a cost-benefit analysis. From an alliance war declaration that rocks the political landscape to an obscure border skirmish that is forgotten the next day, the decision to engage is always made according to what each party has to gain or lose. Other player interactions are also based on the same economically rational patterns of thought - buy and sell orders, contracts, scamming, mining operations and wormhole expeditions - but these instances are hardly surprising.
What sets EVE apart from the MMO norm is that when two players, gangs, fleets, corporations, alliances, power blocs, or any other arrangement bring their arms to bear, the order to engage or to mobilize for war is not given based on the answer to a subjective question like "will this be fun?" but is instead framed by an objective question like "what do we stand to gain, and does that outweigh what we stand to lose?" This peculiar, inexorable consideration that is forced upon the capsuleer is is source of the foremost complaint about PvP in EVE - "blobbing" - and the quasi-mythological status of its opposite, the "1v1."
The choice to engage in PvP combat is made according to a cost-benefit analysis because the "death" of the player - the destruction of their ship - is final. Destruction is a possibility that the player must confront and accept every time they undock a ship, whether it be to other players, NPC belt pirates, or an accidental click of the self destruct button. However it happens, once a ship is destroyed, it doesn't come back. The player doesn't rise as a ghostly apparition out of a nearby graveyard, make the trek back to the scene of his death, and slip back inside his pristine, intact ship. When a ship dies, the player doesn't just lose the time and effort he put into getting the ship, but also the time and effort attached to the modules, rigs, cargo, and - if he is unlucky - his pod and its implants.
The numerical measure of a ship's existence is how much it and its accessories cost to obtain, as is the measure of its destruction. Killboards everywhere tirelessly tally and record the ISK forever consigned to space dust; according to BattleClinic, I've helped send over two billion ISK to its cosmic grave. Money flows in and out of EVE every day, entering the world through the magical printing presses of Game Time Cards, bounties and loot, and leaving it again in thousands of brilliant blue flashes. It enters and exits through incessantly flashing wallets, leaving each player to make the call when the time comes to throw themselves headlong into PvP. How much they will lose if they die is the cost factor of the analysis.
The benefit can take several forms, but it is essentially the same monetary measure of how much the opponent will lose. Sometimes - such as in alliance fleet battles - it is enough to inflict the monetary loss, betting that the enemy's will to continue fighting cannot outweigh the costs they incur. Piracy aims to extract money through ransoms or high security ganks, manifesting the cost differently. Complications aside, the deciding factor in whether or not two forces come to blows boils down to at least one of the two coming to the conclusion that the potential benefits outweigh the potential losses - the risk of death is worth taking.