Generally, game theory assumes that people are rational and selfish; they're always angling to get what's best for them, which means their behavior can often be predicted.
Repeat after me: game theory never assumes that people are selfish. It does assume they're rational; but rationality and selfishness are two different things. The selfish/selfless criterion applies to ends, whereas the rational/irrational criterion applies to means. For example, suppose your most important goal is to sacrifice your own life in order to save somebody else's. You find out you can be a donor for someone who needs a liver transplant but can't find a match and will die unless you donate. So you give them your liver and die saving their life. That's definitely not selfish behavior; but game theory would say it's rational. If, however, instead of doing that you'd participate as a victim in a human sacrifice ceremony meant to convince Jupiter to take your life instead of that other person's, that would be selfless and irrational.
The above-quoted sentence actually contains another error: it implies that it's the assumption of selfishness that's making it possible for human behavior to be (more or less) predictable. Not true. It's rationality that enables predictability; selfishness is completely superfluous.
To sum up: game theory does not assume people won't do selfless things. It assumes they won't do stupid things.
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