Game theory tends to assume that people should act rationally, but when they are put in a real world position they can deviate and try to second guess what other participants in the game or market will do.
There was even a rubbish game show which tried, albeit mostly unsuccessfully, to show how this might work in practice.
Paradox of thrift
Too much saving in an economy can lead to a decline in aggregate demand, in turning becoming harmful to the economy.
However, if we all do so simultaneously it then we'll end up with lower demand for goods and services, in turn company revenues, profits, and taxes payable will decline, hiring may sag, and so on.
So what starts out as an apparently good idea for the individual household becomes problematic on a widespread scale.
Firstly, it's important to note that the saving ratio is a derived figure, based upon estimates of what happened to household incomes (which was very weak in the quarter) and consumption (which didn't fare too badly).