Then I have to raise the question why one should bother to discuss models that don't reflect reality well enough to make accurate predictions, in this case a real-world example.

The post consists of 6 examples. The first three are pure theory and wouldn't stand a chance in practice. It's however insightful to think about them to realize how powerful the designer of a game, in theory, can be.

The fourth example is a game that has been tried in practice, with apparently highly profitable results. Here, game-theory with a "rational actor model" delivers accurate predictions (that is, if every player is, in a Bayesian Game, confident enough that his opponent will eventually not bet more money, one SPE is to always invest more, correct me if I'm wrong). Thus, it's in this case fine to apply game theory to the real world, as it works in most cases, under certain assumptions.

The fifth example, as you noted, stems from the realm of fiction and is useful for the pondering of game theory, but not useful in practice.

The last example is, like the fourth example, something that has actually happened. However, in this case, after Nick has uttered a few words that seem meaningless from a game theoretic point of view, game theory (with the payoff matrix for Golden Balls and the "rational actor model") no longer makes accurate predictions. This means that perhaps, we should modify our model in order to get out a better prediction. One way to do so is to change the payoff matrix, another is to see the game as an instance of repeated PD. Also, one could choose to model the people with a rule-based or behavioural model - If my opponent has openly, in public, announced that he wants to split fairly if I do X, then I do X.

What's left is that, while game theory is useful in modelling the real world at times, at times it is not. And when it is not, in my opinion one should accept this fact and use a different model.

Another note about "rational actor model" vs. "rule-based model" and "behavioural model":

• The rational actor model often applies in the real world if the stakes are high, the game is repeated several times, it's a group decision and/or the coices to be made are fairly easy. It says that people have a goal and optimize for it. The objective can be money, but people are also allowed to have a different payoff function. It is, of course, not a model of rational people in the sense that these are always winning, more like academia-rational.

• Behavioural models attempt to model people based on how they behaved before. These models take into account biases that we may have.

• Rule-based models are based on simple rules that agents follow. These are often easy to write down, but can be exploited.