Without a theory of focal points, it is very hard to analyze this interaction.

One point, however, is very clear—the slight change away from symmetry reveals two agents arguing over what should be focal, without the slightest interest in a Nash equilibrium/

There are two ways of thinking about the problem.

1. You see the problem as decision theorist, and see a conflict between the expected utility recommendation and the dominance principle. People who have seen the problem this way have been led into various forms of causal decision theory.

2. You see the problem as game theorist, and are trying to figure out the predictor’s utility function, what points are focal and why. People who have seen the problem this way have been led into various discussions of tacit coordination.

Newcomb’s scenario is a paradox, not meant to be solved, but rather explored in different directions. In its original form, much like the Monty Hall problem, Newcomb’s scenario is not well stated to give rise to problem with a calculated solution.

This is not a criticism of the problem, indeed it is an ingenious little puzzle.

And there is much to learn from well defined Newcomb like problems.