(latest update as of 01/04/25)

Lately, I’ve been diving into game theoretic concepts, especially through the Cooperative AI course I’m taking. Around the same time, I was watching a video on forecasting where the explainer said something that stuck with me: “The best strategy is to report your true estimate.”

That line caught my attention. Did they mean best strategy in the everyday sense? Or were they hinting at something deeper - a game theoretic best strategy?

Let’s see, what are the main elements in a game (according to game theory). Players, Actions and of course Payoffs.

Game Structure:

1. Players: Two forecasters.
2. Actions Each player submits a probability forecast. For the sake of simplicity, assume that the question is binary. And the player will forecast their probabilities p1, p2 for the Yes option. The complement would be the corresponding prob for the alternative outcome.
3. Payoffs: The players' payoffs depend on the Brier Score (or another proper scoring rule). The objective would be to minimize their own forecasting error while possibly considering the forecast of the other player.

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