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Is this a simple random event, or was Mr. Dalio using a dominant strategy?
In other words, the payment rule makes truthful reporting a dominant strategy for all players.
So in fact, in this little sub-game, actually, Player 3 has a dominant strategy.
In the language of game theory, confessing is a "dominant strategy," even though it leads to a disastrous outcome.
We first consider single-valued preference domains and characterize the space of decision policies that can be truthfully implemented in a dominant strategy equilibrium.
So we know that, in fact, Player A here has a dominant strategy, the dominant strategy is to fight in period 1 in this analysis of the game.
Since these are the only relevant payoffs looking forward, in the last period of the game, we know that there's actually a dominant strategy.
As can be seen from this new, more accurate, payoff matrix, there is no longer a dominant strategy to believe in God.
It is well-known that truthtelling is not a dominant strategy in this auction and that inefficient equilibria can arise.
By contrast, Z has a dominant strategy of "vote for z," which leads to outcomes at least as good as and sometimes better than his other two strategies.
And joining is a dominant strategy. .
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com