I've become to study Game Theory and have encountered with matching pennies game.
1) All games have at least one Pareto Optimal profile.
2)" Idea: sometimes, one outcome $o$ is at least as good for every agent as another outcome $o'$, and there is some agent who strictly prefers $o$ to $o'$
in this case, it seems reasonable to say that $o$ is better than $o'$
we say that o Pareto-dominates $o'$
An outcome $o^{*}$ is Pareto-optimal if there is no other outcome that Pareto-dominates it."
According to 2) there is no Pareto Optimal profile for this game, but the statement 1) says the opposite.
Why does PO profile exist?
Does this mean that Pareto Optimal profile consist of all $4$ states?
Matching pennies is a zero-sum game. In a zero-sum game, all strategy profiles are Pareto-optimal, as there is a fixed sum to be distributed and it's impossible to redistribute it without making someone worse off.