Payoff Matrices can be an important part of a strategist's toolkit,
especially as it relates to understanding the competitive dynamics between two or
more competitors.
The purpose is to identify dominant strategies,
especially in single-period simultaneous-move games.
We see here illustrated a game for a price cutting scenario between two firms.
From one can either cut their prices or not and similarly firm two could as well.
The payoff matrix is a way of mapping out the pay offs associated with these various
strategic actions.
They could be probabilistic, we could be talking in expectation we'll make a $100,
or they could be very precise we know for
a fact this is the amount we're going to make.
By creating this little matrix here, we're able to start to understand
the incentives for each player in taking each of these strategic actions, and
in particular we're going to look for in our steps here, dominated strategies,
ones that we will pursue no matter what happens to the other player.
So consider firm one.
They get a path of $200 if they do appraise cut and the other firm doesn't.
They increase their market share,
they gain more demand as a result of that scenario.
So, $200 is better than the no cut situation so they prefer a cut.
But interestingly, even in the situation where firm two cuts their prices,
we also decide to cut our prices here because $0 is better than negative 30.
So this creates a dominated strategy for firm 1 to take over and cut their prices.
Now this is a symmetric game where the payoffs are the same for both firms, so
interestingly enough,
firm 2 has exactly the same logic and they end up here in a cut, cut scenario.
So the payoff matrix here provides insight for us to understand what
would likely happen if we start to engage in a price cuttings scenario here.
And perhaps then suggest to us, other ways that we can restructure their game
to avoid the competitive outcome that we don’t desire here.
Maybe changed in the deferential and fails between us and our competitor, or
maybe just simply restructuring the game in a fundamental way, so
we don't have this result for us.
In general Payoff Matrices, could be useful again to understand the moves and
counter moves of various competitors in a rivalrous situation.