qgames-2-widgets1.txt

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Consider the following classical game,
which illustrates another core concept in classical game
theory.
Suppose Shor has created some widgets
which he would like to sell.
He would like to sell these at either $1, or $2,
or $3 a piece.
He is competing with Farhi's gadgets,
which also may be on the market for $1, $2, or $3 a piece.
At these different prices Shor and Farhi
would earn the following profits.
Of course, the profits that they earn depend on the cost
they sell their widget or gadget at and also the competition's
price point.
If Farhi's gadget goes for $1, Shor will either earn $0,
lose $1, or lose $2.
On the other hand, if Farhi's gadget sells for $2,
Shor may earn $5, $2, or $1.
In a similar way, Farhi earns nothing, loses $1,
or loses $2, or $5, $2, or $1, $4, $9, or $5,
depending on what Shor does.
What is the dominant strategy for each player
given this payoff matrix?