Harsanyi transformation
Turning a game where players do not know who they face into an ordinary game by letting chance pick the types first and telling each player only their own.
Often misread asTreating it as a substantive claim that nature really does draw players' characteristics at random, rather than as a device for putting incomplete information into a form the standard tools can handle.
How to see it
Let chance deal the hands, then play an ordinary game
A game where nobody knows who they are up against is rewritten as a game where chance moves first, deals each player a private situation, and shows each of them only their own. After that everyone knows the rules, and the usual machinery applies.
The checkThe chance move is bookkeeping. It records what players do not know; it does not assert that the world randomises.
Try itTake any situation where you are unsure whether your rival is tough or soft. Draw a chance node at the top that picks one, and an information set that stops you seeing which branch was taken. If the drawing works, the transformation is done.
Know these first
Leads on to
Easily confused with
Sources
- Harsanyi, J. C. (1967-68). Management Science 14(3), 159-182; 14(5), 320-334; 14(7), 486-502.
- Fudenberg, D. & Tirole, J. (1991). MIT Press.
- Myerson, R. (1991). Harvard University Press.