Bayesian Nash equilibrium
Each type of each player picks the action that is best given what they know, assuming every other type is doing the same.
Often misread asSolving for one action per player rather than a plan covering every type, and so checking optimality only for the type that happens to be realised.
How to see it
Equilibrium in rules, not in moves
Each player commits to a rule saying what to do in each situation they might turn out to be in. Equilibrium means every one of those rules is the best available given the rules everyone else is using and the known odds on who ends up where.
The checkEvery type has to be content with what the rule tells that type to do, including the types that are unlikely and the ones that never show up.
Try itIn a two bidder auction with values drawn from a range, state your answer. If it is bid sixty pounds, you have not finished. If it is bid two thirds of your value, you have the right kind of object, and you can now test whether a bidder worth ninety would deviate.
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.
- Osborne, M. & Rubinstein, A. (1994). MIT Press.