The value of the game is taken as a function of player one's information structure.
The answer lies in the fact that sports valuations are founded on more than championships; they are also a function of player costs, stadium real estate and the population of the home market.
Giants Coach Jim Fassel has always viewed his team's march to last season's Super Bowl as a maturation process, a function of veteran players and a developing head coach blossoming together during a charmed season.
A differential equation, called the dynamics equation, which defines how the states vary with time as a function of the players' controls, states, and time.
This is the main theoretical innovation of this paper: payoffs are not exogenously defined, but rather endogenously determined as a function of the players' past actions.
So the best response for Player 1, as a function of what Player 2 chooses, q2, is just equal to the q1 hat in this expression and if I solve that out carefully, I will no doubt make a mistake, but let's try it.
In this model a player's choice probabilities are given by a logit best response that is a function of the player's first order beliefs.
Furthermore, we estimate a model of noisy introspection (Goeree and Holt, 2004) where a player's choice probabilities are given by a logit best response that is a function of the player's first order beliefs, and where beliefs are again a function of one level higher order beliefs.
More generally speaking, the beliefs of order z are given by a logit best response that is a function of the player's beliefs of order z+1.
Moreover the first-order beliefs are given by a logit best response that is a function of the player's second order beliefs.
