A HYBRID GENETIC ALGORITHM FOR THE MAXIMUM LIKELIHOOD ESTIMATION OF MODELS WITH MULTIPLE EQUILIBRIA: A FIRST REPORT
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Important exceptions are Dorsey and Mayer 11 and Beenstock and Szpirob. 12
u σ i∗
Let τ t be the equilibrium type of observation t. These equilibrium types are unobservable to the researcher. And let P t 0 (x t ) be the distribution of y t conditional on x t in the population that generates observation t. Since y t comes from an equi- librium of the game, we have that P t 0 (x t ) = P τt
Assumption 2. (A) For every observation t the equilibrium type τ t is determined by a function τ 0 ( ·) of the common knowledge state variables, i.e. τ t = τ 0 (x t ). And (B) there is a unique pair (θ 0 , τ 0 ) such that P 0 (x) = P τ0
log P i τt
subject to the restriction that τ t = τ t
subject to: P t = Ψ(x t , θ, P t ) for every observation t P t = P t
the mutation probability. d t is the indicator for the identity of the parent who transmits the tth chromosome and it is i.i.d. over t with Pr(d t = 1) = 1/2. Let { ˆ P m1 , . . . , ˆ P mT } and { ˆ P m
1 − d t P ˆ m
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