Event Construction

Optimal Behavior

The EPA profile for the behavior that would minimize unlikeliness-uncanniness-uniqueness and maximize normality is obtained by setting partial derivatives of the right side of (18) to zero and solving for behavior terms. Before doing this, though, the behavior variables in [f' t'] must be removed to a separate vector. This is accomplished by defining z_�, a vector that draws out the behavior terms in [f' t'] and which has ones corresponding to entries in [f' t'] that lack a behavior term.

(19)

Assuming that behaviors are recalled from memory with transients set equal to fundamental values, this becomes

(20)

A diagonal matrix, I_�, also is defined to contain elements of [f' t'] that were not moved to z_�.

(21)

Now [f' t'] can be expressed as

(22)

and (18) as

(23)

    At this point a behavior profile

(24)

can be obtained from z_� by defining a selection matrix:

(25)

Ones in the first row of (25) show where B_e terms arise in z_� , ones in the second row designate B_p terms, and ones in the third row show B_a terms. The product, S'b, reconstructs z_� except that there are zeros where ones should be. Thus another vector of zeros and ones is defined - a vector in which ones show the terms of [f' t'] that lack any behavior term:

(26)

Then

(27)

    Using (27) the equation for unlikeliness-uncanniness uniqueness can be expressed with the behavior profile explicit

(28)

For convenience, symbolize the matrices of constant parameters

(29)

and

(30)

Then (28) becomes

(31)

or

(32)

    The fundamentals and transients for actor and object can be treated as constants during the search for an optimal behavior to link the two. Then the derivative of (32) with respect to b is:

(33)

Setting the expression equal to zero and solving for b gives

(34)

which defines the optimal behavior profile, given fundamentals and transients for actor and object.

    Analyses by Heise (1985) have indicated that reasonable simulations of social interaction can be produced while treating W_ff, W_ft, and W_tt as identity matrices - the weights in the diagonals all being equal to 1.0 - and V_f and V_t as vectors of zeros. For this case define

(35)

and h₀=0. Then the solution for the optimal behavior profile is

(36)

An alternative way of representing H_I provides a more convenient formulation for some kinds of calculations.

   (36a)

whereupon the solution is

   (36b)