Divergence 46 signal where mk0 will be punished

Divergence 46
signal where m(k)=0 —will be punished because individuals who send out novel signals
will fail in their interactions. Note also, that if Type A’s are the only type that choose this
signal, that is, s=0 , then the meaning of the signal m is 1. In other words, the receiver is
sure of the sender’s identity.
The first stage is essentially a coordination game, so nearly any set of signals can be part
of a coordination game equilibrium. For our purposes, we are interested in the signals that
would be picked if types were unitary actors. In this simple example, we have perfect
alignment of preferences. If each type chooses a different signal, then there will be
perfect identification whenever the signal is observed. Thus we would expect Type A to
choose a signal i and Type B to choose a different signal j .
Utility for each individual is given by the benefits of interaction minus the cost of
signaling. The benefits of interaction are equal to the probability of visibility times the
expected payoff from interaction, where the expected payoff is the probability of correct
identification times the benefit of a correct interaction plus probability of incorrect
identification times the benefit of incorrect interaction (assumed to be zero).
U
A
= v(i)[ m(i) σ + (1-m(i)) 0] - c(i,A)
U
B
= v(j)[ m(j) σ + (1-m(i)) 0] - c(j,B)
However, since in this simple case, each signal identifies the other individual with
probability 1, and the receiver will always treat the sender as she wants this simplifies to
U
A
= v(i) σ - c(i,A) and U
B
= v(j) σ - c(j,B)
Thus, the optimization problem is given by
max
i ∈ Z
U
A
= v(i) σ - c(i, A) and max
j ∈ Z
U
B
= v(j) σ - c(j, B)
We maximize by differentiating the actor’s utility functions with respect to visibility, v
i
,
and cost, c
i
.
1 − =
∂
∂
=
∂
∂
c
U
v
U
A
A
σ
Since the derivative with respect to visibility is positive, actors would choose signals with
the highest possible visibility. Since the derivative with respect to costs are negative,
actors would choose signals that minimized costs.
5
5
Side note that is not discussed in the paper: Since there is often a trade off between high visibility and low
costs, in point of fact, actors would choose a signal where these partial derivatives were equalized. If we

Divergence 47
Choice of Domains
The above intuition can be applied toward the choice of domains. Potentially, we could
have a model where visibility is determined endogenously, and actors had to choose
which signals to look for. When there are more domains to signal in, each domain has
lower visibility. Then signaling will only occur in certain domains, and there will have to
be coordination so actors look for signals in the same domains other actors choose to
signal in.
Formally, let us pre-pend another stage before the stages in the game above. Before
signals are selected, actors select a domain in which to signal.