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Divergence 46 signal where mk0 will be punished

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Divergence 46signal wherem(k)=0—will be punished because individuals who send out novel signalswill fail in their interactions. Note also, that if Type A’s are the only type that choose thissignal, that is,s=0, then the meaning of the signalmis 1. In other words, the receiver issure of the sender’s identity.The first stage is essentially a coordination game, so nearly any set of signals can be partof a coordination game equilibrium. For our purposes, we are interested in the signals thatwould be picked if types were unitary actors. In this simple example, we have perfectalignment of preferences. If each type chooses a different signal, then there will beperfect identification whenever the signal is observed. Thus we would expect Type A tochoose a signaliand Type B to choose a different signalj.Utility for each individual is given by the benefits of interaction minus the cost ofsignaling. The benefits of interaction are equal to the probability of visibility times theexpected payoff from interaction, where the expected payoff is the probability of correctidentification times the benefit of a correct interaction plus probability of incorrectidentification times the benefit of incorrect interaction (assumed to be zero).UA= v(i)[ m(i)σ+ (1-m(i)) 0] - c(i,A)UB= v(j)[ m(j)σ+ (1-m(i)) 0]- c(j,B)However, since in this simple case, each signal identifies the other individual withprobability 1, and the receiver will always treat the sender as she wants this simplifies toUA= v(i)σ- c(i,A)andUB= v(j)σ- c(j,B)Thus, the optimization problem is given bymaxiZUA= v(i)σ- c(i, A)andmaxjZUB= v(j)σ- c(j, B)We maximize by differentiating the actor’s utility functions with respect to visibility,vi,and cost,ci.1==cUvUAAσSince the derivative with respect to visibility is positive, actors would choose signals withthe highest possible visibility. Since the derivative with respect to costs are negative,actors would choose signals that minimized costs.55Side note that is not discussed in the paper: Since there is often a trade off between high visibility and lowcosts, in point of fact, actors would choose a signal where these partial derivatives were equalized. If we
Divergence 47Choice of DomainsThe above intuition can be applied toward the choice of domains. Potentially, we couldhave a model where visibility is determined endogenously, and actors had to choosewhich signals to look for. When there are more domains to signal in, each domain haslower visibility.Then signaling will only occur in certain domains, and there will have tobe coordination so actors look for signals in the same domains other actors choose tosignal in.Formally, let us pre-pend another stage before the stages in the game above.Beforesignals are selected, actors select a domain in which to signal.

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Term
Fall
Professor
NoProfessor
Tags
Sociology, Social Psychology, Summer, cultural practices, Snyder, Fromkin, Subculture The Meaning of Style,

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