Reputations, Market Structure, and the Choice of Quality Assurance Systems in the Food Industry

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proven wrong. Unlike the situation in which reputation is a public good, when a processor’s
reputation is lost, the other processor fills the market and behaves as a monopolist until its
product fails and is discovered by consumers.

To accommodate this sequencing we need to expand the number of states of the world
from 2 to 4. In state 1, both processors are trusted. State 2 arises if processor 2 loses its
reputation. In state 3, processor 2 acts as a monopolist. The market disappears when state 4 is
reached (both processors lose reputation). Reputations can then be modeled as following a
stochastic process, where the probabilities of reaching the different states of the world are
affected by the choices made by the market participants. Since only the immediate past
determines the state of the world in the following period, the stochastic process exhibits the
Markov property. Therefore, it is natural to use the concept of a Markov process to model the
dynamics of this market.

A Markov process is defined by the possible states of the system, the transition matrix,
and a vector that records the initial state (Ljungqvist and Sargent). The states of the world are
described in the previous paragraph, and the assumption that processors will be trusted until
proven wrong is equivalent to assuming that the system starts at the first state with probability
one (and hence the remaining three entries of the initial state vector are assigned zero
probability). The transition matrix M is as follows:

^λm₁m2 m₁ (1 - m2 ) m2 (1 - m₁ ) (1 - m₁ )(1 - m2 )'

The probabilities of success m₁(s₁) and m₂(s₂) are defined as before. Then, entry

M_{i, j} denotes the probability that the system will be in state j in the next period, given that the

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