We examine empirically and theoretically the multiperiod pricing pattern in the real estate market. First, in a game theoretic framework, we identify conditions for determining whether potential closing prices increase or decrease and marginally increase with time on market. Then, by observing rental housing transactions, we empirically find evidence that the difference between the list price and the settlement price rises and marginally decreases with time on market. This empirical result is consistent with a perfect Nash equilibrium previously proposed in the model.
We examine empirically and theoretically the multiperiod pricing pattern in
the real estate market. First, in a game theoretic framework, we identify conditions
for determining whether potential closing prices increase or decrease and marginally
increase with time on market. Then, by observing rental housing transactions,
we empirically find evidence that the difference between the list price and the
settlement price rises and marginally decreases with time on market. This empirical
result is consistent with a perfect Nash equilibrium previously proposed in
the model.
Several models in the real estate literature refer to the optimal stategy for
pricing real estate units. Stull (1978), for example, analyzes the rental housing
market and concentrates on the properties of a rental probability function. He
deduces that the greater the potential tenants arrival rate, the higher the probability
of locating a tenant willing to pay the asked rent price, ceteris paribus, and
further, that the probability of locating a renter declines faster with a rise in the
rent price asked for less desirable properties. The two major results in his model
are the declining sequence of asked rent prices and the associated decreasing
expected waiting time.
In his derivation of a declining sequence of asked prices in real estate sale
transactions, Read (1988) emphasizes the seller’s imperfect information regarding the housing quality. He numerically solves for the sequence of optimal asked
prices, exogenously assuming a consumer arrival rate, a fixed sale period, and a
maximum number of buyers. His simulation produces an optimal pricing schedule
which, once again, decreases over time. The intuition underlying his result is
that when a landlord fails to reach a match with a buyer—given the specific
flow of shoppers—he concludes that his property is of lower quality and drops
the price.
The empirical literature in the area provides evidence from real estate sale
transactions.1 It generally finds that the ratio of selling price to list price is
inversely related to time on market.
In contrast to previous studies, we provide empirical evidence of pricing
patterns in the rental housing market. Furthermore, we incorporate a game theoretic
approach to analyze real estate pricing under a multiperiod framework.
We should note that while our theoretical framework may conceptually also
include sale transactions (as well as transactions of a family of other goods2),
we restrict our empirical attention to the rental of real estate.
We first construct a game theoretic framework where potential renters and a
landlord interact in a multiperiod setup. At each period the seller encounters one
potential renter, arbitrarily drawn from a set of possible renters, who distribute
according to their willingness to pay for real estate services.
We examine the attained equilibrium under two settings: in the first (second)
the landlord (a potential renter) provides a price offer to which a potential renter
(the landlord) may agree or disagree. If a rejection occurs, the round is replayed
in the subsequent period with a new arbitrary potential renter. The game terminates
at the first period in which the price offered by one party is accepted by the other.
In general, conditions of perfect Nash equilibrium in mixed strategies require
that the landlord’s reservation price at any period be equal to the expected present
value of his future reservation prices. Therefore, when the landlord is the first
mover, the outcome of the equilibrium is a price that is declining (rising)
and marginally increasing with time on market, if the conditional probability of
a transaction is relatively low (high) and if the landlord is relatively patient
(impatient).
If a potential renter is the first mover, however, then equilibrium closing prices
never decrease with time on market. The specific price pattern in this case depends
on the landlord’s time preference factor and is independent of the conditional
probability of realizing a transaction.
Our empirical test is conducted along the lines of Belkin et al. (1976), Janssen and Jobson (1980), Kang and Gardner (1989), and Yavas and Yang (1995).
However, in contrast to those studies, all of which are based on sale transaction
data, our study is the first, to our knowledge, to report rental market evidence
on the subject.
Most importantly, we find a pattern indicating that the proportional difference
between the original list price and the actual transaction price rises and marginally
diminishes over the duration of the rental process. This empirical evidence is
consistent with a perfect Nash equilibrium derived in our model, where the
landlord is the first mover to whose asked price the tenant responds.
In Section 2 we derive and examine the conditions which determine the attained
asked price pattern under perfect Nash equilibrium. Then, in Section 3, we present
the empirical findings. We summarize in Section 4.
We analyze empirically and theoretically the multiperiod pricing pattern in the
real estate rental market. Though we restrict our attention to the rental of real
estate, our theoretical framework may also incorporate real estate sale transactions,
as well as family of other types of goods and transactions where the price
of the transacted good may not be perfectly determined by market forces ex ante
and nor may bind future transaction prices ex post.
First, we construct a simple game theoretic framework and derive perfect Nash
equilibrium, under which potential closing prices might rise or decline with time
on market. It turns out that the equilibrium price pattern depends on the party
who plays first as well as on the model parameters: landlord’s patience and the
distribution of potential renters’ willingness to pay.
Specifically, the model shows the conditions under which the optimal strategy
of a landlord, who is informed only about the distribution of potential renters’
willingness to pay, is to decrease (or increase) and marginally increase the price
during time on market, so that his reservation price at each period is equal to
the expected present value of prospective future prices.
We further present empirical evidence from the rental housing market showing
that the proportional difference between the list price and the transaction price
indeed rises and marginally diminishes during the rental process. As shown in
the model, this empirical result is consistent with the framework in which the
landlord is the first mover to whose proposed price reacts the potential renter.
Further empirical work, using data sets from other real estate rental markets,
might shed more light on our conclusions.
Another possible direction for future research is to model the change in price
trends that produce a price cycle or a mean-reverting price process, which is
commonly believed to prevail in real estate markets.
