A Case for Percentage Commission Contracts: The Impact of a “Race” Among Agents (P.4)

price. This is clearly a departure from the current practice in the industry where the
commission rate is typically 6% and independent of the asset price. Such findings
obviously have important policy implications.
This study proceeds as follows. The next section describes the basic model and
presents the efficient commission rate in a contract with a single agent. “Agent
Competition” extends the model to an MLS scenario with multiple agents and one
seller and solves for the efficient commission rate in this setting. “Efficient Search”
considers the efficiency of the MLS contract modeled here. “Conclusion” concludes.
The Model
It is important to note that objective of residential home sellers is likely a
combination of minimizing time to sale and maximizing sale price. Various models
in the literature address one or both of these objectives. For the purposes of this
paper, we will take the expected sale price of the property as given and focus on the
time to sale as the criteria for maximizing seller utility.4 This simplifies the problem
and allows us to focus on the optimality of the commission structure. It is also in line
with the argument that the price is determined by the supply and demand forces in
the market. We assume that the seller and all agents are risk neutral and have a
common discount factor, r.
First, we consider the game between one seller and one agent. The two players enter
into a listing contract which grants the agent exclusive rights of sale, meaning that the
agent receives the full sales commission upon sale of the property. While the outcome
of this case will follow the insights of standard principal-agent theory, it is useful to
develop this case for the purposes of comparison to a model with multiple agents.
Let 1 be the intensity of search that the agent selects at time 0 and maintains until
the buyer is found. The agent searches continuously until a buyer is found. Although
a strategy for the agent is to determine the optimal search intensity time path, we
only consider the non-cooperative Nash equilibrium of stationary pure strategies.5
Let X be the stochastic time until the agent procures a buyer for the listed real estate,
where X  expðlÞ, EðXÞ ¼ 1l
, and ldt is the probability that an agent procures a
buyer in the short time interval dt. Search is costly and the agent incurs a cost, c(l),
for the chosen intensity level. The cost per unit of time is increasing and strictly
convex in intensity l, c′(l)>0, c″(l)>0. Supply and demand forces in the market
determine the sales price of the real estate, P. The seller will pay a commission to the
agent at the time of sale equal to αP, where 0<α≤1. The commission rate is taken as
exogenous by the players.6
4 An alternative is to argue that the agent’s effort impacts the selling price rather than the selling time (e.g.,
Anglin 1994). We believe that the agent’s effort impacts the time on the market more so than it affects the
selling price.
5 This is common in the R&D studies of continuous time models (e.g., Mortensen 1982).
6 An alternative would be to have the commission rate determined as part of the contract between the
seller and the agent. Determining the optimal contract between the seller and the agent is out of the scope
of this paper. Our objective is to study if, for a given commission rate, the percentage commission
structure could lead to efficient effort intensities by agents.

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