The Pricing Problem – Game Theory Used to Determine Optimal Rates For Assisted Living Facilities
By Jeffrey Cole
When aging seniors begin to need basic assistance with daily living, they can essentially choose from one of the following to get the long-term care they need:
(1) receiving assistance at home from a loved one;
(2) hiring a caregiver from a homecare agency; or
(3) moving into an assisted living facility. While approximately 70% of seniors over 75 years of age obtain help from a loved one in the US, home care agencies (HC) and assisted living facilities (ALF) are growing, lucrative industries. ALFs and HC services provide quality senior care and assistance for those in the aging elderly US population who have the ability to lessen the burden on their children by paying for expert long-term care services with their home equity, pensions, retirement savings, and/or government funding.
ALFs naturally compete with HC agencies for seniors and it is typically the adult daughter who decides if her aging parent will either move into an ALF or hire an in-home caregiver. Presumably, an adult daughter will choose the option that cultivates the most health and happiness to her aging parent at the lowest cost (especially in the current economic climate), and the goal of an ALF is to maximize revenue while keeping occupancy rates high by not losing seniors to HC companies. However, ALFs (known in signaling games as the sender (Source 1), since they send a price signal to the adult daughter) can vary greatly in quality (i.e. ‘good’ or ‘bad’) and HC quality is more stable (See Note). Ideally, operators of ‘good’ ALFs would signal their high quality to adult daughters with high prices, but because HC is a valuable alternative and there are ‘bad’ ALF that could raise their prices to falsely signal quality, the ‘good’ ALF operator has to carefully set its rates. This uncertain price-quality signaling between high revenue for the ALF and optimal benefit to the senior resident can be analyzed using game theory, particularly an extensive form signaling model, to help owners and operators of ALFs answer the question:
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