Socially Optimal Contract Design A Study in the Fitness Market Peter Hayes

Motivation Humans suffer from self-control problems Such problems manifest in several areas Credit/Debt, Health/Lifestyle, Savings Large Social Impact Contracts in these industries exploit consumers’ irrational behavior Market-friendly ways to address these issues?

Theoretical Background Hyperbolic Discounting (aka Two-Selves, Time- Inconsistency, Naïve/Sophisticated Consumers) Consumers with “current” preferences (u) and “future” preferences (v). Θ factor determines degree of naïvety. Consumers play a sequential game with their later selves. “Commitment Devices”

Example 1 Consider a new casino visitor Values first slot use at $1.00 (“for fun”) Present: Values more slot use at $0.00 Actual: Values more slot use at $0.50 Contract 1: $1.00 per game (flat rate) Contract 2: First game free, can continue for $0.50 per game Naïve/Sophisticated: Who picks what?

Example 2 ACTIONT = 0 PreferencesT = 1 Preferences Go to the GymCost: $5Cost: $15 Become HealthierBenefit: $10 Sign ContractCost: $50 Pay-per-useCost: $2 per use Sophisticated and naïve consumers make different choices Can a contract benefit both?

Commitment Devices Contracts that entice sophisticated consumers are called “commitment devices” Setting prices to choose correctly in future Are these applicable in the real world?

Theoretical Results Companies offer a menu of contracts for sophisticated and naïve consumers All consumers above threshold pick arbitrary commitment device Naïve consumers exploited to different degree Competition between firms drives profit to 0 Lost surplus from unrealized preferences Empirical Evidence

Stickk Contracts Website offers commitment-based contracts Contract based on completion of a goal Example: “Write 100 pages of my novel or I pay $100” Can this be applied on a contractual level?

Benefits of Goal-Based Commitment Attractive to both types of consumer Sophisticated consumer recognizes incentives Naïve consumer assumes success Can be revenue-neutral, even with possibility of bad luck Leads to positive social outcomes But at what cost to profits? Is it sustainable?

A Simple Example “Peter” wants to lose 50 pounds Utility equals pounds loss Cost per trip (effort) to the gym is 2 (Θ = 0) Each trip can lose 1 pound. Contracts fail: Benefit per trip is 1, cost is 2

Goal-Based Contract Consider a contract with fixed cost = $150, $1 refund/pound Now MC = MB, consumer will complete the contract Offering this new contract benefited both parties, social surplus

What about Naïve Consumers? Naïve consumer assume greater future effectiveness. Believe future gym attendance less costly But also believe in future success. Thus, also willing to sign goal-based commitment contracts!

Basic model Consider two types of contracts Standard, flat fee: C Goal-based: C + G, where G is the motivator In standard, utility of completion is U In goal-based, utility of completion is U + G Firm sets C = U to maximize profit Naïve consumer assumes completion of goal, indifferent between contracts Sophisticated consumer sees commitment

Basic Model 2 – Each Period In each period, consumer has negative utility for gym attendance Suppose N visits required to complete goal T periods before goal expires On period T-N, consumer sees looming loss of G, begins attending (assuming G high) After that point, constant attendance Can we incorporate discounting?

Why not more Prevalent? Possibility of failure to complete goal Data from DellaVigna/Malmendier shows most consumers naïve Perhaps naïve about chance of failure – risk aversion? Underestimate of device strength? “Completion fee” thus must be lower Reduces gym profits Can we compensate for this?

Risk of Failure Consumer may assume risk of failure to complete goal “P” (due to outside chance) Goal-based contract must now have C = (1-p)U Risk aversion worsens this: C = α(1-p)U; α=f(p) Regular contracts would have C = U Can this account for the non-existence of such contracts? Naïve types no longer indifferent. Can we estimate α and p? How much revenue does this lose firms?

Goals for Research Why don’t more firms offer Stickk-like contracts? Is it because of profits or consumer psychology? Can we account for this? How much would offering such contracts lose gyms in profits? Can we incentivise them to offer them? Is this an effective use of public or non-profit funds (vs advertising/education)? Are these contracts exploitable? That is, do customers have an incentive to misrepresent their preferences? Can we help prevent procrastination? Is a single goal enough? Or do more complications lead to instability?

Data Sources Data about gym membership from DellaVigna and Malmendier’s paper Data about commitment contracts from Stickk.com Survey of Brown students to gauge interest in commitment-device contracts?

Further applicability Other situations with time-inconsistency? Probably not credit-cards, gambling: firms make their money from naïve consumers. Other potential markets? Suggestions?

Benefits/Feasibility Game Theory for contract design Available data Addresses a significant social problem Alternative approach, old strategies not very effective