University of Toronto July 20, 2017
: A Theory of @KimKardashian and @charliesheen University of Toronto July 20, 2017 : A Theory of @KimKardashian and @charlies
Broad Interest: Non-Price Discovery of Goods The Internet means that content is everywhere Prices don't do most of the work in allocating resources; search is key This paper's narrow topic: People nd content through free advice, but advice is often mixed with ads Model repeated relationship between inuencer (gives advice, runs ad) and follower
I never, ever link to anything I wouldn't want to buy for myself, commission or no commission.
This Paper Construct a simple model, capable of understanding basic trade-os and some policies Not meant to be a full model of Twitter or Google, but rather an abstract way to think about this kind of relationships Borrow ideas from contracting literature without monetary transfers especially Li, et al. (2015) and DeMarzo and Fishman (2003) Show that this channel leads to dierent policy results: disclosure can be bad for consumers Key: Ads play two roles: as temptation for which incentives are needed (currently) and reward (in the future) by which those incentives are achieved
Basic Model Continuous time, innite horizon, discount rate normalized to 1 If follower follows inuencer (f t = 1, observable), good advice arrives to follower at rate (1 a t )λ Inuencer (privately) chooses ad level a t Inuencer gets payo λa t from ad technology Follower gets value 1 for each piece of good advice; follower's payo is public If the follower chooses not to follow the inuencer (f t = 0), follower gets s > 0 (but s < λ) and inuencer gets 0
Alternative interpretations 1 Constant ow of advice, occasionally good, at a rate that depends on ad level of advice 2 Inuencer like a strategic bandit arm with known return: one unit arrives at rate λ, inuencer decides whether to keep or pass on to follower
Full Information Pareto Frontier f = 1 at all t together with dierent sequences of a traces out Pareto frontier Let V be follower's value and W be inuencer's value: V + W = λ
Contracts No monetary transfers, reward comes via (public) history dependent choice of f t and a t Public history is the list of dates at which good advice was received, plus entire history of f No commitment for inuencer. Consider both commitment and no commitment for follower Qualitatively similar results Assume inuencer needs a xed level W of payo ex ante to make advice technology feasible
Some Related Literature Theory Literature: Dynamic contracts without money: Hauser and Hopenhayn (2014), Guo and Horner (2015), Lipnowski and Ramos (2016), but especially Li, et al. (2015), and Bird and Frug (2016). Goal: similar economics especially to the last two papers, but in a more streamlined way designed for IO applications IO literature: Reputation and trust (Klein and Leer (1982), etc) Policy literature on paid endorsement: Inderst and Ottaviani (2012)
Roadmap Characterize outcome for case when follower can commit to plan Policy exercise: FTC disclosure rules Extensions (no commitment, bad advice, good advice that also generates revenue)
Recursive Formulation Summarize the contract at t by 0 d t 1, the discounted number of expected periods of following in the future: d t = E 0 e j f t+j dj Describing contracts this way turns out to be WLOG Inuencer utility is a monotonic transformation of d
Intuition on role of d Expected discounted surplus is an increasing linear function of d: TS(d) V (d) + W (d) = λd + s(1 d) Higher d makes incentives on inuencer more dicult Incentives come from threat of not following in future, which is far o for high d Trade o for follower: higher total surplus vs. lower share When d = 0, total surplus is s, all follower When d = 1, total surplus is λ > s, all inuencer
Recursive problem: Choice variables Static: f, a Dynamic (commitments to future f 's and a's): d : rate of change of duration promise after no good advice d : duration promised after good advice is given
Follower's dynamic program V (d) = max f,a,d, d (1 f )s+f (1 a)λ ( 1 + V (d ) V (d) ) +V (d) d subject to PK: d = f (1 + (1 a)λ(d d)) + d 1 if a = 0 IC: W (d ) W (d) = 1 if a (0, 1) 1 if a = 1 TS: W (d) + V (d) = s(1 d) + λd
Value Function V (d) dλ + (1 d)s W (d) a = 0 a = 1 1 d
Concavity of V: Intuition Fix V (d) for some d and let x = (1 α)d. One feasible way to deliver promise of x: set f t = 0 for T periods, then follow plan from d with payo V (d) Choose T so that e T = 1 α, so this delivers (1 α)d units of discounted following time Follower's discounted payo: s T 0 e t dt + e T V (d)
Concavity of V: Intuition Fix V (d) for some d and let x = (1 α)d. One feasible way to deliver promise of x: set f t = 0 for T periods, then follow plan from d with payo V (d) Choose T so that e T = 1 α, so this delivers (1 α)d units of discounted following time Follower's discounted payo: s T 0 e t dt + (1 α)v (d)
Concavity of V: Intuition Fix V (d) for some d and let x = (1 α)d. One feasible way to deliver promise of x: set f t = 0 for T periods, then follow plan from d with payo V (d) Choose T so that e T = 1 α, so this delivers (1 α)d units of discounted following time Follower's discounted payo: s(1 e T ) + (1 α)v (d)
Concavity of V: Intuition Fix V (d) for some d and let x = (1 α)d. One feasible way to deliver promise of x: set f t = 0 for T periods, then follow plan from d with payo V (d) Choose T so that e T = 1 α, so this delivers (1 α)d units of discounted following time Follower's discounted payo: sα + (1 α)v (d)
Concavity of V: Intuition Fix V (d) for some d and let x = (1 α)d. One feasible way to deliver promise of x: set f t = 0 for T periods, then follow plan from d with payo V (d) Choose T so that e T = 1 α, so this delivers (1 α)d units of discounted following time Follower's discounted payo: αv (0) + (1 α)v (d)
Concavity of V: Intuition Fix V (d) for some d and let x = (1 α)d. One feasible way to deliver promise of x: set f t = 0 for T periods, then follow plan from d with payo V (d) Choose T so that e T = 1 α, so this delivers (1 α)d units of discounted following time Follower's discounted payo: V (x) αv (0) + (1 α)v (d)
Concavity of V Implies Always Incentivize Good Advice if Possible Concave V implies W is increasing and convex IC binds: a < 1 = W (d ) W (d) = 1: any extra d must be combined with lower d, eectively a randomization, costly with concavity Net return to good advice, after accounting for incentives required to get it: 1 + V (d ) V (d) Since a = 1 generates nothing for follower, only choose it when even d = 1 is not enough for a < 1, i.e. λ W (d) < 1 W ( ˆd) = λ 1
Concavity of V Implies Always Incentivize Good Advice if Possible Concave V implies W is increasing and convex IC binds: a < 1 = W (d ) W (d) = 1: any extra d must be combined with lower d, eectively a randomization, costly with concavity Net return to good advice, after accounting for incentives required to get it: 1 + ( TS(d ) W (d ) ) (TS(d) W (d)) Since a = 1 generates nothing for follower, only choose it when even d = 1 is not enough for a < 1, i.e. λ W (d) < 1 W ( ˆd) = λ 1
Concavity of V Implies Always Incentivize Good Advice if Possible Concave V implies W is increasing and convex IC binds: a < 1 = W (d ) W (d) = 1: any extra d must be combined with lower d, eectively a randomization, costly with concavity Net return to good advice, after accounting for incentives required to get it: 1 + ( TS(d ) TS(d) ) ( W (d ) W (d) ) Since a = 1 generates nothing for follower, only choose it when even d = 1 is not enough for a < 1, i.e. λ W (d) < 1 W ( ˆd) = λ 1
Concavity of V Implies Always Incentivize Good Advice if Possible Concave V implies W is increasing and convex IC binds: a < 1 = W (d ) W (d) = 1: any extra d must be combined with lower d, eectively a randomization, costly with concavity Net return to good advice, after accounting for incentives required to get it: ( TS(d ) TS(d) ) Since a = 1 generates nothing for follower, only choose it when even d = 1 is not enough for a < 1, i.e. λ W (d) < 1 W ( ˆd) = λ 1
Value Function V (d) dλ + (1 d)s W ( ˆd) = λ 1 a = 0 a = 1 1 d
V + W = λ V (W ) λ 1 λ W
Initial Conditions Since the inuencer needs to get at least W, the initial conditions that are follower-optimal are d 0 = argmax d:w (d) W V (d) Either this is unconstrained (i.e. supply elastic) or constrained (i.e. supply inelastic). Mostly focus on elastic supply today.
Varying Ad Return Suppose the inuencer's payo is taxed (for all t) to τλa Proposition Denote the solution by W τ (d) and V τ (d). W τ (d) = τw (d), V τ (d) = V (d) Nothing about the allocation changes Intuition: τ impact on IC constraint present and future rewards equally
Disclosure as Comparative Static on Ad Return Disclose ads â a Can interpret disclosure as an observable choice chosen by follower in dynamic program If ads exceed â, excess makes u 1 Reects potential penalty for non-disclosure Ads up to â earn m < 1 Disclosure might make ad less appealing, or just take up resources In Inderst and Ottaviani (2012), disclosure can make impact of advice less in a way that lowers its informativeness The payo to choosing ad level a with disclosure â mâ + u(a â)
Disclosure Rules in Practice One way FTC responds is by hunting/taking down suspected ads
Impact of Weak Disclosure Rules: m u If m u, â = 0 and every ad earns u Just like taxation with τ = u: reduces W and leads V unchanged
Stronger Disclosure Rules: m > u If m > u, â(d) = 1 for d > ˆd, â(d) = 0 d < ˆd Proposition Suppose u < m. Then V (d) is decreasing in u. Relaxes IC, so for any d (0, 1), raises V (d), lowers W (d)
Welfare and u V (d 0 ) + W (d 0 ) m u
Alternative Disclosure Policy Ideally would want to treat undisclosed ads harshly for d < ˆd and leniently (i.e. make return as high as possible, higher than m) for d > ˆd A policy that deregulated top inuencers (i.e. high d) would be better if 0 < m < 1 Opt-in policy: if your Twitter account says you disclose, you must disclose. All paid tweets disclosed with #ad; could be turned o when you become a top inuencer (high d)
Extension: No Commitment Threat: reversion to static Nash, payo (s, 0) Implies constraint that V > s
V + W = λ V (W ) λ W
Extension: Other forms of revenue Suppose either inuencer gets v whenever f = 1, regardless of a. I.e. a xed term in the ad revenue function Examples: visible ads that are always on, attention seeking inuencer that values followers inherently Increases V for each d; good for followers Interpretation: Google's ad business (or a celebrity's attention-seeking nature) makes its a better source of advice May NOT be better for inuencer
Extension: Good advice that is also an ad Suppose that some good advice arrives even when a = 1 I.e. a xed term in the arrival rate function Interpretation: arrivals that are both good advice and generate revenue Similar to prior extension, but reduces incentive to reward good advice; might have come anyway Presents another reason not to regulate ads: lowers the return to ads that are both good advice and generating revenue, which is bad for followers
Summary Dynamic model of one sided trading favors with trust form of reputation Helpful for thinking about advice that is mixed with ads That sort of advice is not new but growing, and we will need models to think about those markets, and regulation of these markets Theory literature is already moving this way and can be adopted in IO Fundamental dierence from monetary transactions: actions to be regulated are sometimes what the consumer wants to avoid (spam) but the way the consumer pays for services. Can inuence the way we think about disclosure, competition, taxes, etc.