Social learning, social networks, & revenue optimization

Social learning, social networks, & revenue optimization Costis Maglaras Columbia Business School

Acknowledgments (chrono order): Bar Ifrach (Airbnb, Inc.), Marco Scarsini (SUTD) Davide Crapis (Columbia), Alireza Tahbaz-Salehi (Columbia)

2014 Mostly OM Conference Beijing, China

Ex.1: Book reviews

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Bestsellers receive high number of reviews on amazon: in the order of 10,000

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Average Score tends to be high in the first months after publication (few 1’s and 2’s)

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For many books average score stabilizes after some time (∼ 1yr)

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Reviews provide valuable information on book characteristics: unobservable otherwise

Ex.2: Advertising campaign on Twitter

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Targeting superstars: pushing a message through key nodes that can make it viral – eg.: sponsorship of US athletes in 2012 Olympics

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Array of Twitter promotional products: – – – –

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Promoted Accounts Promoted Tweets Promoted Trends Analytics

Pricing: – Pay per Engagement – # impressions; # retweets

Ex.3: “Social engineering" and election campaigns

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In 2012 US Presidential Elections, Obama invested a lot in social media: – Twitter account @BarackObama in the top ten worldwide (for followers and followed) – Facebook campaign: target swing-state voters; under age 29 ; had no listed phone number – Microtargeting: Analytics Team selects targets that are most likely to vote for Obama and asks supporters to target these specific friends

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2014 India Elections: – Narendra Modi becomes the second most “liked” politician after Obama – ∼ 20 millions likes; a single picture liked and shared by > 2.2 million people

Outline I

Broad research overview – – – –

interdisciplinary field of study (Econ / Socio / CS / Eng / OR/OM) typical questions some classic results modeling/analysis tools Bayesian learning; Naive learning; Information structures (signals vs. reviews);

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Price optimization in the presence of social learning – Bayesian learning models – naive learning models – revenue optimization

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Some interesting, unresolved questions (very partial list)

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References (brief list)

Interdisciplinary area of study I

Economics: – How do agents behave? Information structure? Do they learn? Empirical analysis. . . .

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Sociology: – Who to befriend? What network topologies emerge? Small world; Influencers (measures of centrality; connection to network models and (I − P)−1 . Experiments. . . . (not reviewed in this talk)

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Computer science: – Which nodes to target to achieve strongest word-of-mouth effect? How to detect cascades? Algorithmic considerations on social networks, . . .

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Engineering: – How to design networks and communication protocols to achieve fast and robust information propagation? Collaborative filtering, . . . , (questions and methodological tools are closely related to social network field of study – not reviewed in this talk)

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Operations research / Operations management – How to tactically influence consumers’ social learning with firm’s controls (pricing, service level) to optimize performance? . . .

Outline (2) I

Broad research overview (not exhaustive) – – – –

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interdisciplinary field of study (Econ / Socio / CS / Eng / OR/OM) typical questions some classic results modeling/analysis tools

Plan: review a handful of papers that highlight some important considerations (modeling, style of analysis, results, applicability)

Underlying themes: – Information: signals; heterogeneity; observable actions / reviews – Agent behavior: Bayesian (rational?) vs. “naive” learning mechanisms (tractable / plausible?) – Dynamics: t → ∞ analysis vs. characterization of transient path – Timing of decisions: exogenous or strategic (endogenous)

Economics literature on social learning (intro)

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Typical questions: – Do agents learn/herd asymptotically? – Agent behavior: how to aggregate observed information? Interaction? – When to purchase or adopt a new product/technology? (endogenous/strategic vs. exogenous timing) – What is the effect of the social network structure on learning outcomes and speed of learning? – What is the effect of pricing on the dynamics of social learning? – Empirical analysis of the effect of social learning and social network on market outcomes; Lab experiments on learning behavior.

Informational cascades (Bikhchandani, Hirshleifer, and Welch (BHW), 1992; Banerjee, 1992) I

product of unknown quality Q ∈ {0, 1}

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utility = V + Q − P

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agents are homogeneous wrt base valuation V ; static price $P

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Information structure: – – – – – –

exogenous sequence of agents i = 1, . . . arrive and make purchase decision prior belief π0 = P(Q = 1) = 1/2 agents receive iid private signals si = Q w.p. p > 1/2 agent i receives si , observes actions Aj of all predecessors j = 1, . . . , i − 1 forms a posterior for Q, πi i purchases (Ai = 1) iff V + Eπi (Q) − P = V + πi − P ≥ 0

– assume V − P = −1/2 so Ai = 1 iff Pπi (Q = 1) = πi > 1/2

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Q: do agents learn the true quality of the product?

Informational cascades (Bikhchandani, Hirshleifer, and Welch (BHW), 1992; Banerjee, 1992) I

product of unknown quality Q ∈ {0, 1}

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utility = V + Q − P

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agents are homogeneous wrt base valuation V ; static price $P

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Information structure: – – – – – –

exogenous sequence of agents i = 1, . . . arrive and make purchase decision prior belief π0 = P(Q = 1) = 1/2 agents receive iid private signals si = Q w.p. p > 1/2 agent i receives si , observes actions Aj of all predecessors j = 1, . . . , i − 1 forms a posterior for Q, πi myopic Bayes i purchases (Ai = 1) iff V + Eπi (Q) − P = V + πi − P ≥ 0

– assume V − P = −1/2 so Ai = 1 iff Pπi (Q = 1) = πi > 1/2

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Q: do agents learn the true quality of the product?

BHW (2): Bayesian updates & information cascades I

Posterior: π1,1 =

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P0 (Q = 1, s1 = 1) π0 p = =p P0 (s1 = 1) π0 p + (1 − π0 )(1 − p)

i = 1 (action): A1 = s1

(i.e., purchase if s1 = 1)


Posterior: π1,1 =

P0 (Q = 1, s1 = 1) π0 p = =p P0 (s1 = 1) π0 p + (1 − π0 )(1 − p)

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i = 1 (action): A1 = s1

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i = 2: – if s2 = s1 , then A2 = A1


(agent 2 knows that A1 = s1 )

– if s2 6= s1 , then “signals cancel out" and π2 = · · · = π0 ; A2 randomizes


Posterior: π1,1 =

P0 (Q = 1, s1 = 1) π0 p = =p P0 (s1 = 1) π0 p + (1 − π0 )(1 − p)

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i = 1 (action): A1 = s1

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i = 2: – if s2 = s1 , then A2 = A1


(agent 2 knows that A1 = s1 )

– if s2 6= s1 , then “signals cancel out" and π2 = · · · = π0 ; A2 randomizes

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i = 3: – if A2 = A1 , A3 = A2 irrespective of s3 – if A2 6= A1 , then i = 3 acts as i = 1

(informational cascade)

BHW (3): Bayesian updates – key insight I

Posterior: π1,1 =

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P0 (Q = 1, s1 = 1) π0 p = P0 (s1 = 1) π0 p + (1 − π0 )(1 − p)

Q: do agents learn the true quality of the product if they observe past sequence of actions?


Posterior: π1,1 =

P0 (Q = 1, s1 = 1) π0 p = P0 (s1 = 1) π0 p + (1 − π0 )(1 − p)

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A: “Cascade (or herding sample path)” w.p. > 0 to the wrong outcome


Posterior: π1,1 =

P0 (Q = 1, s1 = 1) π0 p = P0 (s1 = 1) π0 p + (1 − π0 )(1 − p)

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Why?


Posterior: π1,1 =

P0 (Q = 1, s1 = 1) π0 p = P0 (s1 = 1) π0 p + (1 − π0 )(1 − p)

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Why? – new information is not “sufficiently strong” to reverse a trend e.g., if π0 ≈ 1 and wrong – correct information was available but it was not used

Smith & Sørensen 2000: sufficient conditions for Bayesian social learning I

Bounded Private Beliefs (aka. Bounded Likelihood Ratio BLR): recall π1,1 =

P0 (Q = 1, s1 = 1) π0 p = P0 (s1 = 1) π0 p + (1 − π0 )(1 − p)

– cascade of k similar actions ⇒ πi ≈ 1 (or πi ≈ 0 if Aj = 0) – p has to approach 1 so as to “reverse" prior and “stop" cascade . . . so, bounded p, will allow incorrect cascades to occur – general signal structure: s ∼ F0 (when Q = 0) and s ∼ F1 (when Q = 1) BLR:

0