37 WashU Analytical Model
Interview:
Don’t even show your findings first (people will attack them)
Never deny that you have a problem (always accept or have good answers for your problem).
Only present summary, main results, and leave extension in the end if there is no question asked.
37.1 Platforms
37.1.1 (Jiang, Jerath, and Srinivasan 2011) Amazon’s midtail
Firm strategies in the “mid tail” of platformbased retailing
For two sellers on Amazon (high vs. low demand sellers), the threat to entry from the platform benefit them.
Upon entry, the platform decreases consumer surplus in the early period, while increases in later period
Intuitively, Amazon should sell highvolume products and independent sellers should sell lowvolume longtail products.
For midtail sellers, if they sell too good, they will be taken over by Amazon. Hence, reducing sales can avoid Amazon’s notice.

Findings:
After observing demand, the platform can separate the high demand and lowdemand seller by setting high fee. Thus only highdemand seller can remain, and later the platform will take the market share of these ones. With low probability of high demand, the platform can set low fee (which allows the highdemand sellers to mask).
The platform can forgo the option to independently sell altogether (so that both types of seller will provide high level of service and subsequently high sales). But both types of sellers prefer the threat of entry because of the low perunit fee for ex ante probability of high demand.
If the platform enters, it will reduce consumer surplus at first and increase it later.
With the consumer reviews (to proxy seller service quality), the platform can increase its optimal sales fee if the ex ante probability of a highdemand type is low and vice versa.

Related literature:
Internet retailing
Twosided market
Distribution channel
Asymmetric information games
Model
Amazon’s fixed cost: \(F >0\)
Seller fixed cost = 0 (sunk)
Demand in each period
\[ q^{(i)} (p, e) = \gamma + e{(i)}  bp^{(i)} \]
where
\(p\) is the price of the product
\(e\) = service level
\(\gamma, b\) are constant
Uncertainty about product (= uncertainty about the seller’s type:
 High with probability \(\theta\)
 Low with probability \(1  \theta\)
Perunit marginal cost is \(s(e) = k e^2\) where \(k\) is constant
There are two conditions for Amazon to make decisions:
 If the fixed cost is too high, Amazon will let the sellers to sell
 If the fixed cost is low enough, and Amazon know the true demand is high (\(\gamma = \gamma_H\)) then it will sell directly
Twostage game:
 Nature determines the seller’s type, Amazon charge a perunit fee \(f\) (constant in 2period). Sellers choose to sell or not (both service level \(e^{(1)}\) and price \(p^{(1)}_t\) where \(t \in \{L,H\}\))
 Amazon updates beliefs about the seller’s type, Amazon decides to sell directly or not.
3 case studies:
 Amazon with full info
 Amazon promises to not enter: without threat, both types of seller will have the same service levels for both periods
 Amazon with incomplete info and decide whether to enter

Separating equilibrium, based on the fee \(f\)
Htype could mimic Ltype to avoid Amazon notice
Only Htype can sell on Amazon. Hence, it makes profit in the first period and 0 in the second.
Pooling equilibrium

37.1.2 (Zou and Zhou 2021) search neutrality

Counterintuitive idea: Search neutrality hurts consumers, but good for platforms (due to reduced price competition)
Search neutrality decreases seller’s price competition (only apply to online platform with personalized search, not to offline store with uniform display)
it decreases consumer surplus but increases consumer’s search relevancy
Search neutrality is different from net neutrality

Related literature:
Intermediary biases (e.g., recommendation results, copycat products, etc.)
Consumer search
Model
2 groups of consumers:
Consumer prefer firstparty products than thirdparty products
Consumer prefer thirdparty over firstparty
Consumer dynamics (sequentially):
 Presearch:
no costs
Consumer learn expected valuations from presearch
 Search:
 Search costs to determine match and exact value
Consumers’ action set
 buy the prominent product
 end search (no purchase)
 incur search cost to inspect nonprominent product
3 stages:
 Set prices
 Personalized search rankings
 Consumer purchase
It’s still hard to implement the search neutrality policy (similar to the loan policy is not based on race).
Tradeoff between commission (profits from true ranking) and product sales from fake order. (but in the paper, they already assumes that the platform capture higher profits from selling the firstparty products)
37.1.4 (GalOr and Shi 2022) Subscription platform
Designing entry strategies for subscription platforms
Platforms like ClassPass (fitness) or MoviePass, MealPass, Inspirato Pass (hotel and resorts) offer physical service subscriptions.
Reason for limited offer is the transportation cost

2 conditions:
Consumers: varietyseeking
High transportation cost
Assumptions:
 One platform offers a bundle of two vendors (on the Hotelling’s line)
Possible variables in contract:
Quality of the service
Transfer payments between the platform and the vendor: variable fee per customer + fixed fee
The number of platform customers that vendors agree to serve.
No deal if there are only 2 variables: a fixed transfer payment + quality of service (due to intensified competition in prices). Only when we add either (1) transfer fee per customer or (2) the number of customers the that vendors agree to serve.
Additional requirement: balanced bargaining positions between vendors and the platform.
Recommendations:
Enter markets where vendors are differentiated (varietyseeking consumer will be enticed > higher industry profits)
Weak competitions between vendors (e.g., local vendors are local monopoly because of high transportation cots)

Appropriate tools to avoid price competitions:
transfer fee per customer
impose restrictions on the quantity
Do not: offer lower quality service for platformuser as compared to vendorusers. (restrictions on quantity is better than restriction on quality).
Contributions:
Bundling: Different from retailer’s bundles, because platform (bundle) competes against the independent sellers as well. Different from information goods bundling, this study provides suggestion on the bundling of physical services
Platforms: different types of platform (e.g., as a marketplace, as a retailer), this study focuses on competition between a platform (not an independent seller) and vendors.
Channel management: possible only when there is little price competition.
Model
2 vendors, 1 platform
\(p_i\) = price charged by vendor \(i\)
\(s\) = subscription fee charged by the platform.
\(v\) = gross utility

\((1 + \alpha) v\) is the gross utility when the consumer wants variety where \(\alpha \in (0, 1]\)
 \(\alpha\) denotes the preference for variety
If we assume that the vendors offer \(0 \le k_i \le 1\) (lower quality service) to the platforms subscribers, the gross utility will be \([(k_1 + k_2)/2](1+ \alpha)v\) (i.e., the gross utility reduced by the average quality offered by vendors). (not too sure why the authors introduce this assumption so early)
Say that a subscriber after purchasing the pass, only utilize one, her utility is \(k_i v\)
The net utility when a consumer pick only \(i\) is
\[ U(x_i, \text{only vendor } i) = \max\{[ v tx_i  p_i], [k_i v  tx_i  s]\} \]
Either the customer has to purchase directly, or via the platform
The net utility when a consumer want to choose both
\[ U( x_i, \text{both vendors} ) = \max \{ [ (\frac{k_1 + k_2}{2}(1 + \alpha) v  t  s], [ (1  \alpha) v  t  (p_1 + p_2)] \} \]
again, either purchase from the platform, or directly from the service providers.
Notice difference in transportation costs between one or two services utilization.
Restriction for model tractability: \((1+ \alpha)v  t >0\) (see for both vendors) means that consumers always derive a net positive (not including total price paid). (questionable assumptions)
In a market that has both vendors and platform (i.e., positive market share), their prices have to satisfy:
\[ p_1 + p_2  v(1+ \alpha)[1  \frac{k_1 + k_2}{2}] \ge s \ge p_i  (1  k_i) v \]
Lower bound: if a consumer only buys from one vendor, she will directly purchase it from the vendor
Upper bound: if a consumer wants to buy both, she will subscribe.
Defensible assumptions:
 Vendors continue to offer services independent of the platform
 If there is no market share for vendors (i.e., vertical integration), it will attract antitrust law suit.
Market share:
\[ MS_i = x_i^* = \frac{t + s  p_i  v[(\frac{k_1 + k_2}{2})(1 + \alpha)  1]}{t} \]
where \(i, j = 1,2; i \neq j\)
and
\[ MS_p = \frac{v[(k_1 + k_2)(1 + \alpha)  2]  t  2s + p_1 + p_2}{t} \]
Stages:
 The platform decides whether to negotiate with the vendors
 The platform negotiates with the vendors separately (i.e., different terms, different contracts)
 Pairwise negation between the platform and the individual vendors, use Generalized Nash bargaining solution
 The parties (vendors + platform) set prices noncooperatively and independently
2 regimes (common variables: The quality of the service \(k_i\) and the fixed payment \(F_i\)):
 Variable transfer fee: Fee per customer \(m_i\) > higher platform fee > lower market share
 Quantity restriction: Number of customers agree to serve \(y_i\) > directly lower market share
Pairwise negotiations:
 Platform vs. vendor 1: \(k_1, F_1, m_1\) (or \(y_1\))
 Platform vs. vendor 2: \(k_2, F_2, m_2\) (or \(y_2\))
To establish the Generalized Nash Bargaining solution, we have to see the outside options for each party
 Platform = 0: cannot be formed if there is no agree with either vendor
 Vendor (pick only the equilibrium that yields the highest aggregate industry profits because of allowance for side payments): \(w_i = f(\alpha, v, t)\)
Lemma 1: The best possible outside option for both vendors (\(w_1 + w_2\)) to be highest satisfy 4 conditions
When  \(w_i\)  Implication 

\(\frac{1}{1 + \alpha} < \frac{v}{t}< 1\) Since the transportation cost is so high, the market is not covered (i.e., those far away drop out, and those in also go to one vendor) 
\(w_i = \frac{v^2}{4t}\) Each vendor becomes local monopoly (\(\pi_i = w_i\)) 
Without the platform, the lower the transportation cost, the more intense the competition on price is. 
\([\alpha < \frac{2\sqrt{2}}{e} \& 1 \le \frac{v}{t} \le \frac{3}{2}]\) or \([\alpha \ge \frac{2\sqrt{2}}{3} \& 1 \le \frac{v}{t} \le \frac{1  \sqrt{1  \alpha^2}}{\alpha^2}]\) Market is covered Consumer only buys from 1 vendor 
\(w_i = \frac{1}{2}(v  \frac{t}{2})\) Multiple equilibrium satisfying sum of vendors prices equal \(2v  t\) 

\(\alpha < \frac{2\sqrt{2}}{3}\) and \(\frac{3}{2} \le \frac{v}{t} < \frac{\sqrt{2}}{\alpha}\) Low transportation cost and low variety seeking parameter \(\alpha \le (2 \sqrt{2})/3\) Consumer only buys from 1 vendor 
\(w_i = \frac{t}{2}\)  Price competition is intense 
\([\alpha < \frac{2 \sqrt{2}}{e} \& \frac{\sqrt{2}}{3}\le \frac{v}{t} \le \frac{2}{\alpha}]\) or \([\alpha \ge \frac{2\sqrt{2}}{\alpha} \& \frac{1 + \sqrt{1  \alpha^2}}{\alpha^2} \le \frac{v}{t} \le \frac{2}{\alpha}]\) 
\(w_i = \frac{(\alpha v )^2}{4t}\)  Most intense competition 
Then the Generalized Nash Bargaining solution can be formulated
under the “variable transfer fee”
\[ \begin{aligned} \max_{k_i , m_i, F_i} NB_{ip} &= [MS_i p_i + m_i MS_p + F_i  w_i]^\beta[MS_p (s  m_i  m_j)  F_i  F_j ]^{1  \beta} \\ &= [\text{net vendor i account for outside option}][\text{net for the platform}] \end{aligned} \]
where \(i, j = 1,2; i\neq j\)
under the “quantity restriction”
\[ \begin{aligned} \max_{k_i , y_i, F_i} NB_{ip} &= [MS_i p_i + F_i w_i]^\beta [MS_p s  F_i  F_j]^{1 \beta} \\ &= [\text{net vendor i account for outside option}][\text{net for the platform}] \end{aligned} \]
where \(i, j = 1, 2; i \neq j\)
and \(\beta\) = negotiating power of vendor \(i\) and
\(1  \beta\) = negotiating power of the platform
Prerequisites for the existence of the platform
 The total surplus upon agreement with both vendors is higher than the sum of outsides options
\[ TS = s MS_p + p_1 MS_1 + p_2 MS_2 > w_1 + w_2 \]
(shouldn’t it only be \(p_1 MS_1 + p_2 MS_2 > w_1 + w_2\), why do we need to include \(s MS_p\))
 Under the “variable transfer fee” regime, parties can make decisions on quality of service \(k_i\) and fee per customer \(m_i\) of vendor \(i\) and the platform (given the deal with \(j\) is done already)
\[ \max_{k_i, m_i} TS_{ip} = (s  m_j) MS_p + p_i MS_i F_j \]
(This should be the total surplus \(TS = (s m_1  m_2) MS_p + p_1 MS_1 + p_2 MS_2  F_1  F_2\)
 Under the quantity restriction regime, parties can negotiate on quality of the service \(k_i\) and number of customer agree to serve \(y_i\) for vendor \(i\) and platform (given the deal is done with \(j\) already)
\[ \max_{k_i, y_i} TS_{ip} = s MS_p + p_i MS_i  F_j \]
Introduction of the platform can increase the industry total profit because it widens to pie to include people who value variety and those who are farther away from either vendor.
Proposition 1: With only two variables: (1) \(k_i\) (quality service) (2) \(F_i\) (fixed payment), there will be no agreement.
But with either regime, agreement can be reached
 Variable transfer fee
Maximization problems (i.e., setting prices to maximize profits):
\[ \begin{aligned} \max_{p_i} \pi_i &= p_i MS_i + m_i MS_p + F_i \\ &= \frac{p_i [ t+ s  p_i  v[(\frac{k_1 + k_2}{2})( 1+ \alpha)  1]}{t} \\ &+ \frac{m_i [v[(k_1 + k_2)(1 + \alpha)  2]  t  2s + p_1 + p_2]}{t} \\ &+ F_i \end{aligned} \]
where \(i = 1, 2\)
and
\[ \begin{aligned} \max_s \pi_p &= (s m_i  m_j) (MS_p)  F_i  F_j \\ &= \frac{(s m_i  m_j ) [v[(k_1 + k_2)(1 + \alpha)  2]  t  2s + p_1 + p_2]}{t}  F_i  F_j \end{aligned} \]
After solving
\[ p_i = \frac{6t + 11 m_i + 5 m_j  2v [( 1 + \alpha)(k_1 + k_2)2]}{12} \]
\[ MS_i = \frac{6 t  m_i + 5 m_j  2v [(1 + \alpha)(k_1 + k_2) 2]}{12} \]
and
\[ s = \frac{v[(1 + \alpha) (k_1 + k_2)  2] + 5 (m_1 + m_2)}{6} \]
\[ MS_p = \frac{v (1 + \alpha)(k_1 + k_2)2]  (m_1 + m_2)}{3t} \]
Both \(p_i, s\) increase with \(m_i\) (variable transfer fee) while if we were to negotiate on ly on \(k_i\) (quality), only \(p_i\) will increase while \(s\) will decrease. Allowing for negotiation based on variable transfer fee can facilitate agreement.
Since in the second stage, we have to make that the indifferent customers can buy from both the vendor and the platform. And the net payoff of platform customers are equal (because of same transportation cost)
\[ \max_{k_i, m_i} TS_{ip} = p_i MS_i + (s  m_j) MS_p F_j \]
where \(i, j = 1,2\) subject to (non negative utility for the indifferent customer)
\[ U(x_i^*) = (1 + \alpha) v  t  S \ge 0 \]
Proposition 2:
With the addition of the “variable transfer”, the platform can enter the market. And it has the following properties:
 \(k_1 = k_2 =1\) (same quality both platform and vendor users) (both parties have no interest to offer different quality because of cannibalization) and the whole market is covered.
 For the entry of platform, the variety parameter \(\alpha\) has to be big. If the negotiating position of the platform increase (greater value of \(\alpha\)), the negotiating powers of each vendor should improve as well (i.e., weak competition between the vendors).
Isn’t big value of the variety parameter is the same thing as the two vendors are very much differentiated? No, because two vendors can be local monopoly that has no incentive to agree with the platform (unless there is a segment of consumers that you could serve additionally).
 When before entry competition was weak, the surplus of platform customers will be realized upon entry
 When before entry competition was strong, the platform customer only derive a positive surplus only when the competition continues to be strong (big value of \(\frac{v}{t}\))
 The payoff for the parties are
\[ pi_i = \frac{\beta}{1 + \beta}[ TS + \frac{w_i (1  \beta)}{\beta}] \]
and
\[ \pi_p = \frac{1  \beta}{1 + \beta} [ TS  2w_i] \]
 Quantity Restriction Regime
To specify \(y_i\) as the number of customers vendor \(i\) agrees to serve, we can either use (1) \((y_1 + y_2)/2\) or \(\min(y_1, y_2)\) (the first specification is easier to understand and solve while both yield the same results)
When 2 vendors pick the price and platform inherit its price:
Since the market share is \(MS_1 + MS_2 + MS_p = 1\) and \(MS_p = (y_1+y_2) /2\), the subscription fee is
\[ s = \frac{p_1 + p_2 + v[(k_1 + k_2) (1 + \alpha) 2]}{2}  \frac{t(2 +y_1 + y_2)}{4} \]
(the result is similar when one vendor and the platform picks the price)
Proposition 3: with quantity restriction, an agreement can be reached where
 \(k_1 = k_2 1\) and the market is covered
 When before entry, vendors were local monopoly the variety parameter needs to be sufficiently high
 With moderatle beforeentry competition, consumers can still yield benefit from the platform
 Under very strong competition that consumers always yield positive payoff, and there is no agreement.
Proposition 4: (only under the regions where both regimes exist) industry total profit is higher for the variable transfer fee if \(\frac{9}{4 + 6 \alpha} < v/t\) (i.e., when the transportation cost is small and variety parameter is big), otherwise the restriction on quantity regime is better.
Future research:
Assume: sellers with different market power
Sellers could also bundle products (subscription)
Learning model: customers only use platform to figure out their preference, then pick 1 vendor.
Multiple round negotiation.
37.1.5 (Long, Jerath, and Sarvary 2022) Design Amazon marketplace
2 sellers on a marketplace with search query that consists of sponsored and organic listings.

Consumers preferences are jointly determined by vertical and horizontal aspects.
Vertical component: asymmetric info that are known only by the sellers (product quality \(q_i \sim U(0,1), i \in (1,2)\)).
Horizontal component: asymmetric info that are known only by the platforms about the consumer preference (personal fit \(\lambda_{ki} \in U(0,1), i \in (1,2)\))
Products and sellers will either be match (\(\sim Ber (m_{ki})\)) or no match
The match probability is
\[ m_{ki} = \theta_k q_i + (1 \theta_k) \lambda_{ki} \]
where
 \(\theta_k\) (consumer’s private info) the relative weight that consumer \(k\) put on the vertical vs. horizontal components.
 \(q_i\) = seller’s private info
 \(\lambda_{ki}\) = the platform’s private info
 All three parameters follow \(\sim U(0,1)\)
Platform chooses seller to put in the organic slot with the highest value of
\(T\tilde{q}_i + (1 T) \lambda_{ki}\)
where
\(T\) = info weight (i.e., info sharing parameter)
\(\tilde{q}_i\) = partial info on product quality from the auction
\(\lambda_{ki}\) = platform’s personal fit info
Assuming that the bidding price from seller to the ad place reveals some info about their product quality
Platform’s revenue can come from either
 Sales commissions: \(\phi \in [0,1]\) (percentage charge per transaction)
 Ad Revenue (either payperclick payment rule or payperimpression)
Timeline
 Platform decides on \(T\) (info weight) and \(\phi\) (commission rate)
 Sellers decide to join
 Consumers decide \(\theta_k\) (personal preference), sellers decide on \(q_i\) (quality), platform decides on \(\lambda_{ki}\) (platform’s private info)
 Sellers bids \(b_i\)
 Platform infers \(\tilde{q}_i\) from \(b_i\) and decides who gets the ad placement
 Consumers decide on \(m_i\) (matching probability), search
Analysis
Additional assumption: seller’s bid \(b(q_i)\) strictly increases in \(q_i\) (verifiable in the seller’s optimal bidding behavior)
Then, the platform can infer the true value of \(q_i\) from sellers’ bids and places the seller with the higher \(Tq_i + (1T) \lambda_{ki}\) in the organic result
Hence, consumers also infer that ad position is seller with higher product quality (\(q_i\)) and organic place is the seller with higher \(Tq_i + (1T) \lambda_{ki}\)
Consumer choice:
When the same seller appears in the ad and organic result (she is the higherquality seller) (results don’t change with multiple slot

When the ad slot seller (\(i\)) (higher quality product) is different from the organic slot (\(j\)) (higher personal fit)
\(i\) is chosen, if consumer value quality more
\(j\) is chosen, if consumer value personal fit more.
Seller’s Ad Bids: optimal bid verifies the bidding behavior of sellers (seller with higher product quality is going to bid higher)
Platform’s Sales Commission and Ad revenue
Sales Commission: \(\phi D(T)\)
Ad revenue: \(2 \int_0^1 \int^{q_i}_0 b(q_i) dq_i dq_j\)
Proposition 2: Sales Commission revenue is concave while Ad revenue is increasing.
Sales is concave (information effect of strategic listing) because if
 \(T\) is too small (personal fit is overvalued), consumers will not benefit from the product quality info revealed from sellers’ bids
 \(T\) is too large (product quality is overvalued), consumers will not benefit from the personal fit info, in turn worsen the match probability.
Ad revenue is increasing (competition effect of strategic listing):
 As \(T\) increases, platform ad revenue increases (because sellers’ probability of being in the ad slot as well as the organic slot increases)
Platform’s design decision
 Platform’s choice of commission rate (fixed platform’s info weight \(T\)): the total revenue increases with the commission rate because commission revenue (from both organic and ad slots) dominates the losses in ad revenue (from only the ad slot)
 Platform’s choice of commission rate (fixed platform’s info weight \(T\)) and the sellers’ have an outside option \(u_0\) is \(\phi^* = 1  \frac{u_0}{U(T, 0)}\), meaning as the optimal commission rate decreases as \(T\) increases because a larger \(T\) increase the bids and increases advertising fee.
 With varying info weight and commission rate
If seller’s outside option is small (first region), the optimal commission rate decreases as seller’s outside option increases
If the sellers’ outside potion is intermediate, the optimal information weight decreases as seller’s outside option increases, and the optimal commission rate is 0
If the outside option is large enough, sellers will not participate in the first place.
Extensions:
 Comparison with Independent listing (no strategic listing  using info from the bidding side to list organic search): When comparing with the benchmark that there is no strategic listing behavior, the commission ate under strategic listing leads to lower commission revenue, but higher advertising revenue. Hence, overall the platform benefit from strategic listings
 Comparison with Independent Listing (Under Exogenous Commission rate)
If the commission rate is small, strategic listing leads to higher to both higher commission and advertising revenue
If the commission rate is intermediate, strategic listing leads to lower commission and ad revenues
If the commission rate is large, both listing strategies lead to 0 revenue.
 When seller’s information \(q_i\) and platform’s info \(\lambda_{ki}\) overlap (correlated), results do not change
37.1.6 (Hajihashemi, Sayedi, and Shulman 2021) Personalized Pricing with Network Effects
 Read (Katz and Shapiro 1985) for fulfilled expectations equilibrium
Stages
Without personalized pricing
Firms know the type of consumers, set uniform price \(p\)
Consumer \(i\) knows \(p_i, s_i\)
With personalized pricing
 Firms know the type of consumers, set price \(p_L, p_H\)
 Consumer \(i\) only knows
Proposition 1: Without network effect, price personalization leads to a lower equilibrium price for consumer \(L\), but with network effect, price personalization leas to higher equilibrium for consumer \(L\)
 If the network effect is too small, the marginal effect of price decreases on the reservation price is minimal.
Proposition 4: Consumer Surplus: price personalization can decrease the unconditional expected surplus of consumer \(L\)
37.2 Dynamic Pricing and Bundling
 A monopolist sells products in a bundle to homogenize consumer heterogeneity in willingness to pay for individual products. and to sell individual products to price discriminate
37.2.1 (Prasad, Venkatesh, and Mahajan 2017) Bundling

3 static bundling strategies:
Products are sold separately (pure components PC)
Products are sold only in a bundle (pure bundling PB)
Products are sold under both (mixed bundling MB) seconddegree price discrimination

Selling products under the
purebundling in two stages is optimal when the marginal costs are low
pure components in two stages is optimal when marginal costs are high (with lots of myopic consumers)
pure bundling then pure components is optimal when marginal costs are moderate (with lots of strategic consumers)
mixed bundling in both stages when the market is mostly strategic consumers.

Scenario:
PBPC: bundle first then component
PCPB: component then bundle

Assumptions:
Monopoly with either high or low marginal cost
Heterogeneous consumers (regarding product preference)
2 types in the population: myopic (\(\alpha\)) (maximize at each stage independently) and strategic \((1 \alpha)\) (maximize both stages)
Marginal cost of the bundle = sum(component costs)

Interesting
 optimal bundle price can be higher than the sum of individual products

Literature:
Bundling
Intertemporal pricing
PCPC
Demand for each product from myopic consumers in the first stage is \((1P) \alpha\)
\(P  \delta\) is the price for the second stage where \(\delta\) is the discount.
Demand for each product from myopic consumer in the second stage is \(\alpha \delta\)
Demand for each product from strategic consumer is \((1\alpha)(1  P + \delta)\)
For the seller, the first stage profit is \(2(Pc) (1P)\alpha\)
and the second stage profit is \(2(P  \delta  c)[\alpha \delta +(1  \alpha)(1  P + \delta)]\)
Hence, optimal prices are
\[ P_1 = \frac{1 + c}{2} + \frac{(2  \alpha)(1  c)}{2(4  \alpha)} \]
and
\[ P_2 = \frac{1 + c}{2}  \frac{\alpha (1c)}{2 (4  \alpha)} \]
the total profit is
\[ \frac{2(1c)^2}{4  \alpha} \]
37.2.2 (Diao, Harutyunyan, and Jiang 2019) Intertemporal price, consumer fairness concern
Consumer fairness concerns (unfair due to increased price) lead to lower retail prices in both periods while the wholesale prices might be higher in the first period.

Consumer fairness concerns can decrease the first and second period retail prices.
 The intuition that retailers increase in the first period and decrease in the second period only hold under a centralized system (wholesale to consumer), not under a decentralized one.
If the demand intercept does not raise much in the second period, the cost reduction incentive usually prevails over fairnessmitigation incentive.
A larger secondperiod demand can cause both the producer and the store to lower their pricing.
When consumers have fairness costs, the secondperiod equilibrium unit sales is actually still higher than when they don’t, because fairness concerns alleviate the doublemarginalization problem.
To model fairness concern heterogeneity, they model 2 types of consumers (those with fairness concern and those without), where \(\alpha\) is the fraction of customer with fairness concerns. And it should affect the retailer’s secondperiod demand function.
37.2.3 (Dana and Williams 2022) Intertemporal price
Oligopoly model

Pricing on capacity:
 fixed capacity, firms dynamically set price.

Stage:
Choose capacity
Compete in prices
Inventory control (i.e., sales limit restriction) can help mitigate price competition.

Contributions:
Equilibrium prices are flat or uniform over time
Intetemporal price discrimination is possible when firms adopt inventory controls (if the demand is more inelastic over time).
Firm choices: capacity and 2 prices (2 periods)
37.2.4 (Kolay and Tyagi 2022) Event bundle
Two events sold as a bundle in 2 periods.

Contribution to current literature:

Consumer expectations of future prices
Durable goods pricing
Product obsolescence
Loyalty programs
Consumer uncertainty regarding valuations


Features:
Events with different popularity
Popular event in stage 1 or 2
Consumers can be uncertain about their valuation of the second event
Uncertainty in seller’s commitment to the price of a future event
Consumers valuations are independently distributed or positively correlated

Examine when it’s optimal to sell
event independently
as a bundle
or mixed

Events are different from products in that are
perishable
temporal
If the seller can choose the order of introduction, popular events should be saved for later. (“save the best for last”). Similar to that we introduce the lower quality products before the higher quality ones. (K. S. Moorthy and Png 1992)
Model
Consumer valuation of the less popular event \(L\) is \(v_L \sim U(0,1)\) and of the more popular event \(H\) is \(v_H \sim U(0, 1 +x)\) where \(x\) represents how more popular the second one is (i.e., the proportion of consumers preferring \(H\) over \(L\)).
Consumers understand the order and importance of events before the game begins.
Demand function depends on seller’s strategies
No bundling at all: consumers only buy products \(L, H\) can only be purchased separately
Pure bundling: Either buy bundle or not
Full and partial mixed bundling: can buy either \(L, H\) separately or in a bundle.
37.3 Consumer Fairness
Also see (Diao, Harutyunyan, and Jiang 2019)
37.3.1 (Fu et al. 2021) Unfair machine learning algorithms

Compares the consequences of Equal treatment (ET) and equal opportunity (EO)
Regular and protected groups are better off if we change from ET to EO?
Optimal learning efforts under ET and EO?
Is the firm better off if ET to EO?
Strategic behavior of a firm: decide the amount of leaning effort. The firm invest for better ML algorithm to predict the outcomes.
Settings
Consumers
Good consumer (nondefaulters) and bad consumers (defaulters)
Consumers are in either regular or protected group
Firm
Riskneutral, and want to select good consumers
Invest in ML by paying the learning costs to separate the good and bad consumers
Set approval thresholds for each group
A fairness constraint: either ET or EO
Main Results:
Firm less motivated to invest in learning under EO than under ET
Profit is lower under EO because it’s hard to separate the good and bad consumers in the protected group

EO makes everyone (regular + protected) worse off
Regular group has higher threshold under EO (than under ET)
Firm invests less on the algorithm under EO
Model
Firm
accepts or rejects an application
A consumer can either be good or bad
the profit/loss (\(\alpha, \beta\)) where it comes from good/bad consumer
firm exerts leaning efforts (s) for better separability between the two groups
Consumer
Either regular or protected (size = 1)
% of bad consumer in each group is \(d\)

Expected gains:
\(\alpha_p = \alpha(1  d_p), \beta_p = \beta d_p\)
\(\alpha_r = \alpha(1  d_r), \beta_r = \beta d_r\)
The bank uses ML and assigns scores to candidates to represent their goodness where \(\gamma_r, \gamma_p\) are learning efficiency
Summary
 The optimal threshold and the profit depend on \(\beta_p\)
37.4 Decentralized Channels
37.4.1 (Jiang and Tian 2022) Reactive capacity on product quality and profitability in uncertain markets
Under “pull” contracts, the retailer designs the product quality and makes the wholesales and retail pricing decisions, but the risk of excess production is assumed by the upstream suppliers or contract manufacturers, rather than brandowning retailers or OEMs.
How much improvement in reactive capacity will benefit the supplier and how much it will benefit the retailer?
Model
Production Setup
A supply chain where before the selling season, a brandowning retailer designs a production quality \(q\) and offers a wholesale price \(w\) to outsource its production to ta supplier.
At the beginning of the selling seasons, the retailer will decide how many units \(Q\) of the product to order from the supplier and choose its retail price \(p\)
Supplier’s marginal cost = \(k q^2\)
Market uncertainty setup
Then consumer utility from product with quality \(q\) at price \(p\) is \(u = q \theta  p\)
where \(\theta\) is the consumer’s WTP
Assume that the market uncertainty is about the distribution of the consumer’s rather than about the total number of consumers in the market. Then a fraction of \(\alpha \in (0,1)\) of consumers have \(\theta = \theta_H\)
Time setup
Supplier’s production lead time \(T\) = total production time + shipping and handling
\(T = T_S + \frac{N}{c}\) quantity independent time + quantity dependent time
Denote A as the acceptable delivery time. The supplier will have to manufacture the product before the selling season if \(T_s > A\) and could produce some units during the selling season other wise
The market outcome \(T_S > A\) is equal to \(T_S = A\)
Model
The supplier’s reactive capacity is measured by \(\bar{Q}\), which is the maximum quantity (number of units) of the product that the supplier can produce and deliver to the retailer within the selling season
\(T = T_S + \frac{Q}{c} \le A\) Hence, \(\bar{Q} = (A  T_s)c\)
The supplier’s reactive capacity, \(\bar{Q}\) is driven by both the amount of production capacity \(c\) and how reactive and flexible that capacity is (\(T_s\))
Whether is it the retailer or the supplier that bears the inventory risk?
Timeline

Before selling seasons
Retailer decides product quality and wholesale price
Supplier: preseason inventory I

Within the selling seasons
\(\alpha\) is known to the retailers
Retailer: product quantity \(Q\)

Supplier:
\(Q \le I\) revenue \(w Q\)
\(Q>I\) decide \(I' \le \bar{Q}\) to produce within A
Retailer: selling price
Consumer: purchase decisions
Analysis
Without market uncertainty (\(\alpha = \alpha_g = \alpha_b\))

With market uncertainty

Extreme cases
 When \(\alpha_b \ge \frac{\theta_L}{\theta_H}\) even the bad market has many highvaluation consumers, the retailer will find it optimal to charge a high price to target only highvaluation consumer regardless of the market state

Inbetween cases
Low reactive capacity

Medium reactive capacity
Opportunistic targeting with stockout: the retailer sets the wholesale price low at the supplier’s marginal cost and the supplier will produce the riskfree inventory of \(I = ag\)
Opportunistic targeting with overstock: the retailer chooses a high wholesale price to induce the supplier to optimally produce a higher preseason inventory of \(I = 1  \bar{Q}\)
High reactive capacity: the supplier has enough time to produce during the selling season within the acceptable delivery time. Anticipating the supplier’s high ability to fulfill its order, the retailers will target only high valuation costumers at a high retail price

37.4.2 (Hu, Zheng, and Pan 2022) Wholesale vs. Agency
Literature

Distribution channels
Previously examine wholesale contract and downstream consequences (double marginalization problem)
This paper examines channel efficiency of agency contract.
Strategic contract choices: wholesale vs. agency
Retail passthrough
Model setup
\(n \ge 2\) competing suppliers selling substitutable products to consumers through a dominant online retailer \(r\)
Each supplier has a unique product
Assume same marginal cost across supplier, etailer has marginal cost for each unit of products demanded by costumers
Demand structure
Consider the demand of product is given by continuous \(q_i(p)\)
where \(p\) = market prices
Common assumptions:
 Demand is downward sloping
 Demand function is symmetric
Let \(\gamma >0\) be the product substitutability for specific demand function
\(\lambda(p) =  \frac{q(p)}{q'(p)}\) be a measure of sensitivity of demand
Additional assumptions on \(\lambda(p)\)
 profit functions are quasiconcave
 elasticity of demand decreases with \(p\) increases
Game Structure
Wholesale
 Supplier announces wholesale price \(w_i\)
 Etailer sets selling price \(p_i\) for each product
Agency
 Etailer sets revenue share rate \(1  \alpha\)
 Suppliers can choose to accept and sell directly to costumers on etailer platform, setting retail prices \(p_i\)
37.5 Consumer Search
37.5.1 (Jiang and Zou 2020) Consumer Search and Filtering on Online Retail Platforms
Findings
Lower search cost reduces seller’s profit margin (due to increased competition), but also attract more consumers to the platform

If referral fee is exogenously determined, a decrease in search cost can either increase and decrease the platform’s profit

Hence, platform should compensate by raising its referral fee, but it actually depends on the effect of search cost on demand elasticity:
If the search cost increases the demand elasticity, platform should lower its referral fee
If the search cost decreases the demand elasticity, the platform should increase its referral fee.

If referral fee is set optimally, the platform’s profit will increase (kinda intuitive)
With the filtering feature, consumers will be more likely to buy after searching due to reduction in uncertainty about the product match value for consumers
Motivation:
The search costs tend to decrease overtime
However, there is not study that study the platform’s optimal referralfee in respect to search costs, filtering.
Research questions:
How search cost affects optimal referral fee and profit?
How filtering affects the platform, sellers, and consumers?
How filtering impact differs from that of a reduction of the search cost?
Results are robust to
heterogeneous search costs
heterogeneous product quality
platform charges a fixed perunit referral fee (instead of percentage)
Related Literature
Consumer search: mixed literature on whether to increase or decrease search cost
Information structure effect on consumer search and firm profits

This paper:
Add filtering (different from target search)
search cost affects platform’s and sellers’ optimal pricing decision
search cost affects platform’s optimal referral fee
Setup
Horizontally differentiated products
After search (cost), consumers learn the price and match value (with the product)
Match value = f(filterable match value + unfilterable match value)
Consumer utility
\[ u_{ij} = M_{ij} + p_i \]
where

\(M_{ij} = \mu_{ij} + m_{ij}\) = match value of product \(i\) to consumer \(j\)

\(\mu_{ij} = \delta \times \hat{\mu}\) = filterable match value
\(\delta >0\) is a cosntnat scale factor
\(\hat{\mu}\) = meanzero discrete random variable with \(K\) realizations
\(m_{ij}\) = unfilterable match value
It’s ok if \(\mu_{ij}\) correlates with \(m_{ij}\)

\(p_i\) = product price
Consumer search
 Consumer know her outside option \(u_{0j}\) and \(\mu_{ij}\) (filterable match value)
 Consumer do not know \(m_{ij}\) (match value) and price before hand, only after search cost \(\tau\)
Consumers decisions
 Whether to search on the platform
 Search sellers sequentially and learn \(m_{ij}\) and \(p_i\)
 Consumers can buy, search more (to the next product with highest \(\mu_{ij}\)), and leave
Game Timing
 Retail platform sets a percentage referral fee \(r \in (0,1)\)
 Sellers set price where profit is \((1r)p_ic\)
 Consumers make search and purchase decisions.
Notes:
\(p^*(r)\) = equilibrium retail price
\(r^*\) = optimal percentage referral fee
In equilibrium, consumers will continue search until the next product expected utility beyond \(u_{ij}\) is less than \(\tau\) (search cost) (Wolinsky 1986)
Result 1: consumer purchase if \(m_{ij} \ge \bar{m} (\tau)\) where \(\bar{m}(\tau)\) satisfies \(\int_{\bar{m}(\tau)}^{m_{max}} (m  \bar{m}(\tau)) dF(m) = \tau\)
Result 2: \(\bar{m}(\tau)\) decreases with \(\tau\)
In equilibrium, \(\bar{m}(\tau)\) is the equilibrium acceptance threshold for the unfilterable match value
For exogenous referral fee
Lemma 1: retail price, sellers’ profit, total demand
Result 3: As the cost of searching reduces, a consumer’s expected number of searches before purchasing increases, as does the expected aggregate match value \(M_{ij}\) of the product she will buy.
Lemma 2: Market demand and sellers’ profits change with the search cost (\(\tau\)). Lower search cost intensify sellers’ competition, which reduces their prices and increase profits due to a demandexpanding effect (increase the whole pie). The platform’s equilibrium profit can also increase or decrease as the consumer’s search cost decreases
Endogenous referral fee
Proposition 1: A decrease in search cost increases the platform’s expected profit
Proposition 2: As the consumer’s search cost \(\tau\) decreases, the platform will
 Increase its referral fee if the search does not increase the demand elasticity (but communication is important here)
 Decreases its referral fee if the search cost increase the demand elasticity
Effects of Filtering

Consumer’s optimal search strategy

Lemma 3: Filtering increases the consumers’ acceptance threshold for the aggregate match value by less than \(\mu_K\)
Filtering allows consumers to have smaller consideration set, which raises acceptance threshold for the aggregate match value
Filtering reduces the direct benefit of searching. Hence, consumers are more likely to stop searching at a lower acceptance threshold.
But the first effect > the second effect.
Proposition 3: filtering increases a consumer’s probability of buying a product after searching it, and reduces the consumer’s expected number of search.


Seller’s pricing decisions: filtering reduces retail price

Proposition 4: Filtering reduces consumer’s uncertainty about the product’s match value
Consumers only search products with the highest filterable attributes, reducing the matchvalue differentiation among product (increase price competition, and lower equilibrium price)
filtering decreases consumers’ equilibrium probability of continuing search after searching a product, reducing competition and higher equilibrium prices.
Proposition 5: Filtering increases the platform’s demand, seller’s profit, and platform’s profit, and consumer surplus under small scale factor for the match value and referral fee is exogenous

Conclusion
Reduction in search cost makes consumers search more, while filtering reduces the benefit of search making consumers search power products
Decrease in search cost intensifies seller’s competition, leading to lower retail prices. While filtering softens seller competition, and lead to higher retail prices
When the referral fee is exogenous, a lower search cost can either be good or bad for the platform, and consumers. Whereas filtering will always benefit the sellers, the platform, and consumers if filtering only reveals a small amount of the variations in the match value.
Heterogeneous search costs:
 Proposition 6: Optimal retail price is the weighted average of the homogeneoussearch cost equilibrium prices
Heterogeneous Product quality:
 Premium sellers charge a higher price (than nonpremium sellers), but the difference is smaller than their quality difference
Fixed Perunit referral fee:
 When the platform’s referral fee is exogenous, a reduction in search costs will always increase the platform’s profit under a set perunit referral price, but it will lower the platform’s profit under a percentage referral fee.
37.5.2 (Yanbin Chen et al. 2021) Consumer Search with blind buying
Objective and Motivation
Consumers don’t have relevant info and must invest effort to purchase a suitable product
Previous search literature, consumers pay a fixed search cost to visit a store and fully informed about the price and match value at the store

These models do not capture
Online search technology that lower the cost of visiting stores and collecting info about prices
Consumers cannot physically inspect and try products.
This paper designs a sequential search model to capture these two aspects
Sequence:
Before searching, consumers observe the prices and prior values of both firms, and they pay a search cost to learn the match value
Consumers have to decide product to search firs, and whethe to continue searching after inspecting the first product. If consumers decide to stop searching, they can either buy the insepcted product or bldinly buy an unispected product
Model construction
Duopoly market, 2 firms sell horizontally differentiated products in price competition.

The random utility (net of nay search cost) fo consumer \(l\), who purchases the product from firm \(i\) is \(\tilde{u}_{il} = \tilde{\eta}_{il} + \tilde{\epsilon}_{il}  p_i\)
\(\tilde{\eta}_{il}\) = observable match value
\(\tilde{\epsilon}_{il}\) = unobservable match value
The key feature is that consumers can blindly buy a product
At any stage of search process, consumers have the option of purchasing a product without inspecting its match value \(\tilde{\epsilon}_{il}\) where no search cost is incurred
The expected utility for consumer blind search is \(E(\tilde{u}_{il}) = \eta_{il} + E(\tilde{\epsilon}_{il})  p_i\)
Search is assumed to be costly
Game sequence
 Firms determine their prices
 Each consumer costlessly observes both the prices and the prior values of the products and decides whether to blindly buy a product. the game ends if a blind buying takes place
 The game continue and after learning product match value, the costumer decides among three 3 options
buy product without uncertainty
blindly buy product without inspecting its match value
discover both realized value
Results

The effects of blind buying on equilibrium prices
 In pricedirected search models without the blind buying option, search friction has 2 effect on prices competition.
When the match value has a symmetric distribution, both consumer and firms are indifferent to the search order, conditioning on searching
An increase int eh first sample search cost has no effect on market prices in existing pricedirected search models, reducing equilibirum prices in the model
37.5.3 (X. Li and Xu 2022) Superior knowledge, price discrimination, and customer inspection
Customer inspection : learn about their intrinsic preferences.
Superior knowledge: firms know customers preferences
Setup
A monopolistic firm selling a product to a continum of customers of unit measure
Customer have heterogeneous match values with the firm’s product (either high or low)
the prior probability of a high match value is \(\alpha\)
Information structure:
Customers know their expected match value, they are ex ante uninformed about their idiosyncratic shock and do not know their match value beyond its prior distribution
Customer inspection: the cost that consumer make for an informed purchase. The inspection cost is independent of rational inferences
firm knows both its product characteristics and preference of individual customers.
Timeline
 Each customer has their match
 Firm offers each customer a personalized price according to her preference. The firm chooses the probability distribution of its price
 Observing the personalized price, customer decides whether to inspect to find out her true preference by incurring an inspection cost with probability
 Based on the inspection outcome, if the customer chooses to inspect, the customer decides whether to make a purchase
37.6 Review paper
To reject, find major flaws
If you propose alternative specification or robustness, provide rationale why it’s necessary.
How to deal with rejections
Let it sit for a few days before/after you read it
Vent your anger with your coauthors
Examine main points of rejection and focus on improvement
Submit to another journal and forget about it
How to deal with revisions
Let it sit for a few days
Vent with coauthors
Examine main concerns (for those papers that you can’t address reviewer’s concern, consider submitting to another journal). If you don’t send back within certain window, editors assume you are not going to submit it.
For major revisions, you don’t send it back right away in a month
Results
Rejection: don’t ever send it back
Reject and resubmit: If you do these certain thing, we treat it as a new paper
Major revision: major problems, but if you revise it, the outcome is still uncertain, but you pass the first round (about 50% will be rejected in the second round)
Minor revision: problems that are easily solvable (less uncertainty)
Conditional acceptance: some small things, wordings (no risk of being rejected)
Accept as is