37.1 Platforms
37.1.1 (Jiang, Jerath, and Srinivasan 2011) Amazon’s mid-tail
Firm strategies in the “mid tail” of platform-based 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 high-volume products and independent sellers should sell low-volume long-tail products.
For mid-tail 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 low-demand seller by setting high fee. Thus only high-demand 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 high-demand 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 per-unit 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 high-demand type is low and vice versa.
Related literature:
Internet retailing
Two-sided 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 \(1 - \theta\)
Per-unit 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
Two-stage game:
- Nature determines the seller’s type, Amazon charge a per-unit fee \(f\) (constant in 2-period). 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 \(f\)
H-type could mimic L-type to avoid Amazon notice
Only H-type 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
Counter-intuitive 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 first-party products than third-party products
Consumer prefer third-party over first-party
Consumer dynamics (sequentially):
- Pre-search:
no costs
Consumer learn expected valuations from pre-search
- 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 non-prominent 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 first-party products)
37.1.4 (Gal-Or 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: variety-seeking
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 (variety-seeking 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 platform-user as compared to vendor-users. (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 before-entry 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 pay-per-click payment rule or pay-per-impression)
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 \(Tq_i + (1-T) \lambda_{ki}\) 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 \(Tq_i + (1-T) \lambda_{ki}\)
Consumer choice:
When the same seller appears in the ad and organic result (she is the higher-quality 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 \(L\)