• Hybrid platform
  • Getting more and more common
  • Seemingly obvious concerns and high-profile competition policy cases
  • Comparatively little reserach

• Bargaining between participants is understudied in the platform setting
  • Authors generally assume take-it-or-leave-it offers

• Shapley-value based bargaining rule
  • Analytically more tractable
  • Has bargaining interpretation (e.g. S. Hart and Mas-Colell 1996; Gul 1989)
  • Has precedents in the IO literature (e.g. O. Hart and Moore 1990; Montez 2007)

• Abstract away all frictions
  • Allows me to focus on the bargaining channel
  • Offers a good benchmark model

• Focus on a continuum of small players case for tractability
  • Good approximation of the finite player case even for not too many players
  • Results have a nice geometric interpretation

• The impacts of hybrid platforms depend on the substitutability of the products
  • When they are substitutes, it increases the platform’s profit share and decreases the fringe’s profits
  • In the presence of investment costs, it can lead to lower fringe entry
  • With Logit demand, hybrid operation leads to welfare losses

• This modeling strategy seems promising
  • The model is surprisingly tractable
  • Quite general results can be obtained

• One platform: $P$
  • Without the platform, no value can be created
  • Might have its own products (hybrid mode)

• A continuum of potential fringe entrants: $F_i,i\in {\mathbb{R}}_0^{+}$
  • Infinitesimally small
  • Have one product each
  • Can only sell through the platform

$$f(N_P,N_F)$$

• $N_P$ is the number of platform products
• $N_F$ is the number of fringe products/firms
• Assume that $f$ is increasing in both arguments

• Platform gets $${\pi }_P(N_P,N_F)={\int }_0^{1}w(s)f(N_P,s{N}_F)\mathrm{d}s$$
• Fringe gets the rest

• Based on the Shapley-value
  • Bargaining interpretation (e.g. S. Hart and Mas-Colell 1996; Gul 1989)
  • Precedents in the IO literature (e.g. O. Hart and Moore 1990; Montez 2007)
• $w(s)$ is a weighting function with ${\int }_0^{1}w(s)\mathrm{d}s=1$
  • Related to the weighted value for a certain class of functions

• Unlimited number of potential entrants

Logit-like demand: $$x_{Ti}=\frac{\exp \left(\frac{v_T-p_{Ti}}{\mu }\right)}{A}$$

where $$A={\int }_0^{N_F}\exp \left(\frac{v_F-p_{Fi}}{\mu }\right)\mathrm{d}i+{\int }_0^{N_P}\exp \left(\frac{v_P-p_{Pi}}{\mu }\right)\mathrm{d}i+1$$

• Assume that the platform prices its products as if they were made by separate, competitive sellers
  • Possible interpretation: profit-maximizing subsidiaries
  • More importantly: “best case scenario”

• The optimal price is an additive markup rule: $$\begin{array}{rl}{p}_{Ti}^{\ast }& =c_T+\mu \\ {\pi }_{Ti}^{v\ast }& =\mu \frac{\exp \left(\frac{v_T-c_T-\mu }{\mu }\right)}{A}\end{array}$$

• Tractable model of hybrid platforms in which bargaining plays a key role
  • Applicable to other settings, too (e.g. vertical markets, franchises)

• Highlight an important aspect if hybrid platforms
  • Hybridness increases bargaining power against entrants
  • This can have negative welfare consequences

• Policy implications for such markets
  • Amazon operating in hybrid mode
  • Microsoft acquiring Activision/Blizzard for $68bn

• In this paper
  • Endogenenize hybridness ($N_P$)
  • Relax separate pricing assumption
  • Alternative benchmarks (e.g. exogeneous split)

• Longer term
  • Endogeneize consumer entry (possibly with them engaging in the negotiation)
  • Apply this bargaining rule to other, similar settings