The number of consumers to the platform on the buyers’ side is given by and on the sellers’ NB side is given by We also assume that no direct transaction between the buyers and the sellers NS. is possible, it happens only through the platform. Also, everyone who joins the platform enters into a transaction on the platform. The net utility of a particular agent on side having usage benefit is defined as, i bi We assume only those agents with non-negative values of their net utility join the platform and carry out transactions. Therefore, the number of agents on side who wishes to join the platform i is derived as, Substituting from (1) can be written as : Following Rochet and Tirole (2004), we assume that the platform sets the per-interaction price as, The number of agents on the th side of the market must be : Since is uniformly distributed over [0,1] continuum, (4) implies, Equation (5) can be elaborately expanded by putting to get, 7
The number of consumers to the platform on the buyers’ side is given by NB and on the sellers’ side is given by NS. We also assume that no direct transaction between the buyers and the sellers is possible, it happens only through the platform. Also, everyone who joins the platform enters into a transaction on the platform. The net utility of a particular agent on side i having usage benefit bi is defined as, We assume only those agents with non-negative values of their net utility join the platform and carry out transactions. Therefore, the number of agents on side i who wishes to join the platform is derived as, Substituting from (1) can be written as : Following Rochet and Tirole (2004), we assume that the platform sets the per-interaction price as, The number of agents on the th side of the market must be : Since is uniformly distributed over [0,1] continuum, (4) implies, Equation (5) can be elaborately expanded by putting to get, 7
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