Marketmaking Middleman Pieter Gautier, Bo Hu and Makoto Watanabe VU University Amsterdam, Tinbergen Institute December 2014 1 / 44
What is a marketmaking middleman? 2 / 44
What is a marketmaking middleman? 3 / 44
What is a marketmaking middleman? Figure: the spectrum, intermediaries de…ned by functioning 4 / 44
literature Two-sided market literature: cross-group externality. Rochet and Tirole (2003, 2006), Caillaud and Jullien (2003), Armstrong (2006). Middlemen literature: high meeting rate, demand variety and the high inventory capacity. Rubinstein and Wolinsky (1987), Shevichenko (2004) and Watanabe (2010, 2013). 5 / 44
the model a mass B of buyers, a mass S of sellers homogenous goods: unit demand/unit sell, common consumption value normalized to 1, marginal cost is c 2 [ 0 , 1 ) 6 / 44
the model D(ecentralized) market I random meeting, meeting rate λ b , λ s 2 ( 0 , 1 ) , B λ b = S λ s I bilateral bargaining, θ for buyers, 1 � θ for sellers 7 / 44
the model C(entralized) market I marketmaker: pro…ts from the transaction and registration fees. I middleman: stock a mass inventory in a competitive wholesale market, resells to buyers 8 / 44
centralized market a two-sided market I cross-group externality I subsidize one type, the other type will come soon price observed by all, buyers can’t coordinate their actions I more buyers than the seller’s inventory, then some buyers will be rationed. (Coordination frictions) suppose buyers visit the middleman x m , the rest visit the marketplace B � x m I on average each seller gets x s = B � x m S I middleman optimally adjusts inventory equal to x m , Pr [ served ] = 1 I sellers have limited 1 unit inventory, Pr [ served ] = η s ( x s ) � 1 (high coordination frictions). 9 / 44
centralized market suppose buyers visit the middleman x m , the rest visit the marketplace B � x m I on average each seller gets x s = B � x m S I middleman optimally adjusts inventory equal to x m , Pr [ served ] = 1 I sellers have limited 1 unit inventory, Pr [ served ] = η s ( x s ) � 1 (high coordination frictions). 10 / 44
centralized market suppose buyers visit the middleman x m , the rest visit the marketplace B � x m I on average each seller gets x s = B � x m S I middleman optimally adjusts inventory equal to x m , Pr [ served ] = 1 I sellers have limited 1 unit inventory, Pr [ served ] = η s ( x s ) � 1 (high coordination frictions). 11 / 44
urn-ball matching process given fees F , suppose B 0 buyers and S 0 sellers participate in C market all participating sellers post a price simultaneously 1 all participating buyers choose a seller to visit simultaneously 2 directed search friction I in a large market, buyers can’t coordinate their visits I if more than one buyers visit a seller, then allocate the good randomly I the number of buyers visits a seller N follows a Poisson distribution Pr ( N = n ) = e � x s ( x s ) n n ! where x s = B 0 S 0 12 / 44
urn-ball matching process for …nite integers B 0 and S 0 , the number of buyers visits a seller, denoted as N , follows a Binomial distribution � B 0 � � 1 � n � � B 0 � n 1 � 1 Pr ( N = n ) = S 0 S 0 n take B 0 , S 0 ! ∞ and B 0 / S 0 = x s , N follows a Poisson distribution e � x s ( x s ) n lim Pr ( N = n ) = n ! b , s ! ∞ b / s = x s 1 � e � x s Pr ( N > 0 ) = lim b , s ! ∞ b / s = x s a deviating seller with an expected queue of buyers, denoted as x I the seller receive at least one buyer with 1 � e � x I a visiting buyer is served with η s ( x ) � 1 � e � x x 13 / 44
timing a competitive wholesale market opens. The intermediary purchases a mass k inventory at wholesale price c two retail markets open to buyers, C market and D market the intermediary announces the fee structure for the marketplace observing these fees and inventory, buyers and sellers simultaneously decide which market to participate in I singlehoming, agents visit only one market I multihoming, agents can visit both markets C & D market 14 / 44
single-homing agents can participate in only one market. intermediary essentially becomes a monopolist I once agents are in the centralized market, switching to the decentralized market is not feasible, all trade surplus can be extracted π Single = ( B � x m ) η s ( x s ) ( 1 � c ) + x m ( 1 � c ) the middleman mode creates more transactions, thus is preferred x m � = B 15 / 44
multi-homing participating all markets is allowed compete against the outside market, the intermediary has to lower price and fees, give buyers their outside option value V b ( D ) the pro…ts of intermediary h i + x m h i π Multi = ( B � x m ) η s ( x s ) 1 � c � V b 1 � c � V b , ( D ) ( D ) ( D ) = λ b e � x s θ ( 1 � c ) , x s = B � x m where V b . S 16 / 44
multi-homing h i + x m h i π Multi = ( B � x m ) η s ( x s ) 1 � c � V b 1 � c � V b , ( D ) ( D ) middleman mode is e¢cient in creating more transactions = ) a higher x m ; ( D ) increases in x m = buyer’s outside option value V b ) a lower x m ; I a higher x m leads to less transactions in the marketplace, more sellers available in D market, buyers are easier to match in D market the trade-o¤ between more transactions and more pro…ts per-trade pins down x m � < B 17 / 44
conclusion non-exclusive intermediation service leads to a hybrid business mode I an active marketplace to lower buyers’ outside option value competition for intermediation can deteriorate the e¢ciency and welfare I social planner’s viewpoint, pure middleman mode since it minimizes market frictions I in the presence of outside competition, hybrid mode is more pro…table for the intermediary 18 / 44
agenda remainder of talk the marketmaking middleman under singlehoming (section 3) I participate in only one market the marketmaking middleman under multihoming (section 4) I allowed to participate in both markets 19 / 44
singlehoming, the model a one-period economy agents: a mass B of buyers, a mass S of sellers, one intermediary homogenous goods: I unit demand/unit sell/a continuum of inventory I common consumption value normalized to 1; I marginal cost is c 2 [ 0 , 1 ) . D(ecentralized) market I random meeting, meeting rate λ b , λ s 2 ( 0 , 1 ) , B λ b = S λ s I bilateral bargaining, θ for buyers, 1 � θ for sellers C(entralized) market I marketmaker: transaction fees f b , f s 2 [ 0 , 1 ] , participation fees g b , g s 2 [ � 1 , 1 ] I middleman: pro…ts from inventory 20 / 44
singlehoming, timing of events a competitive wholesale market opens, the intermediary stocks a 1 continuum of inventory k 2 [ 0 , B ] from producers/sellers retail markets open 2 n f b , f s , g b , g s o the intermediary announces a set of fees F � 1 observing F , buyers and sellers simultaneously decide which market to 2 attend (singlehoming) trade occurs in each market (standard directed search game in C 3 market) 21 / 44
singlehoming, timing of events a competitive wholesale market opens, the intermediary stocks a 1 continuum of inventory k 2 [ 0 , B ] from producers/sellers retail markets open 2 n f b , f s , g b , g s o the intermediary announces a set of fees F � 1 observing F , buyers and sellers simultaneously decide which market to 2 attend (singlehoming) trade occurs in each market (standard directed search game in C 3 market) 22 / 44
singlehoming, the directed search equilibrium sellers a deviating seller with an expected queue of buyers, denoted as x I the seller receive at least one buyer with x η s ( x ) = 1 � e � x I a visiting buyer is served with η s ( x ) � 1 � e � x x I the problem V s = x η s ( x ) ( p � f s � c ) max p � 1 � p � f b � s . t . V b = η s ( x ) equilibrium values e � x s ( 1 � f � c ) V b = � 1 � e � x s � x s e � x s � V s = ( 1 � f � c ) where x s = B 0 S 0 , f � f b + f s 23 / 44
singlehoming, the directed search equilibrium middleman expected queue of buyers visiting middleman x m , S 0 x s + x m = B 0 the serving probability of a buyer visiting the middleman η m ( x m ) = min f k , x m g x m the middleman’s problem min f k , x m g ( p m � c ) , p m V m max = s . t . V b ( x m ) η m ( x m ) ( 1 � p m ) . = note the large market assumption does not hold V b ( x m ) optimal x m � k 24 / 44
singlehoming, timing of events a competitive wholesale market opens, the intermediary stocks a 1 continuum of inventory k 2 [ 0 , B ] from producers/sellers retail markets open 2 n f b , f s , g b , g s o the intermediary announces a set of fees F � 1 observing F , buyers and sellers simultaneously decide which 2 market to attend (singlehoming) trade occurs in each market (standard directed search game in C 3 market) 25 / 44
singlehoming, buyers’ and sellers’ decision agents hold a pessimistic expectation I they would rather believe no one of the other type is in C market resort to divide and conquer strategies I DbCs � g b � λ b θ ( 1 � c ) , Db : V s � g s � 0 . Cs : I DsCb � g s � λ s ( 1 � θ ) ( 1 � c ) , Ds : V b � g b � 0 . : Cb I these induce all agents to join the C market, B 0 = B and S 0 = S . 26 / 44
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