Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Matching Auctions Daniel Fershtman Alessandro Pavan Tel Aviv University Northwestern University
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Motivation Mediated matching central to " sharing economy " Most matching markets intrinsically dynamic – re-matching - shocks to profitability of existing matching allocations - gradual resolution of uncertainty about attractiveness - preference for variety Re-matching, while pervasive, largely ignored by matching theory
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Th is paper Dynamic matching mediated (many-to-many) interactions evolving private information payments capacity constraints Applications scientific outsourcing (Science Exchange) lobbying sponsored search internet display advertising lending (Prospect, LendingClub) B2B health-care (MEDIGO) organized events (meetings.com) Matching auctions Dynamics under profit vv welfare maximization
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Plan Model Matching auctions Truthful bidding Profit maximization Distortions Endogenous processes Conclusions
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model Profit-maximizing platform mediates interactions between 2 sides, A , B
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model Profit-maximizing platform mediates interactions between 2 sides, A , B Agents: N A = { 1 , ..., n A } and N B = { 1 , ..., n B } , n A , n B ∈ N
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model Profit-maximizing platform mediates interactions between 2 sides, A , B Agents: N A = { 1 , ..., n A } and N B = { 1 , ..., n B } , n A , n B ∈ N Period- t match between agents ( i , j ) ∈ N A × N B yields gross payoffs v A ijt = θ A i · ε A v B ijt = θ B j · ε B and ijt ijt θ k i : "vertical" type ε k ijt : "horizontal" type (time-varying match-specific)
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model Profit-maximizing platform mediates interactions between 2 sides, A , B Agents: N A = { 1 , ..., n A } and N B = { 1 , ..., n B } , n A , n B ∈ N Period- t match between agents ( i , j ) ∈ N A × N B yields gross payoffs v A ijt = θ A i · ε A v B ijt = θ B j · ε B and ijt ijt θ k i : "vertical" type ε k ijt : "horizontal" type (time-varying match-specific) Agent i ’s period- t (flow) type ( i ∈ N A ): v A it = ( v A i 1 t , v A i 2 t , ..., v A in B t )
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model Profit-maximizing platform mediates interactions between 2 sides, A , B Agents: N A = { 1 , ..., n A } and N B = { 1 , ..., n B } , n A , n B ∈ N Period- t match between agents ( i , j ) ∈ N A × N B yields gross payoffs v A ijt = θ A i · ε A v B ijt = θ B j · ε B and ijt ijt θ k i : "vertical" type ε k ijt : "horizontal" type (time-varying match-specific) Agent i ’s period- t (flow) type ( i ∈ N A ): v A it = ( v A i 1 t , v A i 2 t , ..., v A in B t ) Agent i ’s payoff ( i ∈ N A ): ∞ ∞ δ t ∑ U A v A δ t p A ∑ ∑ i = ijt · x ijt − it t = 0 j ∈ N B t = 0 with x ijt = 1 if ( i , j ) -match active, x ijt = 0 otherwise.
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model Platform’s profits: � � ∞ it + ∑ jt − ∑ δ t p A p B ∑ ∑ i ∈ N A ∑ c ijt · x ijt t = 0 i ∈ N A j ∈ N B j ∈ N B
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model In each period t ≥ 1, each agent l ∈ N k from each side k = A , B can be matched to at most m k l agents from side − k . - one-to-one matching: m k l = 1 all l = 1 , ..., n k , k = A , B - many-to-many mathcing with no binding capacity constraints : l ≥ n − k , all l = 1 , ..., n k , k = A , B m k
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model In each period t ≥ 1, each agent l ∈ N k from each side k = A , B can be matched to at most m k l agents from side − k . - one-to-one matching: m k l = 1 all l = 1 , ..., n k , k = A , B - many-to-many mathcing with no binding capacity constraints : l ≥ n − k , all l = 1 , ..., n k , k = A , B m k In each period t ≥ 1, platform can match up to M pairs of agents - space, time, services constraint - platform can delete previously formed matches and create new ones. Total number of existing matches cannot exceed M in all periods.
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model θ k Each θ k l = [ θ k l , ¯ l drawn independently from (abs cont.) F k over Θ k l ] l
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model θ k Each θ k l = [ θ k l , ¯ l drawn independently from (abs cont.) F k over Θ k l ] l Period- t horizontal type ε k ijt drawn from cdf G k ijt ( ε k ijt | ε k ijt − 1 )
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Model θ k Each θ k l = [ θ k l , ¯ l drawn independently from (abs cont.) F k over Θ k l ] l Period- t horizontal type ε k ijt drawn from cdf G k ijt ( ε k ijt | ε k ijt − 1 ) Agents observe θ k i prior to joining, but learn ( ε k ijt ) over time
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Plan Model Matching auctions Truthful bidding Profit maximization Distortions Endogenous processes Conclusions
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Matching auctions At t = 0 (i.e., upon joining the platform), each agent l ∈ N k purchases membership status θ k l ∈ Θ k l at price p k l ( θ ) - higher status → more favorable treatment in subsequent auctions
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Matching auctions At t = 0 (i.e., upon joining the platform), each agent l ∈ N k purchases membership status θ k l ∈ Θ k l at price p k l ( θ ) - higher status → more favorable treatment in subsequent auctions At any t ≥ 1:
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Matching auctions At t = 0 (i.e., upon joining the platform), each agent l ∈ N k purchases membership status θ k l ∈ Θ k l at price p k l ( θ ) - higher status → more favorable treatment in subsequent auctions At any t ≥ 1: agents bid b k lt ≡ ( b k ljt ) j ∈ N − k , one for each partner from side − k
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Matching auctions At t = 0 (i.e., upon joining the platform), each agent l ∈ N k purchases membership status θ k l ∈ Θ k l at price p k l ( θ ) - higher status → more favorable treatment in subsequent auctions At any t ≥ 1: agents bid b k lt ≡ ( b k ljt ) j ∈ N − k , one for each partner from side − k each match ( i , j ) ∈ N A × N B assigned score S ijt ≡ β A i ( θ A ijt + β B j ( θ B i ) · b A j ) · b B ijt − c ijt
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Matching auctions At t = 0 (i.e., upon joining the platform), each agent l ∈ N k purchases membership status θ k l ∈ Θ k l at price p k l ( θ ) - higher status → more favorable treatment in subsequent auctions At any t ≥ 1: agents bid b k lt ≡ ( b k ljt ) j ∈ N − k , one for each partner from side − k each match ( i , j ) ∈ N A × N B assigned score S ijt ≡ β A i ( θ A ijt + β B j ( θ B i ) · b A j ) · b B ijt − c ijt matches maximizing sum of scores s.t. individual and aggregate capacity constraints implemented
Introduction Model Matching Auctions Truthful Bidding Profit Maximization Distortions Endogenous processes Conclusions Matching auctions At t = 0 (i.e., upon joining the platform), each agent l ∈ N k purchases membership status θ k l ∈ Θ k l at price p k l ( θ ) - higher status → more favorable treatment in subsequent auctions At any t ≥ 1: agents bid b k lt ≡ ( b k ljt ) j ∈ N − k , one for each partner from side − k each match ( i , j ) ∈ N A × N B assigned score S ijt ≡ β A i ( θ A ijt + β B j ( θ B i ) · b A j ) · b B ijt − c ijt matches maximizing sum of scores s.t. individual and aggregate capacity constraints implemented unmatched agents pay nothing
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