Ride Sharing Platform Vs Taxi Platform: the Impact on the Revenue Benjamin Bordais 1 , Costas Courcoubetis 2 1 ENS Rennes 2 Singapore University of Technology and Design March 28, 2019
Introduction There is great need of mobility in major cities! Possibilities to get a ride: Public transportation Ride sharing One’s own car A taxi
Introduction: related work Consists in optimizing the choices of a platform Choose efficiently the point of departure and arrival 1 An optimization algorithm to efficiently match supply and demand 2 1Service region design for urban electric vehicle sharing systems, Long He et al., 2017 2On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment, Alonso-Mora et al., 2017
Introduction: our approach Our point of view Effect of the introduction of a ride sharing/taxi platform Game theory → predict the outcome Original paper 1 Impact of the introduction of a ride sharing platform Game theory: new model of the population Extension What happens if a taxi platform competes with the ride sharing platform ? Impact on the revenue (can it increase ?) Original model + choice for the users 1Drivers, riders and service providers: the impact of the sharing economy on mobility, Courcoubetis et al., 2017
Outline The Model 1 Theoretical analysis 2 Numerical analysis 3 Conclusion 4
The Model Theoretical analysis Numerical analysis Conclusion The individuals Society = { Individual } . Individuals have type χ ∈ X = R 2 + : Nonatomic game: negligible impact of any individual continuum of players ρ > 0 = utility for using private transportation ν > 0 = wage rate when working at a regular job 6/24
The Model Theoretical analysis Numerical analysis Conclusion The platforms The ride sharing platform The taxi platform Rental price r 1 : Rental price r 2 : - user(s) - user(s), + riders Supply: fixed number of taxis Supply: from the population n t Demand: from the population Demand: from the population Some other constants of the game: Number of seats per car: k Cost of ownership: ω Cost of usage: c 7/24
The Model Theoretical analysis Numerical analysis Conclusion Individuals’ possibilities Transport state Non-Transport state Has to fulfill a transportation Two possiblities: need: • Work to get an income • Use public transport at rate ν > 0 • Request in one of the two • Drive and offer seats (no platforms (get ρ > 0) utility ρ ) • Offer seats (get ρ > 0) → Time spent: 1 /λ n → Time spent: 1 /λ t Standardized time: 1 /λ n + 1 /λ t = 1, λ t , λ n > 1. 8/24
The Model Theoretical analysis Numerical analysis Conclusion Strategies Five strategies in Σ = { A , D , S , U l , U h } : Abstinent ( A ) Driver ( D ) Service Provider ( S ) Low User ( U l ) High User ( U h ) For σ ∈ Σ , µ σ : fraction of the population opting for strategy σ 9/24
The Model Theoretical analysis Numerical analysis Conclusion Strategies (in the case r 1 ≤ r 2 ) Riders Taxis • # drivers, µ D • # of taxis, n t • # service providers, µ S Supply Supply Platform 1 Platform 2 • Ride sharing • Taxis • Rental price r 1 • Rental price r 2 ≥ r 1 Demand Demand Demand Low Users High Users µ U l µ U h 10/24
The Model Theoretical analysis Numerical analysis Conclusion Payoffs: r = min ( r 1 , r 2 ) , ¯ r = max ( r 1 , r 2 ) π A ( ρ, ν ) = ν/λ n π D ( ρ, ν ) = ν/λ n + ρ − ω + k ¯ pr 1 − c π S ( ρ, ν ) = ρ − ω + λ t ( k ¯ pr 1 − c ) π U l ( ρ, ν ) = ν/λ n + p l ( ρ − r ) π U h ( ρ, ν ) = ν/λ n + p l ( ρ − r ) + ( 1 − p l ) p h ( ρ − ¯ r ) p l , p h , ¯ p : probabilities, depends on the distribution µ = ( µ A , µ D , µ S , µ U l , µ U h ) . 11/24
The Model Theoretical analysis Numerical analysis Conclusion Nash Equilibrium Informal definition A situation where it is not in the interest of any player to unilaterally change his strategy At equilibrium: Strategy of players given by σ ∗ : X → Σ ∀ χ = ( ρ, ν ) ∈ X , ∀ σ ∈ Σ , π σ ∗ ( χ ) ( ρ, ν ) ≥ π σ ( ρ, ν ) X partitionned into sets P σ = { Player choosing strategy σ } , σ ∈ Σ 12/24
The Model Theoretical analysis Numerical analysis Conclusion Example of equilibrium Figure: Equilibrium with parameters λ t = 6 , k = 2 (o stands for ω ) 13/24
Outline The Model 1 Theoretical analysis 2 Numerical analysis 3 Conclusion 4
The Model Theoretical analysis Numerical analysis Conclusion The revenue of the ride sharing platform: R Proportionate to: The rental price r 1 The number of seats sold (depends on which is the cheapest platform) If r 1 ≤ r 2 : If r 1 > r 2 : R = r 1 × p l × ( µ U l + µ U h ) R = r 1 × p h × ( 1 − p l ) µ U h 15/24
The Model Theoretical analysis Numerical analysis Conclusion Some results: when r 1 ≤ r 2 ( r = r 1 ) Theorem If r 1 ≥ ω + c k + 1 , then the equilibrium is the same as in the original game (without taxis). ω = 0 . 1, c = 0 . 4, k = 2, n t = 0 . 1, λ t = 6 . 16/24
The Model Theoretical analysis Numerical analysis Conclusion Some results: when r 1 ≤ r 2 ( r = r 1 , r t = r 2 ) Theorem If ω ≤ c / k then adding the taxi platform can not increase the revenue of the ride sharing platform ω = 0 . 1, c = 0 . 4, k = 2, n t = 0 . 1, λ t = 6 . 17/24
The Model Theoretical analysis Numerical analysis Conclusion Some results: The revenue can increase Theorem There exists some values of our parameters for which the revenue of the ride sharing platform strictly increases Figure: Equilibrium with parameters ω = 0 . 1, c = 0 . 4, k = 2, n t = 0 . 1, λ t = 6 . 18/24
Outline The Model 1 Theoretical analysis 2 Numerical analysis 3 Conclusion 4
The Model Theoretical analysis Numerical analysis Conclusion The Best Response Dynamics Algorithm This algorithm: Works on a large number of players (5000) Does not necessarily converge When it does, we have a Nash Equilibrium 20/24
The Model Theoretical analysis Numerical analysis Conclusion Better revenue Figure: Equilibria without (top) and with (bottom) taxis, for k = 1 21/24
The Model Theoretical analysis Numerical analysis Conclusion Price dynamics Figure: Optimizing price of one platform as a function of the price of the other platform 22/24
Outline The Model 1 Theoretical analysis 2 Numerical analysis 3 Conclusion 4
The Model Theoretical analysis Numerical analysis Conclusion Conclusion and future work Model difficult to study: the model changes if r 1 ≤ r 2 or if r 2 > r 1 However, we do have some results: Conditions that ensure that the revenue does not increase Numerical/Analytical example of an increasing revenue Situations that do not change by adding taxis Future possibilities Condition of existence of service providers (independent of the distribution) Study the price dynamics: numerical simulations may suggest what happens 24/24
Appendix Other functions of interest: definition � Distribution: µ σ ( s ) = δ s ,σ d χ X Ownership: Ω( µ ) = µ S + µ D ; Traffic intensity: Γ( µ ) = µ S + µ D /λ t ; � Social Welfare: W ( s ) = � π σ ( χ ) · δ s ,σ d χ . σ ∈ Σ X 25/24
Appendix Other functions of interest: curves Figure: Curves with parameters ω = 0 . 1, c = 0 . 4, k = 2, n t = 0 . 1, λ t = 6 . 26/24
Appendix The matching functions If r 1 ≤ r 2 : If r 1 > r 2 : p l = k ( µ D + λ t µ S ) n t ∧ 1 p l = µ Ul + µ Uh ∧ 1 µ Ul + µ Uh n t p h = k ( µ D + λ t µ S ) p h = ( 1 − p l ) µ Uh ∧ 1 ( 1 − p l ) µ Uh ∧ 1 µ Ul + µ Uh ( 1 − p l ) µ Uh ¯ ¯ p = k ( µ D + λ t µ S ) ∧ 1 p = k ( µ D + λ t µ S ) ∧ 1 27/24
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