The strategic role of public authority in the control of - PowerPoint PPT Presentation

The strategic role of public authority in the control of countereinfing. A differential game approach. Marta Biancardi* Andrea Di Liddo* Giovanni Villani** *Department of Economics - University of Foggia Largo Papa Giovanni Paolo II, 1 71100 Foggia - Italy **Department of Economics and Finance - University of Bari Largo Abbazia S.Scolastica, 53 70124 Bari - Italy e-mail: giovanni.villani@uniba.it NED2019 - KIEV, 4-6 September 2019 M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Introduction • The counterfeiting is the unauthorized use of a registered trademark on a product that is identical or similar to the product for which is registered and used. • Counterfeiting has consequences on legal producers and consumers. • We have two types of counterfeiting: deceptive counterfeiting and non-deceptive counterfeiting. • To combat the counterfeting there are two importants measures: the monitoring control and the sanctions. M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Introduction-Literature review • Grossman and Shapiro (1988) show a model of counterfeiting in luxury market. They present a dynamic model between two countries and two policies are analyzed: enforcement policy and imposition of a tariff on low-quality products. These measures are exogenous. • Banerjee (2003) examines the government’s role in restricting piracy in a software market. The author assumes government chooses these measures to maximize domestic social-welfare subject to a balanced budget constraint. In these two paper the difference in production cost between the legal firm and counterfeiter is not considered. M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Introduction-Literature review • Yao (2015) examines the price and welfare implications of demand side penalties in the context of deceptive counterfeiting showing that the penalties are not recommended in some countries. The public measures are exogenous. • Tsai (2012) considers a vertical product differentiation model to discuss the influences caused by counterfeiting on price and outputs of original products, counsumer surplus and social welfare. M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

The Model: assumptions We consider a planning horizon [ 0 , T ] . In the absence of counterfeiting, the demand for the genuine firm is: � � D g , nc ( t ) = R ( t ) α − β p g ( t ) + where • p g ( t ) is the price of a unity of the genuine product; • R ( t ) the manufacturers brand reputation; In the presence of counterfeiting, the demand of the fake is: D c ( t ) = R ( t )[ ρ ( p g ( t ) − p c ( t ))] + where p c ( t ) is the price of a unity of the counterfeited product. The parameter ρ can be assumed as a measure of the competition between the two firms. Obviously 0 ≤ p c < p g M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

The Model: assumptions In the presence of counterfeiting, the demand of the legal firm is: � � �� D g ( t ) = R ( t ) α − β p g ( t ) − ρ p g ( t ) − p c ( t ) + We assume that: 0 ≤ ρ ≤ β that is, the direct-price effect is larger than the cross-price effect. Moreover: • The genuine firm and the counterfeiters incurs linear production costs and that c > 0 and b > 0 for a genuine item and a fake, respectively. Obviously b < c . M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

The Model: assumptions • The evolution of the brand’s reputation is described by the following linear differential equation: ˙ R = ka ( t ) − σ R ( t ); R ( 0 ) = R 0 ≥ 0 , where a ( t ) is the advertising effort, k > 0 is an efficiency parameter and σ > 0 is the decay rate; • The advertising cost is convex increasing and given by the quadratic function ω 2 a 2 ( t ) where ω is a positive parameter M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Role of public authority: Confiscation • The (average) counterfeiter profit is � T Π c = { ( 1 − φ ) p c ( t ) − b } D c ( t ) dt , 0 where φ ∈ [ 0 , 1 ] is the monitoring level. • Since counterfeiters can enter/exit the market freely, they sell the fakes at a price p c such that their profit is zero: b p c = 1 − φ • The (average) genuine firm profit is given by � T ( p g ( t ) − c ) D g ( t ) − ω � � 2 a 2 ( t ) Π g = dt + sR ( T ) 0 where sR ( T ) is the salvage value of the brand at T, with s ≥ 0 . M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Role of public authority: Fixed Fine If the counterfeiters are caught, they are forced to pay a penalty of an amount F . For instance the software piracy and so b = 0. • The (average) counterfeiter profit is � T Π c = [( 1 − φ ) p c ( t ) D c ( t ) − φ F ] dt 0 • The price p c must be a solution of the following quadratic equation φ F p c ( p g − p c ) = ( 1 − φ ) ρ R ( t ) . (1) • Eq. (1) has two positive solutions if � 4 φ F p g ≥ ( 1 − φ ) ρ R ( t ) , otherwise it has no solutions. M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Let ˜ p c the price of the pirated software. The (average) genuine firm payoff is given by � T p c )] − ω � � 2 a 2 ( t ) ( p g − c ) R ( t )[ α − β p g − ρ ( p g − ˜ Π g = dt + sR ( T ) . 0 Let � 4 φ F p g < ( 1 − φ ) ρ R ( t ) . Then pirates cannot stay in the market so that the demand of the genuine is given by � � D g ( t ) = R ( t ) α − β p g ( t ) . The (average) genuine firm payoff is given by � T − ω � � 2 a 2 ( t ) � � Π g = ( p g ( t ) − c ) R ( t ) α − β p g ( t ) dt + sR ( T ) . 0 M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Role of Public Authority: Fines counterfeiters • The (average) counterfeiter profit is � T � � Π c = [( 1 − φ ) p c ( t ) − b ] D c ( t ) − φ fp g ( t ) D c ( t ) dt , 0 where f is the ratio of fines. This implies that p c = b + φ fp g 1 − φ . (2) • The (average) genuine firm profit is given by � T ( p g ( t ) − c ) D g ( t ) + y φ fp g ( t ) D c ( t ) − ω � � 2 a 2 ( t ) Π g = dt + sR ( T 0 where y ∈ [ 0 , 1 ] . M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Role of Public Authority: Fines counterfeiters • The social planner chooses the level of enforcement φ that maximizes the welfare. A type of cost function widely used is λ ( φ ) = h φ 2 ; h > 0 . • The welfare W is the unweighted sum of the following components: the profit of the genuine producer Π g , the surplus of consumers S (both original and fake consumers), the amount of sanctions eventually collected by the social planner, minus the enforcement costs λ ( φ ) . • The game is solved as a leader-follower game. The social planner (leader) chooses φ ; the genuine firm (the follower), having observed the choice of the leader, chooses the price p g and the advertising. M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Role of Public Authority: Assumptions • We assume that counterfeiters set the price of a fake as a fixed fraction of the price of a genuine item, that is p c = δ p g ; 0 < δ < 1 . (3) • We assume that y = 0, and so all fines are taken by public authority. The (average) genuine firm profit is given by � T ( p g ( t ) − c ) D g ( t ) − ω � � 2 a 2 ( t ) Π g = dt + sR ( T ) 0 • Social Welfare is: � T W = [ S ( t ) + π g ( t ) + φ fp g D c ( t ) − λ ( φ )] dt + sR ( T ) 0 M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Surplus of consumers • Surplus of legal consumers; We determine pg max , the price such that the demand is equal to zero: α pg max = β + ρ ( 1 − δ ) and so: � pg max D g ( t ) dp = R ( t ) { c ( β + ρ ( 1 − δ )) − α } 2 S ∗ g = . 8 ( β + ρ ( 1 − δ )) pg • Surplus of fake consumers. We have that pc max = p g and so: � pg S ∗ c = ( 1 − φ ) D c ( t ) dp pc and so: c = ( 1 − φ ) ρ ( 1 − δ ) 2 R ( t )[ c ( β + ρ ( 1 − δ )) + α ] 2 S ∗ . 8 [ β + ρ ( 1 − δ )] 2 M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Feedback Nash Equilibria First step: pg , a Π g max subject to: ˙ R ( t ) = ka ( t ) − σ R ( t ) HJB equation for legal firm: − ∂ V g ∂ t ( t , R ( t )) = p g , a ( p g − c ) D g − ω 2 a 2 ( t ) + ∂ V g max ∂ R ( t , R ( t ))( ka ( t ) − σ R ( t )) M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019

Feedback Nash Equilibria Second step: max W φ subject to ˙ R ( t ) = ka ( t ) − σ R ( t ) HJB equation for public authority: − ∂ V P g ) − k φ 2 + ∂ V P ∂ R ( ka ∗ − σ R ) } = max φ { S ( p ∗ g ) + π g ( p ∗ g ) + φ fp ∗ g D c ( p ∗ ∂ t (4) M ARTA B IANCARDI *, A NDREA D I L IDDO *, G IOVANNI V ILLANI ** NED 2019 - K IEV , 4-6 S EPTEMBER 2019