Extension to J > 2 and related cases Sample Clauses

Extension to J > 2 and related cases. The game naturally extends to more than two challengers where Γj is repeated for j ∈ {2, . . . , J} with the only difference being that the Πj payoffs will be based on oligopoly profits ΠN# rather than for instance by triopoly profits given by ΠT# . Appendix C provides an example of profits under a oligopoly with J + 1 firms along with the structure of Γj and where we maintain the assumption that if the brand reaches an agreement with all the challengers, then in the post patent period the order of entry is given by the order of challengers (i.e., first paid off firm gets the first mover advantage). Appendix C also provides other important extensions. Notably changes in listed profits in Γj,G – the payoffs if j-th generic wins the 14An alternative is to be agnostic about the fee setting process and set the profits inclusive of the licensing fees to be V˜T 1 = ΠT 1 + ρΠT 1 (for the branded firm), V˜T 1 = (1 − ρ)ΠT 1 (for generic 1) and, V T 1 = ΠT 1 (for generic 2), where ρ ∈ (0, 1) is an exogenously set parameter based on the relative bargaining power. case – allows us to model (i) the FF system (exclusivity available to only the first generic), (ii) no exclusivity (if a generic wins, all challengers can enter immediately and there is no duopoly period),

Extension to J > 2 and related cases. The game naturally extends to more than two challengers where Γj is repeated for j ∈ {2, . . . , J} with the only difference being that the Πj payoffs will be based on oligopoly profits ΠN# rather than for instance by triopoly profits given by ΠT# . Appendix (A.3) provides an example of profits under a oligopoly with J + 1 firms along with the structure of Γj and where we maintain the assumption that if the brand reaches an agreement with all the challengers, then in the post patent period the order of entry is given by the order of challengers (i.e., first paid off firm gets the first mover advantage). Observe that solving Γj, i.e., finding out whether Gj challenges B and computing Xj, requires the solution to the game Γj+1 first. Hence, SPE payoffs in Γj and all payments XJ, . . . , Xj are found by a recursive computation that uses equation (1) and Lemma (2) at each step J, . . . , x. For example, if this computation yields that the generics GJ, . . . , Gj challenge B and agree on the P4D payments XJ, . . . , Xj, then the brand’s expected SPE payoff in Γj is, 0 u (Γ ) = u (Γ ) − ΣJ s=j where u0(ΓJ+1) is the payoff to the brand B after the game ends with J P4D agreements. If all these P4D payments are positive, condition (2) for a fixed j will be eventually violated when the number of generics J is sufficiently large. In this case, B and Gj will go to court. On the other hand, a condition for a universal agreement on P4D deals is specified in the next proposition. Proposition 1. The brand will pay P4D payments to all challengers in a SPE if for any given challenger Gj, the brands expected payoff from agreements with the current and subsequent chal- lengers (net of payments) is greater than the expected payoff from triggering the litigation against challenger Gj. Specifically, B will agree in the SPE on the P4D payments X1, . . . , XJ if for all j = 1, ..., J, s=j 0 0 0 u (Γ ) − ΣJ X > πu (Γ ) + (1 − π)u (Γ ) − c , (7) where Xj is defined in equation (1). (For Proof see Appendix (A.2)).