Revealing Private Information in a Patent Race Pavel Kocourek 1 - PowerPoint PPT Presentation

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Revealing Private Information in a Patent Race Pavel Kocourek 1 February 15, 2020 1 pk1050@nyu.edu

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Consider competition of Apple and Samsung in patenting a new smartphone technology. Samsung makes an intermediate breakthrough on the way to a patent. Should Samsung disclose the breakthrough?

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Patent Race Two firms compete to patent a specific product or technology. The breakthroughs arrive in a random fashion; the first firm to make two breakthroughs wins the patent, the other firm loses. Most of the patent race literature makes the questionable assumption that firms observe each others progress in the race. Should the firms disclose their breakthroughs? If not, what is the dynamics of the patent race then?

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Assumptions Two consecutive breakthroughs needed to patent. Patenting is public, the game ends. Each firm continuously chooses its effort that is equal to its hazard rate of making a breakthrough. The research happens in secrecy. (Effort and breakthroughs are not observable.) Each firm has the option to disclose its first breakthrough (being successful). Verifiable. No technological spillovers.

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Intuition Under complete information: If Apple is unsuccessful, Samsung’s success discourages Apple’s effort. If Apple is successful, Samsung’s success encourages Apple to hurry up. Under private information: Samsung does not observe Apple’s success. Samsung gets increasingly confident that Apple is successful over time. Samsung has decreasing incentive to disclose its success over time. After observing Apple’s disclosure, Samsung does not want to disclose its breakthrough.

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Results Without revelation: each firm drops its effort until its first breakthrough, after which its effort jumps up and keeps increasing. A firm never discloses after observing disclosure of its rival. Unique symmetric Nash equilibrium. The type of equilibrium depends on research difficulty. If research is difficult, then the first firm to make a breakthrough reveals it instantly; easy, then firms never reveal; moderate, then player’s reveal with a mixed strategy. Voluntary revelations is better for welfare than no revelation or mandatory revelation.

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Literature Complete information version of a patent race: Harris and Vickers (1987) , Grossman and Shapiro (1987). Secrecy versus Patenting: Levin et al. (1987) , Kultti et al. (2007) Two players, hidden effort choice, technological uncertainty: Bonatti and Horner (2011) , “Collaborating”. Closest Related Study: The job market paper of Gordon (2003) , “Publishing to Deter in R&D Competition” (Unpublished).

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Outline Patent Race Under Secrecy 1 One Player Known to be Successful 2 Revealing Breakthroughs 3 Welfare and Policy 4

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Table of Contents Patent Race Under Secrecy 1 One Player Known to be Successful 2 Revealing Breakthroughs 3 Welfare and Policy 4

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Patent Race Under Secrecy Firm’s state is its private information. When a firm patents, it is a common knowledge. Effort is not observed. No option to reveal.

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy The Race Infinite horizon continuous time game with two players. Each player perpetually chooses any positive level of research effort. To win the patent, a firm has to be the first to make two consecutive discoveries. A firm is in state 0: at time t = 0; state 1: after making the first breakthrough; state 2: winning the patent – the game ends.

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Breakthroughs and Patenting Denote x j t ∈ { 0 , 1 , 2 } and e j t ∈ [0 , ∞ ) player j ’s ( j ∈ { A , B } ) state and effort at time t ≥ 0, respectively. Initially, x j 0 = 0. At any time, Player j ’s effort is the hazard rate of making a breakthrough: P [ x j t +∆ t = x j t + 1] = e t ∆ t + o (∆ t ) . Player j patents when he makes the second discovery, let τ j be his patenting time: τ j = inf { t ≥ 0 : x j t = 2 } .

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Expected Payoff Player j incurs flow cost that is quadratic in effort, c ( e ) = 1 2 α e 2 , α > 0; and if he wins, he receives the price v > 0 of the patent; future payoffs are discounted at rate r > 0. His expected payoff is � � τ � EU j = E − exp( − rt ) · c ( e j t ) dt + exp( − r τ ) · 1 j wins · v � �� � 0 � �� � value of patent R&D expenses

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Normalization Parameters: v . . . value of the patent; α . . . effort cost multiplier; r . . . discount rate. Choosing appropriate units of value and time, we can achieve v ′ = 1 , α ′ = 1. Then r ′ = α r v represents the research difficulty.

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Continuation Value Player j ’s current continuation value depends only on his state x ∈ { 0 , 1 } and time t ≥ 0, � ( v x +1 , j − v x , j 2 ( e ) 2 − ( r + ψ − j ) v x , j � v x , j t ) e − 1 − ˙ = max t t e ≥ 0 where ψ − j is the hazard rate with which the rival patents at t . t FOC implies e x , j = v x +1 , j − v x , j t . Then t t � 2 − � � � v x +1 , j v x , j = 1 − v x , j r + ψ − j v x , j − ˙ t . t t t t 2 Solution Concept: Nash Equilibrium (NE ≡ PBE ≡ MPE)

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Posterior Belief Player − j has posterior belief about his rival being successful, p j t = P [ x j t = 1 | none patented yet] . By Bayes rule, p j t = (1 − p j t )( e 0 , j − p j t e 1 , j ˙ t ) . t Rival patents with hazard rate ψ j t = p j t e 1 , j t .

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy ODE Proposition Any Nash equilibrium is characterized by the ODE � 2 − � � � v 1 , j 1 − v 1 , j t e 1 , − j v 1 , j 1 r + p − j − ˙ = t t t t 2 � 2 − � � � v 0 , j v 1 , j − v 0 , j r + p − j t e 1 , − j v 0 , j 1 − ˙ = t t t t t 2 � �� � e 0 , j t e 1 , j p j 1 − p j − p j ˙ = , t t t t with e 1 , j = 1 − v 1 , j and e 0 , j = v 1 , j − v 0 , j t , and the initial t t t t condition p j 0 = 0 , and the restrictions 0 ≤ v 0 , j ≤ v 1 , j ≤ 1 and t t p j t ∈ [0 , 1] , for all t ≥ 0 , j ∈ { A , B } . Not an initial value problem.

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Solution Method The challenge: initial conditions v 1 0 and v 0 0 unknown; an initial error grows exponentially over time. Going back in time: look for solutions that converge to a critical point; go back in time from the critical point,. . . but how? Getting out of the critical point: jump out so that the solution will converge back; go along the eigenvector related to the negative eigenvalue of the Jacobean (at the critical point).

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Unique Symmetric Nash Equilibrium Theorem The patent race with private information has unique symmetric Nash equilibrium. Uniqueness any solution converges to a critical point; the critical point is unique; the Jacobian at the critical point has unique eigenvalue with negative real part. Existence: Going back in time the inequalities 0 ≤ v 0 , j ≤ v 1 , j ≤ 1 are preserved; t t p t eventually reaches 0.

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Posterior Belief Proposition The posterior belief p t about rival being successful steadily grows over time up to its steady-state value p ∗ < 1 . Why? The dynamics of the posterior is � �� � e 0 t − p t e 1 p t = ˙ 1 − p t , t where e 0 t and e 1 t converge to steady-state values e 0 ∗ and e 1 ∗ , respectively. Since e 0 ∗ < e 1 ∗ , p t converges to p ∗ = e 0 ∗ / e 1 ∗ < 1

Patent Race Under Secrecy One Player Known to be Successful Revealing Breakthroughs Welfare and Policy Numerical Solution for r = 0 . 1 Posterior Probability Value Functions 1 1 v 1 p 0.8 0.8 v 0 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 2 4 0 2 4 t t