One Lab, Two Firms, Many Possibilities

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One Lab, Two Firms, Many Possibilities

E. Billette de Villemeur, & B. Versaevel

¹

2017

1Billette de Villemeur: Universit´e de Lille & LEM CNRS; Versaevel: emlyon business school & GATE CNRS

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“After chemotherapy failed to cure Emily Whiteheads severe form of leukaemia, Oxford BioMedica’s new treatment has given her five cancer-free years. (...) In two weeks, America’s Food and Drug

Administration will put the treatment devised by

Oxford BioMedica, in

league with Swiss

pharmaceutical giant Novartis, before a panel of

independent experts. If they like the findings from the human trials, it could pave the way for a full approval in October. A European Medicines Agency filing could follow later this year.”

(Sabah Meddings, July 2 2017, The Sunday Times, UK)

EBdV & BV One Lab, Two Firms, Many Possibilities 2017 2 / 1

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Research questions

Research questions:

1) does more R&D outsourcing imply less internal activity?

2) how are R&D benefits distributed among contracting parties?

3) do firms pay more for equity than for contracted-out R&D?

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Results Preview

In a model where two firms can choose to outsource R&D to an external unit, and/or engage in internal R&D, before competing in a final market:

- internal/external operations neither substitutes nor complements;

- an aggregate measure of technological externalities drives the distribution of industry profits;

- likely abandonment of projects with economic and medical value as a likely consequence of outsourcing;

- founders of a research biotech (more than of a clinical services unit) reappropriate industry profits by selling out the equity.

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Results Preview

In a model where two firms can choose to outsource R&D to an external unit, and/or engage in internal R&D, before competing in a final market:

- internal/external operations neither substitutes nor complements;

- an aggregate measure of technological externalities drives the distribution of industry profits;

- likely abandonment of projects with economic and medical value as a likely consequence of outsourcing;

- founders of a research biotech (more than of a clinical services unit)

reappropriate industry profits by selling out the equity.

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Results Preview

In a model where two firms can choose to outsource R&D to an external unit, and/or engage in internal R&D, before competing in a final market:

- internal/external operations neither substitutes nor complements;

- an aggregate measure of technological externalities drives the distribution of industry profits;

- likely abandonment of projects with economic and medical value as a likely consequence of outsourcing;

- founders of a research biotech (more than of a clinical services unit) reappropriate industry profits by selling out the equity.

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Results Preview

In a model where two firms can choose to outsource R&D to an external unit, and/or engage in internal R&D, before competing in a final market:

- internal/external operations neither substitutes nor complements;

- an aggregate measure of technological externalities drives the distribution of industry profits;

- likely abandonment of projects with economic and medical value as a likely consequence of outsourcing;

- founders of a research biotech (more than of a clinical services unit)

reappropriate industry profits by selling out the equity.

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Stylized facts

1) 16.6% annual growth rate of R&D outsourcing worldwide, expenses from US$ 14 bn in 2003 to 47 bn in 2011 (Morton and Kyle, 2012).

2) from mid 70s onward “[v]irtually every new entrant ... formed at least one, and usually several, contractual relationships with established pharmaceutical (and sometimes chemical) companies” (Pisano, 2006).

3) “... a number of cases of the opposite philosophy, adding in-house research where it previously didn’t exist, is also occasionally in evidence”

(Rydzewski, 2008).

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Stylized facts

4) contract usually designed by the demand side (pharma firms can “go for it alone”; financial constraints faced by specialized units; high entry rate on supply side; see Arora et al., 2004; Golec and Vernon, 2009).

5) complex clauses connect payments received by external unit from a client firm and the R&D supplied to a competitor (“right of first refusal”,

“right to match offer”, see Folta, 1998; Hagedoorn and Hesen, 2007).

6) “Uncertainty related to the success/failure of R&D activities is the major concern for R&D managers in the biopharmaceutical industry”

(Pennings and Sereno, 2011).

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Related literature (theory)

Aghion and Tirole (1994): exclusive division of R (upstream) and D (downstream), relative efficiency of efforts drives separation/integration, no downstream competition.

Anton and Yao (1994): no endogenous R&D effort, two client firms with sequential bargaining, secret reselling, focus on profit distribution.

Bhattacharya and Guriev (2006, 2013): endogenous D effort chosen by two client firms, secret reselling, information leaks, focus on contractual form (“open form & exclusivity” vs. “closed form & reselling risk”).

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Related literature (theory)

Lai, Riezman, and Wang (2009): R&D unified, either upstream (with leakage), or downstream in single firm (higher cost), focus on decision to delegate or not.

Vencatachellum and Versaevel (2009): R&D unified, either upstream (with (dis)economies of scope), or in two competing firms, with spillovers, focus on choice to either delegate, cooperate, or compete, and welfare analysis.

Allain, Henry, and Kyle (2015): R part not considered, D may shift from upstream to downstream client, focus on effect of downstream

competition.

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Related literature (empirical evidence)

Hagedoorn et al. (2012): above (below) a threshold of internal R&D, the marginal returns to internal R&D is higher (lower) when R&D is sourced externally, implying complements (substitutes).

Ceccagnoli et al. (2014): external and internal R&D neither complements nor substitutes (complementarity increases with prior licensing experience).

Higgins et al. (2006): firms with greater R&D intensity are more likely to engage in R&D outsourcing acquisitions.

Danzon et al. (2007): financially strong firms less likely to be part of acquisition, and a merger has little effect on R&D expenses.

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The model

One external for-profit lab (0):

x .

= ( x

₁

, x

₂

) external R&D Two firms (i , j = 1, 2):

y .

= ( y

1

, y

2

) internal R&D z .

= ( z

₁

, z

₂

) commercial strategies

Firms compete (i) on the demand side of the intermediate R&D market,

(ii) in internal R&D levels, (iii) on the final product market.

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The model

Cooperation and Competition in R&D Contracts

Etienne Billette de Villemeur & Bruno Versaevel

x2

x1

)

1(x t t₂(x)

x lab. 0

z1 z₂

y1 y₂

firm 1 firm 2

Figure 1: One lab (common agent) and two firms (principals)

which compete in external and internal R&D and in the final product market

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The model

The lab’s net profit:

v

0

( x ) = ^. t

1

( x ) + t

2

( x ) − f

0

( x ) Firm i’s net profit:

v

i

( x, y, z ) = ^. g

i

( x

i

+ y

i

, x

j

, y

j

, z ) − f

i

( y

i

) − t

i

( x ) f

0

: lab’s R&D cost of x

f

i

: firm i’s R&D cost function of y

i

g

i

: firm i ’s gross profit function of x, y, z

t

_i

: firm i’s transfer payment function of x

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The model

Timing:

(i) The firms choose non-cooperatively t

_i

( x ) ≥ 0,

(ii) The lab contracts with both firms, only one, or none,

by choosing x to max v

0

( x ) (i.e., given t

i

the lab contracts with firm j only if

v

₀

( x ) ≥ sup

n

0, max

x

{ t

_i

( x ) − f

₀

( x )}

^o

for some x ≥ ( 0, 0 ) , i = 1, 2, j 6= i).

(iii) The firms choose non-cooperatively y

_i

≥ 0, (iv) The firms choose non-cooperatively z

_i

≥ 0.

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The model

Notation:

ˆ

g

_i

( x

_i

+ y

_i

, x

_j

, y

_j

) = ^. g

_i

( x

_i

+ y

_i

, x

_j

, y

_j

, z

^∗

( x, y ))

˜

g

_i

( x ) = ^. g

ˆ_i

( x

_i

+ y

_i^∗

( x ) , x

_j

, y

_j^∗

( x )) − f

_i

( y

_i^∗

( x ))

By assumption:

Given g

_i

, for any ( x, y ) there exists a unique z

^∗

( x, y ) ,

Given g

ˆ_i

, for any x there exists a unique y

^∗

( x ) .

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The model

Technological assumptions:

∂

g

ˆ_i

∂x_i

≥

∂

g

ˆ_i

∂x_j

(1)

= ≤

∂

g

ˆ_i

∂yi

≥

∂

g

ˆ_i

∂yj

(2) and

∂²

g

ˆ_i

∂y_i∂x_i

≥

∂²

g

ˆ_i

∂y_i∂x_j

(3)

= ≤

∂²

g

ˆi

∂y_i²

≥

∂²

g

ˆi

∂yi∂yj

(4)

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External and internal R&D: complements or substitutes?

Proposition 1

The equilibrium level of a firm’s internal R&D activity y

_i^∗

is decreasing in the contracted external lab’s activity x

_i

if and only if the gross profit functions g

ˆ_i

have decreasing returns in ( x

_i

, y

_i

) :

dy

_i^∗

dx

_i

Q ⁰ ⇔

^∂

2

g

ˆi

∂s_i²

Q ^0, where s

i

.

= x

i

+ y

i

, and i = 1, 2.

^a

aMore specifically, ^dy

∗ i

dxi =0 if and only if either (i) ^∂_∂s²^g^ˆ2ⁱ i

=0, or (ii)

∂²gˆ_i

∂x_i² = ^∂²^g^ˆⁱ

∂x_i∂y_j <0, ^∂²^g^ˆ^j

∂x_j² = ^∂²^g^ˆ^j

∂x_j∂x_j <0, and ^∂²^f^j

∂y_j² =0, wherei,j=1, 2,j6=i.

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External and internal R&D: complements or substitutes?

1) internal and external operations are neither substitutes nor complements in general ,

2) second-order condition bears only on each firm i’s own argument s

_i

not on x

j

or y

j

, i , j = 1, 2, i 6= j ,

3) unlike models of horizontal agreements where inter-firm spillovers drive strategic complementarity/substitutability of R&D choices.

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Distribution of R&D benefits

Value function:

v ( S ) = ^. max

x

∑

i∈S

˜

g

i

( x ) − f

0

( x )

!

where S ∈ {

_∅

, { 1 } , { 2 } , { 1, 2 }} , v (

_∅

) = v

₀

= 0 (normalization).

Aggregate measure of the

two categories of externalities:

e

.

= v ({ 1, 2 }) − v ({ 1 }) − v ({ 2 })

e

=







≥ 0 positive externalities dominate

< 0 negative externalities dominate

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Distribution of R&D benefits

Non-increasing returns to R&D: Assume that

^∂_∂s²^g^ˆ2ⁱ i

≤ 0.

Non-negative R&D externalities.

Suppose that indirect and direct R&D externalities are non-negative:

∂²

f

₀

∂xi∂xj

≤ 0 (5)

∂

g

ˆi

∂x_j

≥ 0

∂

g

ˆi

∂y_j

≥ 0 (6)

Characteristic of

early-stage discovery

with empirical evidence of

economies of scope and significant knowledge spillovers (Henderson and Cockburn RAND 1996; Cockburn and Henderson JHE 2001)

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Distribution of R&D benefits

Proposition 2

Conditions (??-??) imply that

e

≥ 0. In all TSPNE there exists a continuum of firm payoffs ( v

₁^∗

, v

₂^∗

) ≥ ( v

₁

, v

₂

) that verify

v

₁^∗

+ v

₂^∗

=

_Λ

, (7)

and the lab exactly breaks even, that is

v

₀^∗

= 0. (8)

There is delinkage of incentives to invest in external unit from the value

generated to exclusive benefit of downstream sponsors. Efficient projects

at the industry level are vulnerable to upstream unfavorable events.

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Example 1 (adapted from Symeonidis, IJIO 2003):

p

i

( q

i

, q

j

) =

1 −

^2qⁱ

u²_i

−

_u^q^j

iuj

, i , j = 1, 2, j 6= i , where u

i

is firm i ’s

product quality, which depends on R&D: u

_i

= ( s

_i

)

¹⁴

+

β

( s

_j

)

¹⁴

,

β

∈ [ 0, 1 ] is a spillover parameter, s

i

.

= x

i

+ y

i

and s

j

.

= x

j

+ y

j

. Set

β

=

¹₂

, production costs to zero, and solve for Cournot-Nash quantities q

^∗₁

( x , y ) and q

₂^∗

( x, y ) . Inserting the latter expressions in g

i

( s

i

, x

j

, y

j

, q ) = p

i

( q

i

, q

j

) q

i

leads to

ˆ

g

_i

( s

_i

, x

_j

, y

_j

) . We obtain

^∂_∂s²^g^ˆ2ⁱ i

< 0 (decreasing returns) for all s

_i

> 0, so that from Proposition 1 we have

^dy_dxⁱ^∗

i

< 0 (R&D outsourcing reduces internal activity). Any additive cost function for the lab, e.g.

f

0

( x ) = x

1

+ x

2

, satisfies ( ?? ) . Moreover

^∂_∂x^g^ˆⁱ

j

> 0 and

^∂_∂y^g^ˆⁱ

j

> 0 (positive direct externalities) for all x

_i

, x

_j

> 0, so that ( ?? ) is satisfied.

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Distribution of R&D benefits

Negative R&D externalities.

Suppose that indirect and direct R&D externalities are negative:

∂²

f

₀

∂xi∂xj

> 0, (9)

∂

g

ˆi

∂x_j

≤ 0,

∂

g

ˆi

∂y_j

≤ 0. (10)

Characteristic of

late-stage clinical trials

with empirical evidence of

diseconomies of scope and non-existent spillovers (Danzon et al., JHE

2005; Macher and Boerner, SMJ 2006).

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Distribution of R&D benefits

Proposition 3

Conditions ( ??-?? ) imply that

e

< 0. In all TSPNE there is a unique pair of firm payoffs ( v

₁^∗

, v

₂^∗

) that verify

v

_i^∗

= v ({ i }) − |

e

| ≥ v

_i

, (11) i , j = 1, 2, j 6= i , and the lab appropriates a share of industry profits

v

₀^∗

= |

e

| > 0. (12)

The external unit can appropriates all profits in a buyers market where client firms are principals and are no less informed than the external unit.

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Example 2 (adapted from Laussel and Le Breton, JET 2001):

x, y ∈ { 0, 1 }

²

and the lab’s R&D costs are f

₀

( x ) =







1 if x

₁

+ x

₂

= 1 0 if x

1

= x

2

= 0

f

₀

( x ) = +

_∞

otherwise, satisfying condition ( ?? ) . Each firm’s R&D cost is f

_i

( y

_i

) =

γy_i

, with

γ

≥ 1, and production cost is c

_i

( x

_i

+ y

_i

) , with

c

_i

( 0 ) = c

_H

and 0 ≤ c

_i

( 1 ) = c

_i

( 2 ) = c

_L

< c

_H

. Total demand is q = sup { 0, a − p } , with p ≥ 0 and a > c

_H

. Given ( x, y ) , defining

π

.

= ( c

_H

− c

_L

) ( a − c

_H

) , and solving for Bertrand-Nash equilibrium prices leads to g

ˆi

( x

i

+ y

i

, x

j

, y

j

) =

π

> 0 if x

i

+ y

i

≥ 1 and x

j

+ y

j

= 0, and

ˆ

g

_i

( x

_i

+ y

_i

, x

_j

, y

_j

) = 0 otherwise, so the condition in ( ?? ) is also satisfied.

Equilibrium payoffs are v

₀^∗

=

π

− 1, v

_i^∗

= v

_j^∗

= v = 0.

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Distribution of R&D benefits

Non-decreasing returns to R&D. Assume that

^∂_∂s²^g^ˆ2ⁱ i

≥ 0.

Simple sufficient conditions for Propositions 2 and 3 to remain valid:

Proposition 4

Suppose that returns to R&D are non-decreasing. Then Propositions 2 and 3 still hold if

_∂x^∂²^g^ˆ^j

j∂xi

≥ 0, i, j = 1, 2, j 6= i . Otherwise a sufficient condition is

^dy

∗ j

dxi

> − 1.

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Example 4 (d’Aspremont and Jacquemin, AER 1988, & Vonortas IJIO 1994): f

₀

( x ) = ( x

₁

+ x

₂

)

²

−

^δ₂

x

₁

x

₂

, with

δ

≥ 0, f

_i

( y

_i

) =

κ

+ y

_i²

, with

κ

> 0. Production cost is c

i

( x ) = ( c − s

i

−

βsj

) , with c > 0, with spillover parameter

β

∈ [ 0, 1 ] , and where s

_i

= x

_i

+ y

_i

. Inverse demand is p ( q ) = a − q

i

− q

j

, so q

_i^∗

( x, y ) = [( a − c ) + s

i

( 2 −

β

) + s

j

( 2β − 1 )]

/3.

Then

∂²

g

ˆ_i/∂s_i²

= 2 ( 2 −

β

)

²/9

> 0 (increasing returns to R&D), and:

(i) Proposition 2 applies if

β

≥ 1/2 and

δ

≥ 1,

(ii) Proposition 3 applies if

β

< 1/2 and

δ

< 1.

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Incentives to integrate

x lab. 0

z1 z₂

firm 1 firm 2

y1 y₂

x2

x1

) ( )

( ₂

1 x t x

t 

Figure 2: Inter-firm cooperation: joint R&D procurement

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Incentives to integrate

lab. 0

firm 1 firm 2

Figure 3: firm 1 and the lab integrate vertically

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Incentives to integrate

lab. 0

firm 1 firm 2

Figure 4: firm 2 and the lab integrate vertically

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Incentives to integrate

Non-negative R&D externalities (e ≥ 0)

From Proposition 2: v

₀^∗

= 0, and v

₁^∗

+ v

₂^∗

=

_Λ

(where v

_i^∗

≥ v

_i

).

The payoff distribution ( v

₁^∗

, v

₂^∗

) reflects circumstances outside of the model specifications captured by bargaining powers (

φ1

,

φ2

) :

v

_k^∗

= v

_k

+

φk

(

_Λ

− v ) ,

k = 1, 2, where ( v

₁

, v

₂

) is the disagreement point, with v .

= v

₁

+ v

₂

and

φ1

+

φ2

= 1. Then

φk

= ^v

∗

k

− v

_k

Λ

− v .

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Incentives to integrate

Suppose v ({ i }) > v

_i

. In case of vertical integration { 0, i } : v

₀^{₊^0,i_i^}

= v ({ i }) +

φ_i Λ

− v ({ i }) − v

_j

> v

_i^∗

, (13)

v

_j^{^0,i^}

= v

_j

+

φ_j Λ

− v ({ i }) − v

_j

< v

_j^∗

. (14)

From (??-??) willingness to pay for the lab simplifies to:

v

₀^{₊^0,i_i^}

− v

_i^{^0,j^}

=

φj

( v ({ i }) − v

_i

) +

φi

v ({ j }) − v

_j

> 0, for a

strictly

higher payoff to the external unit than with outsourcing:

v

₀^{^0,1^}

= v

₀^{^0,2^}

= ^v ({ 1 }) − v

₁

Λ

− v ( v

₂^∗

− v

₂

) + ^v ({ 2 }) − v

₂

Λ

− v ( v

₁^∗

− v

₁

) > v

₀^∗

= 0.

(35)

Incentives to integrate

Negative R&D externalities (e < 0)

From Proposition 3: v

₀^∗

= |

e

| > 0, and v

_i^∗

= v ({ i }) − |

e

| ≥ v

_i

. In a horizontal arrangement for firms to behave as a unique principal:

v

₀^{^1,2^}

= 0, v

₁^{^1,2^}

+ v

₂^{^1,2^}

=

_Λ

, and the two firms’ payoffs

v

₁^{^1,2^}

, v

₂^{^1,2^}

verify:

v

_k^{^1,2^}

= v

_k^∗

+

ω_k

(

_Λ

− v

₁^∗

− v

₂^∗

) , so bargaining powers are:

ωk

= ^v

{1,2}

k

− v

_k^∗

Λ

− v

₁^∗

− v

₂^∗

.

...

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Incentives to integrate

The two firms’ joint profit is maximized in the horizontal arrangement but each firm has an incentive to depart unilaterally from 1, 2 by acquiring the external unit. The bidding process results in:

v

₀^{^0,1^}

= v

₀^{^0,2^}

= ^v ({ 1 }) − v

₁

|

e

|

v

₂^{^1,2^}

− v

₂^∗

+ ^v ({ 2 }) − v

₂

|

e

|

v

₁^{^1,2^}

− v

₁^∗

≥ v

₀^∗

= |

e

| . With negative externalities the value extracted by the owners of the external unit in the equity market is only

weakly

superior to the positive outsourcing equilibrium payoff.

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Incentives to integrate

Corollary 3

From the viewpoint of the labs owners, incentives to participate in the equity market are weaker in the case of late-stage development (clinical trials) activities characterized by negative externalities, as compared with earlier-stage research (discovery).

Exit payoff results in a long-term financial incentive that motivates the

foundation of a new research biotech (more than a development services

provider).

(38)

Appendix (1/2)

Definitions:

(1) for any t .

= ( t

1

, t

2

) the lab’s profit-maximizing R&D set is X ( t ) = ^. arg max

_x

v

₀

( x ( t ))

(2) for any x ∈ X ( t

i

, t

j

) and x

⁰

∈ X ( t

_i⁰

, t

j

) , firm i’s transfer function t

i

is a best response to the other firm’s t

_j

if g

˜_i

( x ) − t

_i

( x ) ≥ g

˜_i

( x

⁰

) − t

_i⁰

( x

⁰

) , all t

_i⁰

(3) the transfer function t

i

is truthful relative to ˜ x if

t

_i

( x ) = ^. sup { 0, g

˜_i

( x ) − ( g

˜_i

( ˜ x ) − t

_i

( ˜ x ))}

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Appendix (2/2)

Equilibrium concept:

( ^˜ t, ˜ x, ˜ y, ˜ z ) is a Truthful Subgame-Perfect Nash Equilibrium (TSPNE) if:

( i ) ˜ z = z

^∗

( ˜ x, ˜ y ) ( ii ) ˜ y = y

^∗

( ˜ x ) ( iii ) ˜ x ∈ X ( ^˜ t )

( iv ) t

˜_i

is a best response to t

˜_j

( v ) t

˜_i

is truthful relative to ˜ x t

˜i

( x ) = sup { 0, g

˜i

( x ) − v

_i^∗

} , where v

_i^∗

.

= g

_˜i

( ˜ x ) − t

˜i

( ˜ x ) is firm i’s net

equilibrium payoff