Games for Judges: An Approach to the Design of Legal Liability Rules

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Games for Judges An Approach to the Design of
Legal Liability Rules

• Sergey Knysh, Paul M. Goldbart Ian Ayres

Department of Physics University of Illinois
Yale Law School New Haven, CT
Michigan Law Review,100 (Centenary Volume), 1-79
(2001)Preprints (2002) Design of Efficient
Legal Liability Rules I. Continuous Extension
of Multistage Rules II. Comparison of Discrete
Vanilla and Exotic Variants
goldbart_at_uiuc.edu w3.physics.uiuc.edu/goldbart
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Outline

• Property rules liability rules
• Nuisance dispute settings
• Options view of liability rules
• Optimizing liability rules
• Continuum liability rules
• Game-theoretic viewpoint
• Practical advice for courts

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Property rules liability rules

• Property rules protect by deterrence
• Liability rules protect by compensation

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Property rules liability rules

• Example Abbott breaksCostellos arm
• Intentionally?
• focus on takers welfare (a criminal offence)
• traditionally protect via a property rule
• Through negligence?
• focus on takees welfare (compensatory damages)
• traditionally protect via a liability rule

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Property rules liability rules

• But property rules are not very efficient
• Example Laurel steals Hardys hat?
• Property rule Hardy can sue to recover hat
  (replevin)
• Liability rule Can also sue for value of hat
  (trover)
• Advantage? If hat is worth 10 to Laurel, 5 to
  Hardy?

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Property rules liability rules

• Liability rules are more efficient
• Example Fred holds over in Barneys apartment
• Barney can sue for trespass
• or to force Fred to rent for another year
• Goal of liability rules
• Add efficiencyby compensating initial
  entitlement holderfor transfer of entitlement
  (goes beyond mere deterrence)

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Concerns of judges re liability rules

• Traditional view
• identity of the initial entitlement holder
• compensation as deterrence
• Modern view
• identity of the more efficient chooser
• decouple allocative and distributional concerns
• liability rules a means by which an
  imperfectlyinformed court can delegate choice to
  private litigants thus harnessing their superior
  information

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Central aims

• Focus on nuisance dispute settings
• Provide courts with liability rules that are
• economically efficient
• cheap to implement

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Examples of nuisance disputes

• A/c noise reduced value of adjacent residence
• Estancias Dallas Corp. v. Shultz (Tex. App. 1973)
• Hotel addition obstructed view of adjacent hotel
• Fontainbleu Hotel v. Twenty-Five Twenty-FiveInc.
  (Fl. 1959)
• Dog-track lights interfered w/ drive-in movie
  theater
• Amphitheaters, Inc. v. Portland Meadows (Or.
  1948)
• Pollution from Con Ed plant disrupted new
  carpreparation business
• Copart Indus. v. Con. Ed. Co. (N.Y. 1977)

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Property rules liability rules

• What might courts do in nuisance disputes?
• E.g. Boomer v. Atlantic Cement (N.Y. 1970)
• Resident/Plaintiff (Boomer) discomforted by
  pollution
• Polluter/Defendant (Atl. Cem.) factory operator
• After Calabresi Melamed (72)
• Rule 1 nuisance ? injunction on Polluter (stop!)
  
• Property rule
• Rule 2 nuisance ? Polluter pays damages to
  continue
• Liability rule
• Rule 3 not a nuisance ? Polluter continues
• Property rule
• Rule 4 nuisance? ? Resident pays Polluter
  damages to stop
• Liability rule

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Options Calls and Puts

• Call option
• choice of whether or not to pay a non-negotiated
  amount to purchase entitlement
• choice of forcing seller to sell (be paid)
• Put option
• choice of whether or not to be paid a
  non-negotiated amount to sell entitlement
• choice of forcing buyer to buy (pay)

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Liability rules as options (Morris 93)

• Put buyer forced to buy

• Call seller forced to sell

• Rule 2 Polluter can pay damages to continue
• Liability rule initial entitlement to Res call
  option to Pol
• Rule 4 Resident can pay damages to stop Polluter
• Liability rule initial entitlement to Pol call
  option to Res
• Rule 5 Polluter can require damages stop
• Liability rule initial entitlement to Pol put
  option to Pol
• Rule 6 Resident can require dams allow
  Polluter
• Liability rule initial entitlement to Res put
  option to Res

• Who pays? Who chooses who pays?

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Realizations

• Rule 2 Entitlement to Resident call to Polluter
• Boomer v. Atlantic Cement (N.Y. 1970)
• Rule 4 Entitlement to Polluter call to Resident
• Spur Indus., Inc. v. Del E. Webb Dev. Co. (Ariz.
  1972)
• Rule 6 Entitlement to Resident put to Resident
• Thelma builds an encroaching wall on Louises
  land Louise can sue Thelmato remove the wall
  or to force Thelma to buy the encroached land
  permanently

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Basic ingredients for analyzingliability rules

• Imperfectly informed court
• Explore classes of rules
• Which to use? Ex post efficiency as criterion
• Vanilla rules
• Exotic rules
• dual-chooser rules (vetos, higher-order,)
• Emerging guidelines for courts

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Imperfectly informed courts
D is highervaluer

• In any given instance
• Plaintiff P
• Defendant D
• P alone knows her valuation,
• D alone knows his,
• P, D court know j.p.d. i.e. joint probability
  distrib. of valuations (possibly correlated)

value of asset to defendant
j.p.d.
P is higher valuer
value of asset to plaintiff
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Imperfectly informed courts Property rule
D is highervaluer
mean values

• What might the court do?
• compute means w.r.t.
• allocate asset to highermean valuer (here D)

value of asset to defendant
inefficient!

• What can the court do to promote better
  efficiency?

P is higher valuer
value of asset to plaintiff
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Imperfectly informed courts Liability rule
One stage / Call flavour

• The court could
• allocate asset to P
• give call option to D
• set damages
• How would D respond?
• by exercising option when worth it to him
• How to set damages?
• to elicit a responsethat maximizes the expected
  total value

Resp. profits (to P, to D)?
if D exercises
if D doesnt

• So where to arrange the bar?

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Imperfectly informed courts Liability rule
One stage / Call flavour
Resp. profits to P D ?

• Upshot
• optimally efficient (i.e. best mean total
  profit) if D pivots at nonchoosers mean
• (rational) D does this if damages are also at
  nonchoosers mean

if D exercises
if D doesnt
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Imperfectly informed courts Liability rule
One stage / Put flavour

• The court could
• allocate asset to P
• give put option to P
• set damages
• How would P respond?
• by exercising option when worth it to her
• How to set damages?
• to elicit a responsethat maximizes the expected
  total value

Resp. profits (to P, to D)?
if P does put
if P doesnt put

• So where to arrange the bar?

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Imperfectly informed courts Liability rule
One stage / Put flavour
Resp. profits (to P, to D)?

• Upshot
• optimally efficient (i.e. best mean total
  profit) if P pivots at nonchoosers mean
• (rational) P does this if damages are also at
  nonchoosers mean

if P does put
if P doesnt put
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Imperfectly informed courts Veto rule

• The court could
• allocate asset to P
• give call option to D at damages
• give call option to P at same damages
• Transfer to D can be vetoed by D or P

D takes and P takes back
D takes but P doesnt take back
D doesnt take
Resp. profits (to P, to D)?

• So where to arrange the bars?

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Imperfectly informed courts Veto rule

• Upshot
• efficient for D to pivot at damages
• efficient for P, too
• Optimal damages obey straightforward formula

D takes and P takes back
D takes but P doesnt take back
D doesnt take
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Phase diagram for rules
roughlySCR select more vola-tile valuer as
chooser DCR select lower meanvaluer as
vetoee SCR v. DCR selectSCR if diff. in vars
exceeds diff. in means

• Simplest setting

• uniform rectangular j.p.d., 1/t is the golden
  ratio
• P mean , range 2 D mean , range 2
• rules property (Pr), one-stage liability (Li),
  veto (Ve)

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Multi-stage liability rule Call flavour

• The court could give
• asset to P
• call option to D at damages
• call-back option to P at damages
• call-back option to D at damages
• call-back option to P at damages
• ..
• How to choose the damages?

Resp. profits (to P, to D)?

• So where to arrange the bars?

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Multi-stage liability rule Call flavour

• Find pivots that max. expected total value
• Set damages to elicit these responses
• Strategic over-bidding (pivots smaller than
  damages)
• Note shrinking areas of inefficiency

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Infinite-stage liability rule Call flavour

• Discrete pivots ? pivot functions

• Optimal pivot functions ? converge to diagonal
  ? perfect efficiency

• Reparametrization ? can take

• Discrete damages ? damages functions

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Infinite-stage liability rule Call flavour

• Rational D P pivot optimally, provided
  damages functions obey
• simple ODEs
• simple BCs
• Solvable (to quadratures) for any j.p.d.
  (including arbitrary correlations)

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Infinite-stage liability rule Call flavour

• General distributions
• what aspects of j.p.d feature?
• simple geometry if j.p.d. uniform (even if shape
  gives corrs)

• Illustrative example
• uniform triangular (correlated)
• readily solvable

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Infinite-stage liability rule Call flavour
How to use the results

• Court computes parametric damages curve
• And requires D P to bid
• bids separate call-exercise from non-exercise
  ranges
• Asset goes to higher bidder
• for damages projected from lower bid (to higher
  bidders axis)
• Asset ends up in hands of higher valuer

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Infinite-stage liability rule Call example

• j.p.d. a uniform 2 x 1 rectangle (no
  correlations)

• Use? Litigants issue bids
• Asset goes to higher bidder
• At damages set by lower bid

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Game-theoretic aspects

• Introduce generalized damages functions

• And strategy functions
• what P D bid, given their private valuations

efficient

• Ps expected profit

• Ds expected profit

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Game-theoretic aspects

• Seek Nash Equilibrium
• (my strategy is optimal for me if you fix
  yours, vice versa)
• Make simple choice for damages functions
• Demand that the N-E strategies be revealing

• Upshot previous call-option damages conditions
• Court has made it so that it pays not to lie!

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Emerging guidelines

• Explore classes of liability rules
• single-chooser, veto, continuous
• decouple allocational distributional concerns
• Property rules
• give entitlement to (estimated) higher valuer
• suggested as a general practice, but
• Liability rules
• do betterby harnessing private information
• continuous versions can be fully efficient
• go to end-stage, limit transaction costs

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