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Games for Judges: An Approach to the Design of Legal Liability Rules Sergey Knysh, Paul M. Goldbart & Ian Ayres goldbart@uiuc.edu w3.physics.uiuc.edu/~goldbart 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

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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 breaks Costello’s arm Intentionally? focus on taker’s welfare (a criminal offence) traditionally protect via a property rule Through negligence? focus on takee’s 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 Hardy’s 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 Barney’s apartment Barney can sue for trespass or to force Fred to rent for another year Goal of liability rules: Add efficiency — by compensating initial entitlement holder for 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 imperfectly informed 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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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-Five Inc. (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 car preparation business Copart Indus. v. Con. Ed. Co. (N.Y. 1977) Examples of nuisance disputes

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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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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 dam’s & allow Polluter Liability rule: initial entitlement to Res; put option to Res Liability rules as options (Morris ’93) Put: buyer forced to buy Call: seller forced to sell Who pays? Who chooses who pays?

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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 Louise’s land; Louise can sue Thelma to remove the wall or to force Thelma to buy the encroached land permanently Realizations

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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 Basic ingredients for analyzing liability rules

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Imperfectly informed courts 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 plaintiff value of asset to defendant D is higher valuer P is higher valuer j.p.d.

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Imperfectly informed courts: Property rule What might the court do? compute means w.r.t. : & allocate asset to higher mean valuer (here: D) value of asset to plaintiff value of asset to defendant D is higher valuer P is higher valuer mean values inefficient! What can the court do to promote better efficiency?

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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 response that maximizes the expected total value So… where to arrange the bar? Resp. profits (to P, to D)? if D exercises if D doesn’t

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Imperfectly informed courts: Liability rule One stage / Call flavour Upshot… optimally efficient (i.e. best mean total profit) if D “pivots” at nonchooser’s mean (rational) D does this if damages are also at nonchooser’s mean if D exercises Resp. profits to P & D ? if D doesn’t

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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 response that maximizes the expected total value So… where to arrange the bar? Resp. profits (to P, to D)? if P does put if P doesn’t put

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Imperfectly informed courts: Liability rule One stage / Put flavour Resp. profits (to P, to D)? if P does put if P doesn’t put Upshot… optimally efficient (i.e. best mean total profit) if P “pivots” at nonchooser’s mean (rational) P does this if damages are also at nonchooser’s mean

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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 So… where to arrange the bars? Resp. profits (to P, to D)? D takes but P doesn’t take back D doesn’t take D takes and P takes back

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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 but P doesn’t take back D doesn’t take D takes and P takes back

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“Phase diagram” for rules uniform rectangular j.p.d., 1/ is the golden ratio P mean, range 2 ; D mean, range 2 rules: property (Pr), one-stage liability (Li), veto (Ve) Simplest setting… …roughly SCR: select more vola- tile valuer as chooser DCR: select lower mean valuer as vetoee SCR v. DCR: select SCR if diff. in var’s exceeds diff. in means

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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? So… where to arrange the bars? Resp. profits (to P, to D)?

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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 damages damages functions Reparametrization can take Discrete pivots pivot functions Optimal pivot functions converge to diagonal perfect efficiency

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Infinite-stage liability rule: Call flavour Rational D & P pivot optimally, provided damages functions obey simple ODE’s simple BC’s Solvable (to quadratures) for any j.p.d. (including arbitrary correlations)

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Infinite-stage liability rule: Call flavour Illustrative example uniform triangular (correlated) readily solvable General distributions… what aspects of j.p.d feature? simple geometry if j.p.d. uniform (even if shape gives corr’s)

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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 bidder’s axis) Asset ends up in hands of higher valuer

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Infinite-stage liability rule: Call example Use? Litigants issue bids Asset goes to higher bidder At damages set by lower bid j.p.d. a uniform “2 x 1” rectangle (no correlations)

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Game-theoretic aspects Introduce generalized damages functions And strategy functions what P & D bid, given their private valuations P’s expected profit D’s expected profit efficient

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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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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 better — by harnessing private information continuous versions can be fully efficient go to end-stage, limit transaction costs Emerging guidelines

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