Law and economics: game theory

N.J. PhilipsenAssociate Professor of Law and Economics Faculty of Law, Research Institute METRO

Shandong University, Jinan, May 2009

Overview

• What is law and economics?– methodology– history– importance of L&E in US, Europe and China

• The use of game theory in L&E– economic analysis of contract law– economic analysis of procedural law– property rights, competition law, etc.

What is law and economics?

• Methodology– using economic concepts to study the law– influence of the law on people’s behaviour

• efficiency (Pareto efficiency, Kaldor-Hicks efficiency)• maximizing utility, maximizing social welfare• price theory (supply-demand): sanctions as prices• statistical research• game theory

– positive versus normative analysis– efficiency versus distribution– applied to many areas of the law

What is law and economics?

• History and importance of L&E– “Old” law and economics

• ex: competition law, regulation of sectors, tax issues

– “New” law and economics• ex: contracts, torts, criminal law, family law• developments in the US since 1960s• famous books, journals and scholars:

– Richard Posner, Steven Shavell, Guido Calabresi, • Nobel prize winners

– Ronald Coase, Gary Becker, James Buchanan• recent developments in Europe and China

Economic theory of contract

• Why do we need contract law?– what promises should be enforced by law?

– contract law should enable people to convert games with inefficient (noncooperative) solutions into games with efficient (cooperative) solutions

– what should be the remedy for breaking enforceable promises?

• restitution• negative damages (reliance damages)• positive damages (expectation damages)

Example: agency game I

• The first player (principal) decides whether to put a valuable asset, which is worth 100, under the control of the second player– for example: investor in corporation

• Player 2 (agent) decides whether to cooperate or appropriate (that is, take the money and leave)

• Cooperation is productive: 100 in profits– for example: profit from investment

• Profits are split evenly among the parties: 50 each

• Appropriation is redistributive• => question: do we need contract law?

Agency game without contract

Second player(agent)

First player(principal)

Cooperate Appropriate

Invest 50 ; 50 -100 ; 100

Don’t invest

0 ; 0 0 ; 0

Agency game with contract

Second player(agent)

First player(principal)

Perform Breach

Invest 50 ; 50 50 ; -50

Don’t invest

0 ; 0 0 ; 0

Example: Agency game II

• A widow (W) wants to invest €100,000 in stocks and shares for one year

• An investment consultant (IC) claims that in that one year he can produce a return on that investment of 10%, so €10,000

• Parties would split the €10,000 profits => € 5,000 each• Does W lend the money to IC?

– game theory: non-symmetrical game– compare situation with and without contract law (incl.

some system of damages)

Example: agency game III: optimal performance and breach• Extension of agency game I: now

performing is sometimes more efficient than breaching, and breaching is sometimes more efficient than performing

• Promising precedes performing; the gap in time may create uncertainties over the cost of performing– example: the second player does not know

whether urgent business will arise after giving the promise (opportunity costs)

Agency game with contract and variable cooperation costs

Second player

First player

Perform (costs 0)

Perform (c 150)

Breach

Invest 50 ; 50 50; -100 50; -50

Don’t invest

0 ; 0 0 ; 0 0 ; 0

Optimal reliance

• Reliance: investments by the principal induced by the promise– this makes breach by the agent more costly to

the principal

• the probability of agent performing the promise has an effect on optimal reliance (low or high) by the principal

• the law should not compensate too much reliance (overreliance) => foreseeability

Agency game with variable reliance and no enforceable contract

Second player

First player

Cooperate Appropriate

Invest & low reliance

50 ; 50 -100 ; 100

Invest & high reliance

60 ; 50 -200 ; 100

Agency game variable reliance and no enforceable contract

• Expected net payoff from low reliance• p (50 + 50) + (1-p) (-100 + 100)

• Expected net payoff from high reliance• p (60 + 50) + (1-p) (-200 + 100)

• Calculation of ‘tipping point’:• p* = 0,91• high reliance is optimal if the probability of

performance exceeds 91 percent

Agency game: variable reliance, enforceable contract, and simple expectation damages

Second player

First player

Perform Breach

Invest & low reliance

50 ; 50 50 ; -50

Invest & high reliance

60 ; 50 60 ; -160

Agency game: variable reliance, enforceable contract, and perfect expectation damages

Second player

First player

Perform Breach

Invest & low reliance

50 ; 50 50 ; -50

Invest & high reliance

60 ; 50 -50 ; -50

Purposes of contract law according to economic theory (I)

1. to enable people to convert games with inefficient solutions into games with efficient solutions

2. to encourage the efficient disclosure of information within the contractual relationship

3. to secure optimal commitment to performing

Purposes of contract law according to economic theory (II)

4. to secure optimal reliance

5. to minimize transaction costs of negotiating contracts by supplying efficient default terms and regulations

6. to foster long-term relationships (“repeated games”)

Economics of procedural law

• Procedural law: involves legal disputes• Questions that game theory can address

include:– why do people sue (file a complaint)?– what is the expected value of a legal claim?– what is the impact of changes in the probability

of winning/losing the case and changes in the lawyer’s fee, court costs, etc?

Example 1: settling or rejecting offer?

• a company causes a consumer to suffer harm of 100

• consumer offers to settle the dispute for 50• if the company refuses, it will face a lawsuit that

will cost it 10 to litigate• if it loses at trial, the business will have to pay the

consumer 100=> what is the lowest probability of the consumer

winning at which the business expects to gain by settling the case?

injury sue exchangeinf.

bargain trial appealfile yes yes lose

noinjury

don’t filecomplaint

settle settle win win

lose

Ex. 2: Expected value of a legal claim