## Settlements

• Approximately 90% of all private antitrust cases are settled prior to the final judicial decision
• A simple risk calculation of the expected outcome of the case justifies this large proportion of settlements
• We can show the probability of a settlement rests on three things:
• Damages
• Differences between the defendant’s and plaintiff’s view on the success of the case
• Cost of the case

#### Expected return

• Suppose the antitrust violation caused damage $$D$$ and the plaintiff believes they can win the case with probability $$\theta_p$$
• A successful plaintiff recovers treble damages plus the cost of the suit $$C_p$$
• An unsuccessful plaintiff recovers no damages and must pay the cost of the suit
• We can calculate the plaintiff’s expected return (E(R)) from going to court:

$E[R]=\theta_p(3D) + (1-\theta_p)(-C_p)$

• The defendant must always pay their costs $$C_d$$ and believes they will lose the case with probability $$\theta_d$$
• We can calculate the defendant’s expected loss (E[L))

\begin{aligned} E[L]&=\theta_d(3D+C_p+C_d)+(1-\theta_d)C_d \\ &=\theta_d(3D+C_p)+C_d \end{aligned}

#### When will a settlement occur?

• We can think of the suit as a risky asset owned by the plaintiff (with a value equal to the expected return E[R]) and owed by the defendant (with a value equal to the expected loss E[L])
• If the defendant values the ‘asset’ more than the plaintiff, they will attempt to ‘buy’ it (i.e., settle the lawsuit)
• Mathematically, a settlement occurs when the expected loss to the defendant exceeds the expected return to the plaintiff:

\begin{aligned} E[L]&>E[R]\\ \theta_d(3D+C_p)+C_d &> \theta_p(3D)-(1-\theta_p)C_p \end{aligned}

$(\theta_d-\theta_p)3D + (\theta_d-\theta_p)C_p+(C_d+C_p) > 0$

• Intuitively, a settlement occurs if it is cheaper for the defendant to pay everything the plaintiff expects to win, relative to the cost of going to court
• If the defendant believes the plaintiff has a higher chance of winning, relative to the plaintiff’s own belief they will win (i.e. $$\theta_d$$ > $$\theta_p$$), then there will always be a settlement

#### Example 1

Imagine that Channel 5, a small media company, files a lawsuit against Waystar Royco, a media conglomerate accused of predatory business practices.

• Channel 5 believes their probability of winning the lawsuit is 40% where they will pay $$C_p = \30,000$$ in costs.
• Waystar Royco believes their probability of losing the lawsuit is 50% where their costs total to $$C_d = \50,000$$
• If the estimated damages are D = \$100,000 will a settlement occur?

Plaintiff’s expected return

$E[R] = 0.4(3\cdot 100,000)+(1-0.4)(-30,000) = 102,000$

Defendant’s expected loss

$E[L]=0.5(3\cdot 100,000+30,000+50,000)+(1-0.5)50,000 = 215,000$

$$E[L]>E[R]$$ , settlement will occur

#### Example 2

Plaintiff’s expected return

$E[R]=0.4(3\cdot 100,000)-(1-0.4)30,000 = 102,000$

Defendant’s expected loss

$E[L]=0.1(3\cdot100,000 + 30,000+50,000)+(1-0.1)50,000 = 83,000$

Since $$E[L]<E[R]$$, settlement will not occur

#### Summary of steps to solving settlement problems

1. Calculate the expected return from a lawsuit for the plaintiff (remember that, if they win, they receive triple the amount of damages)
2. Calculate the expected loss from a lawsuit for the defendant (remember that they’re required to pay their costs even if they win the case)
3. Compare the two values. If the expected loss is greater than the expected return, the defendant will “buy” the suit and a settlement will occur.

### Instruments of Discovery

• Before the trial begins, both sides should have access to the same information through the process of fact discovery
• Documents: any records that have some bearing on the case
• Interrogatory answers: written responses to specific questions posed before the trial
• Depositions: sworn testimonies (audio or video recorded) of anyone with relevant information (e.g. witnesses)