game theory analysis of legal strategies

Guard

Prisoner

Prisoner

Guard

Give cigarette

Don’t give

Bang HeadDon’t Bang

Give cigarette

Don’t give

Don’t Make

Make Allegation

22

46

Make Allegation

15

34

Don’t Make

51

63

The Prison Guard, The Prisoner & The CigaretteFrom Pages 53 & 54 of You Can Negotiate Anything by Herb Cohen

Analysis by John Dinsmore ([email protected])

Game Theory Project, John Dinsmore, [email protected],

Cohen uses this scenario to illustrate the point that people always have some form of leverage within a negotiation—and usually more than they realize.

We a see a prisoner on death row who notices the person guarding his cell is smoking his favorite brand of cigarette—Marlboro “Reds”. Seemingly, the prisoner would not have leverage of any kind. He is, after all, a condemned man, securely behind bars and posing no physical threat to the guard.

But, being crafty, the criminal says if the guard does not give him a cigarette, he will bang his head against the prison wall until it is badly bloodied. Then, when someone asks the prisoner what happened to him, he will say that the guard beat him up. By rule, an extensive investigation will take place which will drag the guard into months of depositions and other hassles which would threaten his career. And, it’s no skin off the prisoner’s nose as depositions would only break up the monotony of sitting in a cell 24 hours a day. While he would not relish the cracking his head open, he well may enjoy the deposition process. And if the prisoner is found out to be a fraud, what are they going to do, arrest him?

After pondering the prisoner’s threat, the guard gives the prisoner a cigarette.

This game models as a sequential game with perfect information. Both players are aware of each move the other makes. A good example of this is “Greenmail” (Figure 8.2) in the text. The payouts are assigned with the following logic: The guard’s priorities are not making being accused of anything, followed (distantly) by not having to give up a cigarette. The prisoner’s top priority is getting a cigarette, followed (distantly) by not having to bang his head against the wall.

Guard

Prisoner

Prisoner

Guard

Give cigarette

Don’t give


Give cigarette

Don’t give

Make Allegation

22

46

Make Allegation

15

34

Don’t Make

63

#1a

Don’t Make

51

Key To Moves

1.In round four, the Prisoner would always choosea) to make the allegation if not given the cigarette.b) to make the allegation if given the cigarette as well

given the superior payout.2.Since the prisoner would always choose to make the allegation, the guard would always choose to not give the cigarette as his payout is higher (though still bad)

#1b

#2


Guard

Prisoner

Prisoner

Guard

Give cigarette

Don’t give


Give cigarette

Don’t give

Make Allegation

22

46

15

34

Don’t Make

63

Don’t Make

51

Key To Moves

3.When confronted with the choice of whether or not to bang his head after being denied a cigarette, the prisoner would choose to bang his head as there are two potentially superior payoffs down the road.

4.This move is represented below where, through backward induction/elimination, his choice to give a cigarette is a choice between payoffs of 4 and 2. He chooses the payoff of 4 and gives the prisoner a cigarette.

#3

#4

Guard

Give cigarette

Don’t give

46

22


Jackson

Parent

Parent

Jackson

Settle Don’t Settle

Sue PubliclyDon’t Sue

SettleDon’t Settle

Drop Case

Trial

($74,000,000)$2,000,000

($5,100,000)$3,300,000

($50,200,00)$6,600,000

($40,200,000)($20,000)

($100,000)$0

Similar Examples From Real Life—Michael Jackson & Child Molestation


In the instance of a parents weighing whether or not to bring suit against Michael Jackson for sexual misconduct with their children, it follows the “Prisoner-cigarette” example closely. The parent seemingly has nothing to lose and Jackson seemingly has everything to lose.

In fact, even just the accusations becoming public has a significant negative payoff for Jackson in terms of lower record sales and other lost revenue. So, the further the Parent takes the case, the more negative publicity is generated and the more Jackson loses in revenue—which takes the possibility of a countersuit off the table for Jackson. However, similar to the “Prisoner” scenario, the Parent’s payoff is not linear to number of rounds played, there is a point of diminishing returns, and can likely achieve a larger settlement pre-trial than a jury would ever return.

In this instance, I will list the payoffs in terms of financial benefit (loss) which will also reflect legal fees and lost sales to Jackson. The parent faces few costs as the attorney is taking the case on contingency, but as the case becomes more public, there will be some costs incurred—time off from work, security precautions needed as a result of the publicity, etc.

Verdict--JacksonVerdict--Parent

($71,000,000)($40,000)

Jackson

Parent

Parent

Jackson


Sue PubliclyDon’t Sue

SettleDon’t Settle

Drop Case

Trial

($74,000,000)$2,000,000

($5,100,000)$3,300,000

($50,200,00)$6,600,000

($40,200,000)($20,000)

($100,000)$0

Similar Examples From Real Life—Michael Jackson & Child Molestation


Verdict--JacksonVerdict--Parent

($71,000,000)($40,000)

In using backward induction, we see that in round four, the parent would choose a trial over dropping the case as that would be the only positive payout among the three possibilities.

In round three, Jackson would choose to settle, knowing that as big a loss as that is, it’s better than the $70MM loss he would face—win or lose—going to trial.

In round two, the Parent is going to choose “Sue Publicly” as there is a substantial payoff to that move, versus the zero payoff of not suing Jackson.

Finally, Jackson’s choice at the first round is between a $5.1 MM loss and a (best case scenario) loss of $71,000,000. Jackson chooses to settle.

Jackson


($5,100,000)$3,300,000

($71,000,000)($40,000)

Similar Examples From Real Life—Michael Irvin & Sexual Assault Accusation


One example in the real world that is similar to the “Prisoner-Cigarette” negotiation was the recent rape accusation levels against Hall-of-Fame football player Michael Irvin by a woman in South Florida.

Irvin, who had a reputation over the years as someone who enjoyed “Wine, Women and Song” to excess, would fill the role of the guard in this scenario. Given his reputation, an accusation of misconduct would be more easily believed than if he had a stellar reputation. Additionally, his already dubious reputation gives him no reservations about fighting the allegations publicly.

The stakes of the case are financial as she signed a waiver of criminal charges.

Jane Doe likely has an attorney working on contingency, so she incurs no out of pocket legal expense/transactional costs.

Jane Doe has little to lose—or so she thinks. Like the Ransom example in the text (Figure 8.3)**, Irvin and his attorney decide to alter the payoffs of the game. But, instead of putting a bounty on her head, they countersue for $100 Million and threaten to ruin her financially if she fails to bring a substantive case.

**Note: The Payoffs from the “Ransom” example have been changed slightly to reflect the different contexts.

***Please also note: The analysis of either the Jackson or Irvin cases makes no assumptions about guilt or innocence, only legal strategy used to achieve the optimal outcome on their behalf.

Jane

Jane

Irvin

SueDrop Case

Offer Settlement

13

42

31

24



First, let’s analyze Irvin’s strategies without the ‘countersue’ option.

• In round three, Jane would choose to sue, seeking the higher payout.

• In round two, knowing that Jane would take him to court, he would probably choose to settle over the high legal cost, public embarrassment and potential for losing the case.

Given, these payouts, Jane will always choose to sue and Irvin will always choose to settle. Now, let’s look at what happens when we add the ‘countersue’ option.

Don’t Settle

Drop CaseSue

Jane

Drop Case

Sue

24

42

Jane

Jane

Irvin

SueDrop Case

Offer Settlement Countersue

25

Drop Case

74

63

Sue

12

57



The highest priority for both parties, given the context of a civil and not criminal suit, is financial gain OR, more importantly, avoiding a financial loss. By countersuing, Irvin gave Jane Doe “something to lose” financially, where she had previously thought she had nothing to lose. It was, literally, a game-changing move.

Through backward induction, we can see that Jane’s viable strategies in round three are:

• Offer Settlement-Drop Case •Don’t Settle-Sue• Countersue-Drop Case

In round two we see that, given Irvin’s available options, his superior payout is going to be under the “Countersue” option. With all of this taken into account, moving to Jane’s decision at round one, her payoff for “Dropping the Case” is 5 and her payoff for “Suing” is 2. She chooses to drop the case.

36

41

Don’t Settle

Drop CaseSue Drop CaseSue

Jane

Drop Case

Sue

57

25

game theory analysis of legal strategies

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