0:54

In 2008, Cellectis sued Precision BioSciences for

Â patent infringement, and the litigation ended in 2015.

Â Imagine now that it's 2008.

Â Cellectis's legal advisors note that the litigation

Â process has three well established stages.

Â In stage 1, the court decides whether or not Cellectis's patent is valid.

Â In stage 2,

Â if the patent has been considered valid, then the court will determine whether or

Â not Precision BioSciences has infringed on select business patent.

Â 5:56

If it's not infringed, then the litigation ends.

Â If it is infringed,

Â then Cellectis can decide whether to proceed into phase 3 of the litigation.

Â That's the damages phase.

Â At that point it can decide not to, or it can decide to proceed into the damages

Â phase, and pay it's attorneys an estimated fee of $1 million dollars.

Â In the damages phase, there are four equally likely outcomes.

Â Cellectis might be awarded damages of $50 million, $40 million,

Â $30 million or $20 million, so that's the full tree.

Â Next, we want to decide what the probabilities are of the different event

Â nodes, so let's start at the beginning, and work towards the end.

Â In the first event, whether the patent's found valid or not,

Â we know that there's a two-third chance that the patent will be found valid.

Â And a one-third chance that the patent will not be found valid.

Â So notice that those two probabilities add up to one.

Â 6:55

In the second litigation phase, that's patent infringement, we know that there's

Â only a 1 in 4 chance that the patent will be found to have been infringed upon.

Â And that leaves a three fourths chance

Â that the patent will not be found to have been infringed upon.

Â Again, the two probabilities add up to one.

Â In the final damages stage, there are four equally likely outcomes of $50,

Â $40, $30 and $20 million dollars in damages.

Â And each of those is going to accrue with an equal probability, or 1 in 4.

Â So those are all the probabilities in the event nodes.

Â At each event node they add up to one.

Â Finally, at each outcome we want to determine what the payout is for

Â Cellectis.

Â To do that we're going to calculate the payouts associated with

Â the various outcomes.

Â We're going to start at the initial root of the tree, and

Â work through all the cash flows on the branches that lead up to the outcome.

Â We start at the lower left, in the litigation phase.

Â If Cellectis decides not to litigate, then it pays nothing to it's attorneys.

Â On the other hand, if Cellectis decides to litigate,

Â it's going to pay $3 million dollars to its attorneys.

Â And then one of two things can happen.

Â It could lose phase one of the litigation in which case it would have paid three

Â million and got nothing back and so the outcome will be negative three million.

Â On the other hand, it may decide to litigate and pay the three million and

Â then The patents found to be valid, at that point Cellectis has a second

Â decision, it can decide not to proceed with these to the patent infringement.

Â In which case it's paid the three million and got nothing back, so

Â again the outcome is negative three million for Cellectis.

Â Alternatively having initiated litigation and found it's patent to be valid,

Â Cellectis may decided to continue with litigation in phase two and

Â then pay an additional $5 million to it's attorneys.

Â At that point, there are two potential outcomes.

Â The patent may be found to not have been infringed upon.

Â In that case, Cellectis will have paid the $3 million plus another $5 million or

Â it will have lost $8 million.

Â 9:05

On the other hand,

Â it could be that the patent is found to have been infringed upon.

Â At which point Cellectis has yet one more decision.

Â And that is whether to engage in phase 3 of the litigation, the damages phase.

Â If Cellectis having won the patent validity and

Â won the patent infringement phases decides at that point to stop litigation,

Â it will have paid $3 million and $5 million,

Â got nothing back, and it will still have loss $8 million.

Â On the other hand, if at that point Cellectis continues with

Â the damages phase, it will pay an additional $1 million to its attorneys and

Â then face one of four equally likely outcomes.

Â For example, if the outcome is $20 million in damages,

Â then Cellectis will have paid three million and five million and one million.

Â And received 20 million.

Â Or it would have a net payout of $11 million.

Â That's 20 minus one, minus five, minus three.

Â If the damage is at 30 million,

Â you can see that the payout would just be ten million more or 21 million.

Â If the damages are 40 million, it would be a 31 million dollar payout.

Â And, if the damages are 50 million, it would be a 41 million dollar payout.

Â So now, we've constructed our decision tree.

Â We've included decision nodes, event modes, and outcomes.

Â Along the branches we've written the associated payout,

Â the associated cash flows along the way.

Â At each the event nodes we've included probabilities that sum to one and

Â we've calculated the net payout to select this at each of the outcomes.

Â 11:19

To do that we start at the end of the tree and we work backwards towards it's root.

Â At each event node we choose the minimum outcome, the worst outcome.

Â And then at each decision node,

Â we choose the decision that maximizes the outcomes of those decisions.

Â So let's take a look.

Â Here's our tree.

Â We're gonna start up the first node at the end is the event node so

Â we're going to select the minimum [COUGH] outcome.

Â And you can see that, that's 11 million,

Â we'll substitute the event node with the 11 million.

Â And now there's a decision for Cellectis to make.

Â And that is does it proceed to phase three in litigation.

Â And it's gonna choose the decision that maximizes the outcome.

Â In this case it's the 11 million.

Â So yes, Cellectis is going to choose to

Â enter interface re-litigation if it makes it that far.

Â 12:30

Here that would be if Cellectis loses phase two of the litigation.

Â That is, if the patent's determined not to have infringed, in which case,

Â it will have lost $8 million and we'll substitute that for

Â the event node and now, Cellectis has the decision of whether to enter phase 2 or

Â not, given that it made it through phase one.

Â And here you can see that the maximum value for

Â Cellectis would be not to enter into phase 2 litigation and

Â just take the $3 million loss, rather than the chance at an $8 million loss.

Â We'll substitute the $3 million loss for the decision node.

Â And we're finally at the first outcome,

Â which is whether the patent is valid or not.

Â Here, in either case,

Â you can see the outcome is negative $3 million, so we'll substitute that value.

Â 13:29

For the event node, and now Cellectis has it's first decision,

Â that is whether to enter into litigation at all or not.

Â And if it does, it will lose $3 million, and if it doesn't, it will lose nothing.

Â So to maximize the outcome, it will choose not to go into litigation.

Â And we see that Cellectis's maxi-min strategy is

Â to not to enter into litigation at all.

Â The next set of strategies that we're going to look at are maxi-max strategies.

Â Those are the opposite.

Â These are risk-seeking, or reward seeking strategies that are intended to

Â maximize the maximum possible outcome without regard to how bad things can get.

Â Begin, we're gonna start at the end of the tree and work backwards.

Â At each event node we're now going to choose the maximum outcome

Â rather than the minimum cuz we wanna see how good things might be.

Â Then at each decision node, selectors will choose the outcome maximizing decision.

Â And again we'll work backwards towards the root.

Â So here's the decision tree.

Â We'll start at the end, and we'll select the maximum event outcome.

Â So that in this case would be 41 million and we'll substitute that for

Â the event node, and now Cellectis must decide whether to enter into phase 3,

Â if it makes it that far.

Â If it does, would have a maximum outcome of 41 million.

Â If it doesn't, it would have a maximum outcome of negative eight million.

Â So it's going to choose to enter into phase 3.

Â We're going to substitute the 41 million for

Â the decision node, and now we're back to an event node.

Â 15:07

Whether the patent was infringed or not in phase 2.

Â And here, you can see the maximum outcome, again would be $41 million.

Â So we'll substitute that for the event node.

Â That's as good as things could get for Cellectis.

Â And now Cellectis has a decision of

Â whether to enter into phase 2 if it makes it that far.

Â And you can see again that if it makes it that far,

Â if it enters into phase 2 it can earn up to 41 million.

Â 15:43

And if it decides to stop at that point, it would lose 3 millions.

Â So, again, the value maximizing decision would be to enter into litigation.

Â And so we'll take that $41 million and we'll substitute it for the decision node.

Â And, here, we're at the outcome of the event of the Phase one of the trail,

Â determining whether the patent's valid or not.

Â Again, we're going to select the maximum event outcome,

Â which is $41 million, substitute it for the event node, and finally,

Â Cellectis has a decision of whether to enter into litigation at all.

Â If it does enter into litigation,

Â it would have the chance of earning up to $41 million.

Â If it doesn't, its gonna have the chance of earning zero.

Â So Cellectis in this case would choose to enter into litigation.

Â And we see that to maximize its maximum payout,

Â Cellectis should proceed through all stages of litigation.

Â That's the only way it can earn a positive payout.

Â And it has the chance of running up to $41 million, if things work out for it.

Â [COUGH] So we've seen the maxi-min set of decisions,

Â maximizing the minimum outcome is to not enter into litigation at all.

Â And really, at any stage of the litigation, to stop.

Â The maxi-max set of decisions to maximize the maximum possible outcome, would be to

Â proceed through all stages of litigation to have a chance at that $41 million.

Â Finally, we're going to look at the expected value maximizing decision for

Â Cellectus.

Â Those are the risk neutral decisions that place equal weight on good and

Â bad outcomes.

Â As before, we're going to start with the tree's outcomes and

Â work backwards to its root.

Â At each event node, we're gonna calculate the expected value of the outcome.

Â So that's the weighted average of the outcomes.

Â We'll use the probabilities as the weights.

Â At each decision node, then, we'll choose the expected value maximizing decision.

Â So here we go again.

Â We're gonna start at the end, and we'll calculate the expected value of phase

Â three of the trial where we'll equally weight the $41,

Â $31, $21, and $11 million outcomes.

Â And when we calculate the expected value, it's $26 million.

Â And we'll substitute that for the event node.

Â So now, Cellectis must decide whether to enter into phase three litigation,

Â given that it made it that far.

Â If it does, the expected value is $26 million,

Â if it doesn't it's negative eight.

Â So Cellectis is going to choose to continue litigation if it makes

Â it that far.

Â And we'll substitute the $26 million for the decision node.

Â Again, we have an event node and we're gonna calculate the expected value

Â of the two events which would be if it wins phase 2,

Â ten the expected value from then on out would be $26 million.

Â If it loses phase 2, then the expected value is negative $8 million.

Â 18:47

So we'll calculate according to those probabilities of one-fourth and

Â three-fourths, the expected value of the two outcomes, and

Â it's just a half a million.

Â We'll substitute the half a million in for the event node and now Cellectis

Â needs to decide if it makes it to phase 2, should it enter into phase 2 litigation.

Â If it does, the expected value's a half a million, if it doesn't,

Â the expected value is negative $3 million.

Â So we'll decide, should it make it to phase 2 to enter into litigation?

Â And we'll substitute the half million for the decision node.

Â 19:21

The last event is whether

Â Cellectis's patent will have been decided to be valid or not.

Â And here, Cellectis needs to calculate the expected value of the two outcomes.

Â If the patent's valid, then the expected value for

Â Cellectis is a half million, if it is invalid, it is negative $3 million.

Â And when we take the expected value across those two outcomes, with two thirds and

Â one third probabilities, the expected value is negative $0.67 million.

Â Will substitute the negative $0.67 million for the event node,

Â and select this as first decision as whether to enter into litigation at all.

Â If Cellectis does enter into litigation, its expected value is negative

Â $0.67 million and if it doesn't the expected value is $0.

Â In choosing to maximize the expected value Cellectis would choose to not

Â enter into litigation at all.

Â And so, to maximize its expected value

Â Cellectis again would not enter into litigation.

Â That's the same initial strategy as the risk minimizing,

Â maxi/min strategy, not to enter into litigation.

Â 20:35

So what have we seen?

Â We built a decision tree.

Â We used decision nodes, event nodes and outcomes.

Â We made sure that the probabilities that each of the event nodes sum to one.

Â We added up the cash flows from the roots of the tree

Â to each leaf to calculate the appropriate pad at each leaf.

Â We then identified three strategies.

Â The maxi-min, which is the risk minimizing strategy.

Â The maxi-max, which is the reward maximizing strategy.

Â And the expected value maxing strategy, which is risk neutral.

Â We saw that the initial maxi-min and

Â expected-value maximizing decisions coincided.

Â In both cases, it was optimal not to litigate and to collect no money.

Â The maxi-max strategy differed however.

Â To have a chance at collecting damages,

Â it had to continue through all stages of litigation.

Â So, that's it for our review problem.

Â Now that you've got it under your belt, it's time for you to go and

Â work a couple of practice problems in preparation for the quiz.

Â Thanks.

Â