So in the previous session, we derived the willingness to pay for entrants and monopolists. So, in some sense we were looking at an asymmetric situation. So, in this video we'll address one of the most important questions that might arise with multiple symmetric firms. Can select a specific aspect of their R&D strategy? And we're going to be talking about the decision to be active in a particular field at all. Throughout this video, let's assume that players are risk neutral. So, that they only care about expected profits, but let's now get started. So, with innovation under competition, and as always, we're facing a trade-off. So, R&D faces this trade-off between on the one hand, facing the chance of having promising returns. We saw that in the previous videos, that potentially we could get huge returns, or positive returns, if we engage in R&D. And if we end up with getting an innovation. On the other hand, R&D also involves the risk of losing R&D investments. So in the previous case, we didn't look at any degree of uncertainty in the previous videos. Now we're just going to focus on the situation where there's a possibility that you're not going to be successful with your R&D strategy. So, this could be either if you are not successful at all or if the other company is faster. Now let's begin take a very simple setup of two pharmaceutical companies and we'll call them A and B, that have to decide whether to engage in R&D for a new drug against asthma. There is fixed cost of R&D activity of 10 million pounds, right, so that's something that you incur at any rate. If you're successful, if you're not successful, if you're a monopolist, if you're in competition there is a fixed cost of R&D of 10 million. There is a likelihood of p that each of those or any of those firms is going to come up with a marketable innovation. And the profits from that will depend on the question if the other firm also is successful or not in their R&D strategy. So if you are alone in the market, you make profits of 24 million pounds. If you compete with another firm in the market with a similar product you're going to make profits of 10 million pounds. So with those numbers let's have a look at what the payoffs are for company A, and of course the payoffs are going to depend significantly on what the other firm does. So, if company A engages in R&D but company B does not, there are really only two things, we have to think about. So, either firm A is successful or they're not successful. If they're successful, they make profits of $24 million, okay? Because only if they are, there's no problem, no threat of the other firm even entering so they would make $24 million. If they are unsuccessful, they're going to make $0 profits. So, it's 1 minus p, the likelihood of not being successful times 0. And in any case we have to pay the fixed cost of doing R&D, which is 10 million. So, in other words the payoffs for company a, if they are doing R&D on their own is going to be 24 minus 10, so p times 24 minus 10. What if both companies engage in R&D? It gets a little bit messier, but we can still, I think, figure it out. So, right now, there are many more things that can happen. So we could have one case in which we're successful and in which the other firm is not successful. So, this is my own likelihood of success multiplied with the likelihood of the other firm being unsuccessful. And in that case we're going to make 24 million because we become a monopolist. We're still a monopolist. There is a scenario where we are successful, and the other firm successful as well. In that case this is my own likelihood, this is the likelihood of firm B. And we're going to make profits of 10. The scenario where I'm unsuccessful - then we don't really have to distinguish because all I care about is my own profits, and if I'm unsuccessful, I make profits of zero. And as in the case previously, we have to subtract the cost of doing R&D, which is 10 million in any case. So, what if Company A does not engage in R&D, well simple, right? You don't spend anything, and you don't get anything. So, your profits are going to be 0. So, we can now take all these numbers that we saw in the previous slide and put them into a matrix. So, both firms don't do R&D. They, of course, make 0 profits. If firm a does not do R&D and firm b does, then firm a gets zero profits and firm b gets the 24 p minus ten, right? So, if they are successful, they get profits of 24 million because they are the only firm in the market and they always have to pay the 10 million in fixed costs. It's the other way around if we flip the strategies and if we have both firms doing R&D. We have both firms doing R&D, then we're going to get this long expression here. So Firm A does R&D and so does Firm B, Firm A's profits are going to be 24 times p times 1 minus p. Why is that? It's 24 million if Firm A is successful and Firm B is not. They're going to have 10 times p squared. That's 10 million if Firm A is successful and Firm B is also successful. And they will always pay the 10 million in fixed costs of R&D. Now that's not something we can really use at this point because we don't know what the numbers are, we don't know what p is, we don't know what the likelihood of success is. So, let's say use some real examples here, so, if we have a low success rate there is a likelihood of p that R&D generates an innovation of 25%. So, in other words, only one in four projects is successful. Now, this means that this payoff matrix will give us real numbers now that we can work with. So, to be concrete if Firm B does not do R&D, then Firm A's expected profits are going to be minus 4 million, and so on and so forth. So, let's have a look at what the Nash Equilibrium of this game is. So, Firm B does not do R&D, Firm A can choose between minus 4 and 0 and they're going to go for 0. So, they're not going to do R&D if Firm B doesn't do R&D. If Firm B did do R&D, then again, Firm A can choose between minus almost 5 million or getting 0. So there again better off not doing R&D. In other words, it's a dominant strategy for firm A not to do R&D. Now, if firm A, again could do R&D or not do R&D, then firm B will have a dominant strategy as well of not doing R&D. So, in other words we have a dominant strategy. We have a dominant strategy where both firms don't do R&D. Now let's take this forward and let's crank up the success rate by a little bit. So, now the likelihood that you're going to be successful is 50%. So nothing changes if you don't do R&D. Again you just have 0 profits, fine. Things change if you do R&D because your expected value of doing R&D has just changed. So, all the payoffs will change as follows. Now it's negative if both firms do R&D. So, they both make negative one and a half million and it's still positive, it's positive two million if firm A does R&D and firm B does not. So, you know what? Why don't you have a go at this and do an in video quiz and I'll see you later to see if you got the right Nash Equilibrium. Okay, so was that tough? Let's have a look. If firm B does not do R&D, then Firm A can choose between 0 and 2, so they would do R&D. If Firm B does R&D then Firm A chooses between minus 1.5 and 0, so they would be better off not doing R&D. If Firm A does not do R&D, then Firm B can choose between 0 here or 2 here. So, they would prefer to do R&D and if Firm A does do R&D, then Firm B is better off not doing it right? Because it's better getting 0 than loosing 1.5 million. So, in other words, we now have two Nash Equilibria here. No dominant strategy but two Nash Equilibria. One where Firm A does R&D, Firm B does not. And one where Firm B does R&D, and Firm A does not, okay? So, two Nash Equilibria, they're asymmetric. One firm does it the other firm does not. Let's now crank up the success rate even more and see now it's 75%. So, three cases out of four, you're going to be successful with your R&D strategy. Our payoffs change again. And let's see if our Nash Equilibrium also changes. Again, firm B not doing R&D leads to firm A doing R&D. That's what we had before. However, if firm B doesn't do R&D and firm A again is better off doing R&D, so interestingly we have a dominant strategy for firm A to do R&D. And the same thing is going to happen for firm B, so they are going to have a dominate strategy, of doing R&D. So, we have one Nash Equilibrium where both firms engage in R&D. Let's now compare the success rates here. If the success rate is fairly low then the best thing the firms can do is not to do R&D at all, which sort of makes sense. If it's not a good innovation, if it's not a good field to be in then maybe you're better off staying out. If you have a sort of intermediate success rate we're going to find R&D being done by one firm and that firm trying to preempt the other one. Right? So, we want to commit to doing R&D before the other one can. And if the success rate is fairly high, both firms will want to do R&D simultaneously. So, to sum up. We now have a pretty good idea of what will happen to an R&D activity in relation to the likelihood of success. Low probability projects with a high fixed cost of doing R & D will probably not even happen. A medium probability project will be undertaken by which ever firm commits to the project first. And this tries to pre-empt the market for others. Or whenever two firms actually do end up competing in a medium probability field, we're likely to see some losses for these two firms. And thirdly, high probability projects will be undertaken by many firms at once which may turn out to destroy parts of the profits to be made from the innovation in the first place. Why? Well, it's likely that projects with a high success rate will have two or more innovations and therefore competition in the product market which, of course, lowers overall profits compared to a monopoly. So, let's now move on to another strategic aspect of R&D in particular, sleeping patents. See you very soon.