When analyzing growth through entry, game theory can be very useful for helping us understand rivalry between many players who might be participating in that market. Formally, game theory is the analysis of conflict and cooperation among intelligent and rational decision makers. The roots of game theory go back to actually the study of strategizing around war, and its roots as a technical discipline go back to the World War II era. Game theory really grew out of a study of mathematics and operations research, but was appropriated by economists to use to look at these types of competitive situations that we're interested in. Now they're useful in analyzing competitive exchanges especially in situations where there are a limited number of competitors and alternatives. Think again Boeing versus Airbus, Coke versus Pepsi. Not to say that they could be use to analyze situations with numerous competitors with numerous alternatives. But you'll see when we think about different ways to map these out, it's often more useful in a limited number of situations. Also it's useful when we know objectives and payoffs associated with the game being played. It's not to say that the payoffs are known with certainty. They could be probabilistic, there could be uncertainty. But at the very least we have some expectation of what those payoffs are and we have an expressed objective function that firms are reacting to. Now we can think of many different types of games. There are single-period simultaneous-move games. The Boeing versus Airbus in the jumbo, jumbo airplane business is in essence a single-period simultaneous game. Mergers and acquisitions often have that type of dynamic. Large capital investments, new facilities or new manufacturing plants can similarly have a simultaneous-move aspect to them. We can also think about repeated games, ones that have a simultaneity to them when they're played, but then they are repeated over and over again. Think about in the auto industry where you have new generations of cars coming out. In the game player industry, we have about a four or five year cycle in which the big players, Sony and Microsoft, introduce new gaming systems. So there's a simultaneity in terms of when they're playing, but it's repeated over again. We see this also in the allocation of spectrum rights, where they're voted by the different cellular providers and the like. Again, a repeated multi-period game. Last but not least, we have sequential games. This is where the moves by various competitors could come really at any time, and we have kind of the give and take. One takes a move, then another takes a move and so on. And I think this is where we see a lot of competitive behavior. Think about Apple and Samsung and the smartphone business. One will make a new announcement for a new set of products, the other one might wait a few months and they'll make a new announcement. And this goes back and forth, going forward into the future there. Now game theory is a vast topic. We could take a whole course on game theory. There's whole textbooks and books written on the subject. But if you're gonna remember only one thing about game theory, it's the following. It's this idea of look forward and reason backwards. By looking at the potential payoffs, the potential strategic moves of different actors, and then reasoning backwards, we can make a forecast or prediction of how a competitive game is likely to play out. So consider the following. Here we have an entry game. We have two firms deciding whether to enter a market or not, like our Boeing versus Airbus example earlier. Now what we have illustrated here is what we call a payoff matrix. It's a very nice simple tool for mapping out the various payoffs associated with various strategic moves by a number of competitors here. So in one case we see the payoffs to Firm 1 in the lower left quadrant here of each box. So if Firm 1 does not enter the market, they'll lose negative $30. The logic here being that they incur some costs in pursuing and looking into entering the market, and if they fail to enter then those costs will be lost. Firm 2 similarly loses negative $30 if they enter and Firm 1 doesn't enter as well. But what happens if one enters and one doesn't? Well, there we see that the one who doesn't enter still incurs the negative $30 that they incurred from exploring entering the market, but the one who does enter into the market can do quite well. However, like our Boeing and Airbus case here, if they both enter the market, they're actually going to lose money, and lose more money than they've invested so far, because the market just simply can't support two entrants in the market there without driving prices down and eliminating margins. So the interesting dilemma in this particular case is that, while one would like to enter while the other one doesn't, if they both enter, you get the worst outcome here, where they both lose negative $50. And it's unclear, given the way the model's structured, which will result. But if it was a true simultaneous game where they didn't know what the other was going to do, one could see the risk of going to the enter-enter scenario and losing money. Consider another game. Here we have an investment game where you have two firms making a capital investment, let's say build a new factory in one location versus another, so Invest A and Invest B. Now unlike the previous game, which was a symmetric game, this is an asymmetric game. In a symmetric game the payoffs to one firm versus the other are equivalent. In an asymmetric game they might be different. We could imagine they have different capabilities and different resources that could cause a difference in the payoffs associated with the strategic action. So in our case, if both firms choose to invest A, Firm 1 will actually do better than Firm 2, $100 versus $25. On the flip side, if they both invest B, Firm 2 will do better than Firm 1, $75 versus $50 here. What's interesting about this scenario is there's a strong preferred outcome for both firms, which is not to be in the same investment. They should be doing different things. If they both invest A, they'd be better off one investing in B and one in versus A, or vice versa. And similarly if they both invest B. So we have these two outcomes that are desired here. However, it's not clear which one will result. Clearly Firm 1 would prefer to invest in A and have Firm 2 invest in B. But Firm 2 would also like to invest in A if Firm 1 invested in B. One way this could be resolved, if we turn this game into a sequential game. So now imagine that Firm 1 gets to move first. They get to be the first one to make an investment decision. And then Firm 2 will react to that. So what we've constructed here is a decision tree. So a decision tree is one way of illustrating the interchange in a competitive game over time. So if we take Firm 1's actions and then assume Firm 2's actions, we can translate our payoff matrix from the previous slide into the payoffs shown at the bottom of the decision tree. And what we can show is that if Firm 1 invests A, Firm 2 prefers to invest B because they'll get $50 versus $25. Similarly, if Firm 1 invests B, Firm 2 decides to invest A because they get $100 versus $75. Now Firm 1, knowing what Firm 2 will do in each of these scenarios, can look and say, well, they do better if they invest A and get $100 payoff versus investing in B and getting $125. So they decide to invest A. So by taking our simultaneous game and making it a sequential game, we can make a prediction here that Firm 1 will invest A and Firm 2 will invest B, and we have expected payoffs here of $150 and $50. So in summary, when we're analyzing gains we have a number of tools here, two tools that we've introduced for mapping these gains, payoff matrices and decision trees, and a number of considerations that we need to think through. Is this a symmetric game or an asymmetric game? Is this a single shot versus a repeated game? And we also want to be thinking about how long is the game repeated? Is this one that goes on forever? Is this one at least when we don't know when the end is? Or is there some horizon effect here? Do we know there will be a definitive end to the game at some point in time? I raise this because horizons can add a very important implication for strategic behavior, which is that towards the end of the game rivals tend to be more competitive, at least experimentally and the like, than they otherwise would be. So let's end there and we'll come back and talk a little bit more about some of the challenges in analyzing games.