0:01

When analyzing growth through entry, game theory can be very useful for helping us

Â understand rivalry between many players who might be participating in that market.

Â Formally, game theory is the analysis of conflict and

Â cooperation among intelligent and rational decision makers.

Â The roots of game theory go back to actually the study of strategizing around

Â war, and

Â its roots as a technical discipline go back to the World War II era.

Â 0:25

Game theory really grew out of a study of mathematics and

Â operations research, but was appropriated by economists to use

Â to look at these types of competitive situations that we're interested in.

Â Now they're useful in analyzing competitive exchanges especially

Â in situations where there are a limited number of competitors and alternatives.

Â Think again Boeing versus Airbus, Coke versus Pepsi.

Â Not to say that they could be use to analyze situations with

Â numerous competitors with numerous alternatives.

Â But you'll see when we think about different ways to map these out,

Â it's often more useful in a limited number of situations.

Â Also it's useful when we know objectives and

Â payoffs associated with the game being played.

Â It's not to say that the payoffs are known with certainty.

Â They could be probabilistic, there could be uncertainty.

Â But at the very least we have some expectation of what those payoffs are and

Â we have an expressed objective function that firms are reacting to.

Â 1:18

Now we can think of many different types of games.

Â There are single-period simultaneous-move games.

Â The Boeing versus Airbus in the jumbo,

Â jumbo airplane business is in essence a single-period simultaneous game.

Â Mergers and acquisitions often have that type of dynamic.

Â Large capital investments, new facilities or

Â new manufacturing plants can similarly have a simultaneous-move aspect to them.

Â We can also think about repeated games, ones that have a simultaneity

Â to them when they're played, but then they are repeated over and over again.

Â Think about in the auto industry where you have new generations of cars coming out.

Â In the game player industry, we have about a four or five year cycle in which the big

Â players, Sony and Microsoft, introduce new gaming systems.

Â So there's a simultaneity in terms of when they're playing, but

Â it's repeated over again.

Â We see this also in the allocation of spectrum rights,

Â where they're voted by the different cellular providers and the like.

Â Again, a repeated multi-period game.

Â Last but not least, we have sequential games.

Â This is where the moves by various competitors could come really at any time,

Â and we have kind of the give and take.

Â One takes a move, then another takes a move and so on.

Â And I think this is where we see a lot of competitive behavior.

Â Think about Apple and Samsung and the smartphone business.

Â One will make a new announcement for a new set of products,

Â the other one might wait a few months and they'll make a new announcement.

Â And this goes back and forth, going forward into the future there.

Â 2:50

Now game theory is a vast topic.

Â We could take a whole course on game theory.

Â There's whole textbooks and books written on the subject.

Â But if you're gonna remember only one thing about game theory,

Â it's the following.

Â It's this idea of look forward and reason backwards.

Â By looking at the potential payoffs, the potential strategic moves of different

Â actors, and then reasoning backwards, we can make a forecast or

Â prediction of how a competitive game is likely to play out.

Â 3:17

So consider the following.

Â Here we have an entry game.

Â We have two firms deciding whether to enter a market or not,

Â like our Boeing versus Airbus example earlier.

Â Now what we have illustrated here is what we call a payoff matrix.

Â It's a very nice simple tool for mapping out the various

Â payoffs associated with various strategic moves by a number of competitors here.

Â So in one case we see the payoffs to Firm 1 in the lower left

Â quadrant here of each box.

Â So if Firm 1 does not enter the market, they'll lose negative $30.

Â The logic here being that they incur some costs in pursuing and looking into

Â entering the market, and if they fail to enter then those costs will be lost.

Â Firm 2 similarly loses negative $30 if they enter and

Â Firm 1 doesn't enter as well.

Â But what happens if one enters and one doesn't?

Â Well, there we see that the one who doesn't enter still incurs the negative

Â $30 that they incurred from exploring entering the market, but

Â the one who does enter into the market can do quite well.

Â However, like our Boeing and Airbus case here, if they both enter the market,

Â they're actually going to lose money, and lose more money than they've invested so

Â far, because the market just simply can't support two entrants

Â in the market there without driving prices down and eliminating margins.

Â So the interesting dilemma in this particular case is that,

Â while one would like to enter while the other one doesn't, if they both enter,

Â you get the worst outcome here, where they both lose negative $50.

Â And it's unclear, given the way the model's structured, which will result.

Â But if it was a true simultaneous game

Â where they didn't know what the other was going to do,

Â one could see the risk of going to the enter-enter scenario and losing money.

Â 4:57

Consider another game.

Â Here we have an investment game where you have two firms making a capital

Â investment, let's say build a new factory in one location versus another, so

Â Invest A and Invest B.

Â Now unlike the previous game, which was a symmetric game,

Â this is an asymmetric game.

Â In a symmetric game the payoffs to one firm versus the other are equivalent.

Â In an asymmetric game they might be different.

Â We could imagine they have different capabilities and different resources that

Â could cause a difference in the payoffs associated with the strategic action.

Â So in our case, if both firms choose to invest A,

Â Firm 1 will actually do better than Firm 2, $100 versus $25.

Â On the flip side, if they both invest B,

Â Firm 2 will do better than Firm 1, $75 versus $50 here.

Â What's interesting about this scenario is there's a strong preferred outcome for

Â both firms, which is not to be in the same investment.

Â They should be doing different things.

Â If they both invest A, they'd be better off one investing in B and

Â one in versus A, or vice versa.

Â And similarly if they both invest B.

Â So we have these two outcomes that are desired here.

Â However, it's not clear which one will result.

Â Clearly Firm 1 would prefer to invest in A and have Firm 2 invest in B.

Â But Firm 2 would also like to invest in A if Firm 1 invested in B.

Â 6:20

One way this could be resolved, if we turn this game into a sequential game.

Â So now imagine that Firm 1 gets to move first.

Â They get to be the first one to make an investment decision.

Â And then Firm 2 will react to that.

Â So what we've constructed here is a decision tree.

Â So a decision tree is one way of illustrating the interchange in

Â a competitive game over time.

Â So if we take Firm 1's actions and then assume Firm 2's actions,

Â we can translate our payoff matrix from the previous slide into the payoffs shown

Â at the bottom of the decision tree.

Â And what we can show is that if Firm 1 invests A,

Â Firm 2 prefers to invest B because they'll get $50 versus $25.

Â Similarly, if Firm 1 invests B,

Â Firm 2 decides to invest A because they get $100 versus $75.

Â Now Firm 1, knowing what Firm 2 will do in each of these scenarios,

Â can look and say, well, they do better if they invest A and

Â get $100 payoff versus investing in B and getting $125.

Â So they decide to invest A.

Â So by taking our simultaneous game and making it a sequential game,

Â we can make a prediction here that Firm 1 will invest A and Firm 2 will invest B,

Â and we have expected payoffs here of $150 and $50.

Â 7:36

So in summary, when we're analyzing gains we have a number of tools here, two tools

Â that we've introduced for mapping these gains, payoff matrices and decision trees,

Â and a number of considerations that we need to think through.

Â Is this a symmetric game or an asymmetric game?

Â Is this a single shot versus a repeated game?

Â And we also want to be thinking about how long is the game repeated?

Â Is this one that goes on forever?

Â Is this one at least when we don't know when the end is?

Â Or is there some horizon effect here?

Â Do we know there will be a definitive end to the game at some point in time?

Â I raise this because horizons can add a very important implication for

Â strategic behavior, which is that towards the end of the game rivals tend to be more

Â competitive, at least experimentally and the like, than they otherwise would be.

Â So let's end there and we'll come back and

Â talk a little bit more about some of the challenges in analyzing games.

Â