viewof kind = Inputs.radio(
new Map([["Reach — brings new consumption into the market", "reach"],
["Comparative — moves consumption from the rival", "shift"]]),
{value: "shift", label: "Campaign"})
viewof S = Inputs.range([0.25, 2.0], {value: 1.0, step: 0.05,
label: "Units it adds per person"})
viewof K = Inputs.range([0, 1.20], {value: 0.10, step: 0.05,
label: "Cost per person"})17 Which Games Are Worth Playing
Some competitive moves create value and some only burn it, and you can tell which in advance
The advertising game in the last chapter had a comfortable ending. Both firms bought the campaign, both finished better off than if neither had, and the money they spent bought something real. Whatever else was true, nobody was worse off for having played.
That is not how competitive escalation usually goes, and the reason has nothing to do with how well anyone solves the game.
A Campaign That Only Moves Customers
Change one thing about the offer.
The agency in the last chapter sold reach: a campaign that told more people ice cream sandwiches existed, and brought one more unit per person per month of new consumption into the market. Whoever bought it grew the pool.
Now suppose a different agency sells comparative advertising. Not ice cream sandwiches are good, but ours are better than theirs. This campaign does not tell anybody anything new about the category. It moves one unit per person out of the rival’s column and into yours, at every price, and changes nothing else.
In the parameters, that is a transfer between the two intercepts. Whichever shop buys the campaign sees its demand intercept \(\mathsf{a}\) rise by one, and its rival’s fall by one. Price sensitivity is untouched and so is substitution, because the campaign does not make anyone more willing to switch on price; it simply relocates a unit of demand and leaves it there.
Same firms, same estimated demand system, same one unit. The only difference is where the unit comes from.
| Hogi Yogi does not | Hogi Yogi advertises | |
|---|---|---|
| Smart Cookie does not | $1.33, $0.96 | $1.15, $1.54 |
| Smart Cookie advertises | $1.51, $0.52 | $1.33, $0.96 |
Look at the diagonal. When neither firm advertises, Smart Cookie earns $1.33 and Hogi Yogi $0.96. When both advertise, Smart Cookie earns $1.33 and Hogi Yogi $0.96.
Not approximately. Exactly. The two campaigns cancel, the customers end up where they began, and the two firms have each paid an agency for the privilege.
Unilaterally, though, the campaign works. Hogi Yogi alone gains fifty-eight cents of gross contribution, and Smart Cookie alone gains eighteen. Each firm, looking at its own decision, sees a real gain.
When That Becomes a Trap
Whether that structure is a trap depends entirely on what the campaign costs, and the arithmetic is worth doing carefully because the answer is counterintuitive.
For both firms to buy, the gain has to exceed the cost in every situation. The smallest of those gains is Smart Cookie’s seventeen cents when Hogi Yogi is already advertising. So the campaign has to cost less than about seventeen cents before both firms want it regardless of what the other does.
At the fifty cents the last chapter’s agency charged, nobody buys this one. Smart Cookie declines, Hogi Yogi declines, and the comparative campaign never happens. The expensive poaching campaign is not a trap because it is not tempting.
Make it cheap, though, and the structure bites.
| Hogi Yogi does not | Hogi Yogi advertises | |
|---|---|---|
| Smart Cookie does not | $1.33, $0.96 | $1.15, $1.44 |
| Smart Cookie advertises | $1.41, $0.52 | $1.23, $0.86 |
Work through it the way the last chapter did. Smart Cookie earns $1.33 sitting still against a passive rival and $1.41 by advertising; $1.15 against an advertising rival and $1.23 by advertising. Better both times. Hogi Yogi finds the same thing.
So both advertise. Both are behaving correctly. And the equilibrium leaves Smart Cookie at $1.23 against the $1.33 it would have had, and Hogi Yogi at $0.86 against $0.96, each exactly ten cents poorer, which is exactly what the campaign cost.
This is a prisoner’s dilemma, and notice where it came from. It was not assumed for the sake of illustration. It fell out of an estimated demand system, a plausible campaign, and a cost, and it would have fallen out the same way if nobody had ever heard the phrase.
Prisoner’s dilemma — a game where each player’s best move leaves everyone worse off than if none of them had moved. The equilibrium is correct and the outcome is bad, which is why solving it harder does not help.
There is a nasty corollary in the cost. The cheaper the poaching campaign, the more certainly both firms buy it, and the money is burned either way. The trap requires the move to be cheap, and cheap is exactly when it looks most obviously worth doing.
Two Kinds of Move
Strip away the ice cream and the structure generalizes into the question this chapter exists to ask.
Does the move expand the pool, or move it?
A move that expands the pool creates something that was not there before. More people know the category exists, or can reach it, or find it worth buying at all. When both firms make such a move, both can end up ahead, because there is more to divide. That was the last chapter.
A move that redistributes takes from the rival. When both firms make it, the takings cancel, and whatever was spent is simply gone. Every firm behaved sensibly and the industry is poorer.
Which of the two you are looking at is a question about customers rather than about arithmetic, and it has to be answered before anything can be computed. Where do the extra units come from? A machine can solve the four cells and shade the whole map of them in a second, and it cannot tell you whether your campaign creates a customer or takes one. That sentence is yours, and everything downstream inherits whether you got it right.
There is a way of drawing a game that makes the answer visible rather than calculated, and it is worth learning because you will read a matrix faster with it than without.
For each column, ask which row that player prefers, and draw an arrow pointing there. For each row, ask which column the other player prefers, and do the same. Where two arrows point into the same cell, neither firm wants to leave it, and that cell is the equilibrium. A player whose arrows both point the same way has a dominant strategy and does not need to think about the other at all.
Below, the arrows are drawn for you and everything is live. Switch the campaign between the two kinds, and move its effectiveness and its cost.
Smart Cookie is blue and Hogi Yogi orange, in the payoffs and in the arrows alike. Blue arrows run vertically because Smart Cookie is choosing a row; orange run horizontally because Hogi Yogi is choosing a column. The shaded cell is the one both point into.
Dragging those sliders without a map is a good way to watch things change without learning much, so here is the map. Every point in it is a whole game, solved, and colored by which equilibrium comes out. The dot is where your sliders currently sit.
Two things are worth reading off it before touching anything.
The boundaries all slope the same way. A more effective campaign is worth more, so it stays worth buying at a higher cost, and every region boundary drifts right as effectiveness rises. Nothing surprising there, and it is the reason a single threshold is not the answer to is this worth it — the answer is a curve.
What differs between the two campaigns is what lies at the bottom, and seeing it takes one click: set the Campaign control above to reach and watch the map redraw. The cheap end is now entirely green, because when advertising expands the market, both firms buying it is a good outcome at every effectiveness. Switch to comparative and a band of salmon opens along the bottom, and that band is the trap. It sits at low costs, which is the corollary this chapter has already stated and the map now makes geographic: the cheaper a redistributive campaign gets, the more certainly both firms buy it and the more certainly both regret it.
Above that band, under either campaign, is the region where only one firm advertises, and above that the region where nobody does. Notice which firm it is, because it changes. Under reach it is Smart Cookie, because the differentiated firm captures more of any expansion and can therefore justify a higher cost for it. Under comparative it is Hogi Yogi, because the firm with more to gain from poaching is the one with fewer customers to lose.
The absences say as much as the regions. Smart Cookie never advertises alone under a comparative campaign, and Hogi Yogi never does under reach; neither campaign ever produces both outcomes. Each toggle yields three of the six possible regions and never the other three, which is why the legend changes when you switch — it lists what is on the map rather than what could be.
Start where the chapter left off, with the comparative campaign at ten cents. Every arrow points toward advertising, both firms land in the bottom-right, and the readout says what the numbers said: both are worse off than if neither had moved. Now raise the cost. Somewhere near seventeen cents Smart Cookie’s arrows flip, the trap opens, and above about sixty cents nobody advertises at all.
Then switch the campaign to reach and watch what changes. The arrows still converge on both firms advertising, and the warning disappears, because the money is now buying consumption that did not previously exist.
Most competitive moves are recognizable as one or the other once the question is asked plainly.
| Move | Expands or redistributes |
|---|---|
| Advertising that explains the category to people who did not know | expands — raises a for whoever buys it |
| Advertising that compares you to a named rival | redistributes — moves customers between existing columns |
| A genuine product improvement customers would pay for | expands, and also lowers your b, which is the durable part |
| Matching a rival's discount | redistributes, and worse, it is a price move disguised as a competitive one |
| Opening in a location neither firm serves | expands — new population rather than new share |
| Buying exclusive shelf space or a supply agreement | redistributes — it constrains the rival's access rather than creating demand |
| Extending hours, adding a channel, easing access | usually expands, if the constraint was real |
The middle rows are where founders get into trouble, because redistributive moves feel more competitive. Naming your rival, matching their price, locking up the supplier — these read as decisive action in a way that explaining your category to strangers does not. They are also the moves most likely to be matched, and matching is what turns them into a dilemma.
You Cannot Out-Solve a Dilemma
The instinct on recognizing a prisoner’s dilemma is to look for a cleverer play that escapes it. There is not one. The equilibrium is not a mistake; it is what happens when two firms respond correctly to their situations. Solving the game more carefully returns the same answer.
What changes the outcome is changing the game, and the honest list of ways to do that is short.
Change the move. Most redistributive moves have an expanding cousin. Comparative advertising and category advertising cost about the same and land in completely different games. If you are about to spend on something that only moves customers, ask what the version that grows the market would cost.
Do not play. If a move only pays when the rival sits still, and the rival can see the same arithmetic you can, the expected outcome is the one where both of you spent. Declining is a genuine choice and it is usually invisible, because the case for spending is loud and the case against is a calculation nobody presents.
Change what the rival expects. This is the one that genuinely works and it is the subject of the next chapter. Firms escape dilemmas by making commitments that alter what the other side believes will happen, which is a different move from playing the game well.
What does not work is hoping. A dilemma where both firms would be better off cooperating is not resolved by both firms understanding that. They understood it the whole time.
Before committing to a competitive move
- Which does it do — expand the pool or move it? Say it in one sentence about customers, not about your firm. If the sentence is “more people buy this kind of thing,” it expands. If it is “more of them buy mine instead of theirs,” it redistributes.
- What happens if the rival matches it? Not whether they will. Compute the cell — which means handing over both demand systems, both cost structures, and what the move does to the parameters, and getting back four equilibria rather than one. If matched-and-both-spent leaves you worse than nobody-moved, you are looking at a dilemma however good the unilateral case looks.
- Is it cheap? Cheap redistributive moves are the dangerous ones, because cheapness is what makes them individually rational for both firms and therefore certain to be matched.
- Could the same money buy an expanding move instead? Compare them as alternatives rather than comparing the move to doing nothing.
When the Problem Is Agreement Rather Than Rivalry
One more shape worth recognizing, because it looks like a dilemma and is not.
Sometimes two firms would both be better off doing the same thing — adopting the same standard, using a shared supplier or format, entering a market together so it becomes credible to customers — and the difficulty is not that each wants to defect. It is that neither wants to move first and be alone.
Those games have more than one equilibrium. Both adopting is stable; neither adopting is also stable; and which one happens depends on expectations rather than on incentives. The distinguishing sign is that if the two firms could simply talk, the problem would evaporate — which is never true of a real dilemma, where talking changes nothing because defection remains individually rational after the conversation.
This is why entrepreneurial partnerships, standards bodies, and joint launches exist at all. They are machinery for solving coordination, and they are useless against a genuine dilemma.
Ask yourself — where does the customer come from?
Take the competitive move you are most likely to make in the next year. Write down where the customers come from if it works.
If the honest answer is “from my competitor,” you are in the second kind of game, and the question that decides whether it is worth doing is not whether the move works. It is what happens when your competitor does the same thing back.
Now cost it out and ask the question the last chapter taught. What would this have to cost before it stopped being worth doing? If the answer is a large number, the move is cheap relative to its unilateral value, and cheap is precisely the condition under which your rival will also find it worth doing.
Then spend two minutes on the alternative. What could the same money buy that would bring in customers who are currently buying nothing at all?
The move: Ask whether a competitive move grows the market or splits it differently. Moves that only split it get matched, cancel, and leave the money spent, and the cheaper they are the more certainly that happens.
Both this chapter and the last treated the two firms as deciding at the same moment, in ignorance of each other. That is sometimes true and often not. Firms watch each other, move in sequence, and take actions specifically so that the other side has to respond to something already done and impossible to undo. That changes what is possible, including the escape from a dilemma that this chapter said required changing what the rival expects.