Why do people disagree on what prices to charge? Because pricing is a game, in the game-theory sense, and by definition a game cannot be solved. In this article, the author explores why we might be startled, even shocked, by disagreements when making pricing (and related) decisions, using over 16 billion simulated futures from the Top Pricer Tournament™, based on pricing strategies submitted by 2,239 executives, managers, consultants, students, and professors. Mark Chussil is the Founder of Advanced Competitive Strategies, Inc. He has studied competitive strategy for 45 years: conducting research, working in industry, facilitating busi­ness war games, and developing computer-based strategy simulators. He can be reached at mchussil@whatifyourstrategy.com.

The Journal of Professional Pricing, June 2023

Why do people disagree on what prices to charge? Yes, yes, different markets, businesses, products, and competitors. But why do we disagree about what a specific business, in a specific market, should do?

We know the usual suspects. Differences in mental models, risk tolerance, measure(s) of success, time horizons, incentives, experience in related businesses, experience in unrelated businesses, and so on. Many moving parts, not always visible, not always manageable, often only anecdotal.

Of course, pricers don’t disagree willfully. They’re not like the comedian Groucho Marx, who sang “What­ever it is, I’m against it.” Rather, pricers are passionately confused. Stakes are high, careers are at risk, everyone has an opinion, and no one knows the answer.

Why? Because pricing is a game, in the game-theory sense, and by definition a game cannot be solved.^[1]

In this article, I’ll suggest why we might be startled, even shocked, by disagreements when making pricing (and related) decisions. I’ll rely on over 16 billion simulated futures from the Top Pricer Tournament™, based on pricing strategies submitted by 2,239 executives, managers, consultants, students, and profes­sors. Their decisions, and the resulting simulated futures, startled and shocked me, and I’m the guy who wrote the Tournament.^[2]

Tournament entrants’ decisions

The Tournament entry form provides key information — market growth rate, customers’ sensitivity to price, businesses’ mix of fixed and variable costs, etc. — for the generic, fictitious Ailing, Fast Growth, and Mature industries.

Each entrant made key decisions for a business in each industry.

• How much the entrant cares about goals; here, profitability and market share. Each entrant weights each measure of success according to the entrant’s preferences.
• What price move to make in quarter 1, year 1 of the simulation. Q1 options are to cut, hold, or raise the entrant’s prices by a fixed amount.
• What pricing strategy to select for quarters 2-4, year 2, and year 3. Entrants select any combina­tion of pricing strategies (Q2-4, Y2, and Y3) from 17 options.^[3]

With three options for Q1 and 17 options apiece for Q2-Q4, Y2, and Y3, entrants can devise a pricing strategy based on any of 14,739 combinations (3 x 17 x 17 x 17 = 14,739). With 2,239 entries currently in the Tournament, each entrant’s pricing strategy gets simulated in about 2.5 million futures, using all unique combinations of entrants as competitors.^[4] With 2,239 entries per industry, and 2.5 million futures based on competitors’ strategies, each industry runs about 5.6 billion simulations. Bonus: The Tourna­ment gets smarter and smarter as more entrants enter strategies.

Measures of success are scaled relative to the range of performance among strategies with similar prefer­ences. Each strategy’s score can range from 0 (worst of the strategies with similar goals) to 100 (best of the strategies with similar goals).

Differences in strategies’ performance come solely from differences in entrants’ pricing strategies.

Implicit beliefs

Given the differences among the industries, it’s no surprise to find corresponding differences in entrants’ first price move (Figure 2). Note that Q1 moves could shape subsequent competitive ac­tion and reaction, depending on Q2-4, Y2, and Y3 strategy decisions.

Figure . Source: The ACS Top Pricer Tournament™.

Conventional wisdom

In the bleak Ailing industry, 31% of the 2,239 entrants chose to cut their prices in Q1. Another 43% chose to hold, and 25% chose to raise. That’s the most evenly distributed industry. Some entrants saw oppor­tunity, others saw peril, and a plurality coasted along with the same old price. Perhaps some en­trants even considered Ailing unworthy of serious attention. Who, after all, aspires to make their mark in an industry melting away?

Frisky Fast Growth split almost evenly between cutting and holding prices, with raising prices a dis­tant third. Consider conventional wisdom: Gain share when growth is fast, and cash in later. Or the other con­ventional wisdom: Don’t be first to cut prices, and don’t make yourself uncompetitive by raising. Or the other other conventional wisdom: Why cut prices when demand is growing and fortunes are to be made?

Bland Mature was indecisive between holding and raising prices with cutting a far distant third. Should we stimulate the market with lower prices? Should we wait for someone else to show us the new way for­ward? Should we milk the market for all it’s worth? Should we aspire simply not to ruin a good thing? Don’t snatch defeat from the jaws of victory.

Key point: There’s always conventional wisdom. And if not, there’s always a reassuring and/or supportive anecdote.

Conventional predictions

Consider Figure 2 from a different angle. Each entrant was one of 2,239, and each entrant would com­pete with all 2.5 million unique two-business combinations of the other entrants.

If you’re thinking about the Mature industry, what would you predict your competitors would do? Your best guess would be that they’d hold their prices in Q1… but you’d probably be wrong, because 53% of other entrants would not hold their prices. You would, though, have a good clue that Mature competitors wouldn’t start by cutting their prices.

It’s fairly predictable that Fast Growth competitors would want to cut their prices to gain market share… but 57% of Fast Growth entrants chose to hold or raise their prices.

In the Ailing industry, anything could happen. Just like the other industries, though with different proba­bilities.

Or consider Figure 2 from an obey-conventional-wisdom perspective. Go for share in fast-growing mar­kets. Harvest profits in mature markets. Scrounge for scraps in ailing mar­kets, then walk softly away. Of course, your competitors know the conventional wisdom too. Should you try to buck conven­tion? Should they? Is it better to risk a price war or to leave money on the table? Whatever entrants guessed their competitors would do, they’re probably wrong, because no Q1 price move was chosen by more than 50% of entrants.

Key points: Those Q1 patterns echo a lesson I learned in live-action, role-playing business war games. Strategists often think there are just a few possible futures or that they can accurately forecast what com­petitors will do. What they discover is that there are many more possibilities than they anticipated. In one war game, the company imagined 3,938,220 possible futures… in fifteen minutes.

There’s no such thing as the singular future. We can predict weather because we have a science of mete­orology. We cannot predict price (and other) moves because pricing is a game-theory game. That doesn’t mean we’re helpless. It means we must think like game-players.

There’s not even such a thing as the singular past. If hindsight were 20/20, why do we tell such different stories about it?

What do you want?

Entrants indicated how much they cared about two goals: market share (the business’ percentage of units sold in the industry) and profitability (the business’ profit divided by its revenue), both measured at the end of the Tournament’s three-year time horizon (Figure 3). Entrants declared their goals by how they weighted market share and profitability. Weights of 100%/0% mean an entrant cared only about market share. Weights of 0%/100% mean caring only about profitability. Weights of 50%/50% mean car­ing equally about the metrics. And so on.

Figure . Source: The ACS Top Pricer Tournament™.

There were entrants in all three industries who put 0% weight on market share and 100% on profitability. There were entrants in all three industries who did exactly the opposite.

Entrants’ price strategies reflect what they thought would help them achieve their goals. The differences in price moves (Figure 2) strongly suggest that entrants developed narratives of how their strate­gies would play out. In my conversations with entrants, all could recite their rationales, their stories, of how they’d thrive over the next three years.

Key point: Be wary of assumptions, especially those that work in your favor. Your competitors’ goals might be wildly different from, or wildly similar to, yours.

I’ve conducted business war games in which the home team (the people role-playing the client company) asserted that competitors wouldn’t be able to match the home team’s price. Then their own people, role-playing competitors, concluded that competitors couldn’t afford not to match the home team’s price. Those in­sights led to actions that made or saved hundreds of millions of dollars.

How groups’ strategies performed

The very first group of Tournament entrants came from the attendees of a pricing conference that I addressed 16 years ago. Subsequent groups came mostly from executive programs and classes at various universities. In all, 36 groups each had at least 20 entrants, sometimes many more.

Figure 4 shows the Tournament scores for the best- and worst-performing groups. Individual entrants’ strategy-success scores range from 0 (worst) to 100 (best); the group averages show how well the mem­bers of the groups performed. The green, red, and yellow markers show the average scores of the best-performing group, the worst-performing group, and all 2,239 Tournament entrants.

Figure . Source: The ACS Top Pricer Tournament™.

The differences in performance can be large, with the best groups’ strategies outperforming the worst groups’ strategies by about 60%. That’s a big deal, and that’s why it’s so important to develop and adopt good pricing strategies.

Group 1, the participants at the pricing conference I addressed, got the highest average scores in two in­dustries, and it missed a clean sweep by falling less than 1% below the best in the third industry. Strate­gies from three different groups, one corporate and two from universities, performed the worst.

But there’s more. The groups aren’t homogenous. There’s variation within the groups. A lot of variation.

Each industry has a best group and worst group, shown in Figure 4 as the highest- and lowest-average group. Figure 5 shows the variation within those groups. The averages strategy-scores from the best and worst groups appear as the yellow markers in Figure 5. The green and red markers indicate the best and worst individual scores within the group.

Figure . Source: The ACS Top Pricer Tournament™.

Figure 5 shows that:

• Every best-group had at least one entry (the red markers) that performed badly. Someone’s strat­egy worked not-so-well, despite the good company it kept.
• Every worst-group had at least one entry (the green markers) that performed well. Some­one’s strategy worked well, despite the bad company it kept.
• The action is in the yellow markers. The average strategies from the best groups were clearly higher than those from the worst groups, even though each group had winners and losers.

In statistical terms, there’s abundant variance within groups. In business terms, there’s a lack of unanim­ity among the entrants of a given group. It’s hard to know whether an entrant was smart or just got lucky. It’s hard to know whether an entrant was not-smart or just got unlucky.

Key point: In a way, we don’t really care whether an entrant was smart, lucky, not-smart, unlucky, or a combina­tion. We care a great deal, though, about making good pricing-strategy decisions. We can make better pricing-strategy deci­sions by testing many candidate strategies in simulated industries.

Strategy tests: Hold-still and do-nothing

I inserted two special strategies in each of the three Tournament industries. One special strategy moves only to maintain its position at the market-average price. We’ll call that the hold-still strategy. The other special strategy does nothing at all; it’s blissfully calm while competitor strategies risk life and P&L for competitive advantage. We’ll call that the do-nothing strategy.^[5]

If a given strategy’s score beats the hold-still and do-nothing strategies, then the given strategy adds value. If it doesn’t, it subtracts value. It’s not a strategy guarantee, but it’s simple and sensible, and it seems that at the very least we ought to expect a strategy to beat hold-still and do-nothing.

Figure 6 shows that, on average, entrants in all the industries add value to their businesses.

Figure . Source: The ACS Top Pricer Tournament™.

We’d expect that most strategies would add value, meaning that entrants’ strategies made their busi­nesses bet­ter including competitors’ actions and reactions. Still, a sobering 40% of strategies made their businesses worse. That’s startling and shocking. After all, no one says, “I’ve got a good strategy and a bad strategy, I think I’ll take the bad strategy.” But 40% of the time, the strategies performed worse than hold-still and do-nothing.

The key, then, is to compare the high-performing strategies to the low-performing strategies. Were the latter strategies dysfunctional? Were they too aggressive and triggered retaliation? Were they too bashful and let competitors get ahead? Did they underestimate competitors?

There is a clue. Figure 3 showed that entrants valued market share quite a bit more than they valued profit­ability in the Fast Growth industry. (I’m not saying that they should or shouldn’t do so.) Since price was the only way they could gain share, and since there’s always exactly 100% market share to go around, share-growth strategies would often achieve no share-growth advantage.

Key point: The analysis in Figure 6 compared strategies to what would have happened otherwise (in this case, “otherwise” is the hold-still and do-nothing strategies), as opposed to comparing a strategy’s out­come to a previous point in time. Otherwise might seem subtle and unconventional, especially when man­agement wants to see bottom lines go up, up, up. But comparing outcomes to otherwise, rather than to yes­terday, is the better way to judge a strategy.

Is there a best strategy?

Despite sifting through billions of simulations while wearing my strategy-wizard hat, I cannot definitively answer the best-strategy question. Pricing is a game, and there is no definitive solution. But we can im­prove the odds of making better decisions.

Making better decisions means, in part, setting better expectations. “Success” involves goals, and by defi­nition we cannot hit unachievable goals. Thus, there are exactly two ways to fail: performance too low and expectations too high.

Dominance

Game theory includes the concept of dominance.

• Strategy X “strictly” (or “strongly”) dominates Strategy Y if X is at least as good as Y on all rele­vant criteria and X is better than Y on at least one criterion. If X achieves market share of 35% and profitability of 15%, and if Y achieves share of 30% and profitability of 10%, then X strictly domi­nates Y. With those numbers, there is no reason ever to select Y.
• Strategy X “weakly” dominates Strategy Z if X scores higher than Z despite tradeoffs. If X achieves share of 35% and profitability of 15%, and Z achieves share of 30% and profitability of 16%, then X weakly dominates Z if management cares more about market share, and Z weakly dominates X if management cares more about profitability.

The Tournament summarizes the performance of all 2,239 strategies in a dominance graph (Figure 7). Each blue dot shows the average market share and profitability for one strategy, averaged across all 2.5 million of its competitive futures. Darker blue comes from dots piling up. The red square highlights the per­formance of a single strategy in its 2.5 million futures, and the yellow triangle indicates the average per­formance of the do-nothing strategy.

Figure . Source: The ACS Top Pricer Tournament™.

In Figure 7 we can see:

• “Your strategy” performs worse than “do nothing” on both measures of success, share and profit. “Do nothing” strictly dominates “your strategy.”
• Many strategies strictly dominate “your strategy.”
• Many other strategies weakly dominate “your strategy.”

Figure 8 is just like Figure 7 except that it highlights strict and weak dominance. Strategies strictly domi­nate “your strategy” if they fall to the northeast of the L-shaped solid lines. Strategies weakly dominate “your strategy” if they fall to the northeast of the dotted line.^[6]

Figure . Source: The ACS Top Pricer Tournament™.

I should stop calling the red square “your strategy” because it is actually my strategy.

I entered strategies for the three industries, and the dominance graph showed that my strategy for one industry was, charitably, not impressive. That was one of the great experiences of my professional life. First: I learned a key lesson about better strategizing by comparing my strategy to those that outper­formed mine. Second: My technology, with the help of a couple thousand people, taught me.

Key point: What I learned about strategy from the Tournament changed how I think about competitive strategy. I know I wouldn’t have learned that lesson without the Tournament.^[7]

The best strategy

Some strategies add value while others don’t (Figure 6). Some strategies add more value than others (Figure 5). Some strategies are more robust than others; they perform well against more of the 2.5 mil­lion futures that the Tournament simulated. Some strategies dominate others.

But strategy is complex, and there are no guarantees. The Tournament simulated billions of simulations, which seems rather a lot, but we could nominate and test more. I had the Tournament test strate­gies that no human has entered yet. Some of those strategies outperformed all strategies that humans have chosen so far.

We can go deeper. You’ve probably come across the Prisoner’s Dilemma, a simple-yet-unsolvable prob­lem in game theory. The Top Pricer Tournament is like a three-player iterated prisoner’s dilemma, made extra-complicated by having two measures of success (market share and profitability) as opposed to one (years in prison), and even more extra-complicated by having 14,739 pricing strategies as opposed to two (cooperate or defect) available to the three identical businesses.

Game theory includes equilibrium. An equilibrium is a state of affairs in which none of the game-players — businesses or prisoners — can improve their outcomes by switching to another strategy. That doesn’t necessarily mean everyone is happy. As in the prisoner’s dilemma, it means only that no one can do bet­ter through unilateral action.

I adapted the Tournament to see whether it could find equilibria, given three initial pricing strategies for the three businesses in an industry. Here’s the process. First, the Tournament tested all 14,739 strategies for the first business while the other two retained their current strategies. Next, it tested all 14,739 strat­egies for the second business while the first and third used their current strategies. Finally, it tested the 14,739 for the third.

If any of the three businesses found a better strategy, it would switch to the better one and the test would run again. No equilibrium yet. If none of the three found better strategies, that reached an equilib­rium. The test stops.

Did it find equilibria? The answer: maybe, sometimes.

I ran a series of simulations for strategies that Tournament entrants chose for the Mature industry.

Experiment 1. All strategies cared only about profitability. The search for equilibrium stopped after just 16 itera­tions. (Each iteration ran 44,217 simulations; 14,739 x 3.) But it hadn’t found an equilibrium; it had found a loop. In each iteration, at least one strategy could do better by switching, and the businesses’ profitability would twitch a bit. The good news for the businesses: They alternated gently between slightly different levels of profitability.

Experiment 2. Different Mature strategies, with entrants who all cared equally about market share and profitability. The test ran 315 iterations before discovering it had found a 255-iteration-long loop. If they stopped where the loop began, they’d have been okay. But if they continued to tweak, their market shares could lurch up and down by 10 percent­age points, and profitability could quake by about 20 percentage points, including some painful losses.

Experiment 3. Still in Mature, the businesses cared only about market share. This one matched the clue I mentioned near Figure 6: The three businesses cared only about market share, and they quickly started a price war that everyone lost. No one gained share. Everyone lost money.

Key point: Don’t mess it up. You can lose a lot of money trying to make a little more money.

Conclusion: Like AI, only better

The inevitable disclaimer. Do not consider anything in this article to be a recipe for your business’ success. The Tournament was calibrated for specific conditions, and those conditions might not apply to your mar­kets. It is possible to calibrate simulations for real-life businesses, but that’s not what’s shown here.

Key point: The casino has an edge of only a few percentage points, but that’s what makes the casino rich. We don’t need perfection to improve. The experiences I related here have moved hun­dreds of millions of dol­lars up, up, up.

Key point: Strategy tournaments are not a battle between humans and computers. Humans have judg­ment and imagination, without which computers are useless. Computers have precision and speed, with­out which humans can only guess. Humans and computers are natural partners.

Final key point: We can experiment, we can simulate, and we can learn. We can make better decisions.

The Top Pricer Tournament is ongoing. You and your colleagues can enter. All entries are confidential. Please contact TopPricer@DecisionTournaments.com.

1. See Prisoner’s Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb, by William Poundstone. Extraordinary book that even I could understand, including von Neumann’s distinction between puzzles (solvable) and games (not solvable). ↑
2. Inspired by The Evolution of Cooperation, by Robert Axelrod of the University of Michigan. He won a well-deserved MacArthur “genius” award for that book. ↑
3. The entrants’ Q2-4, Y2, and Y3 decisions are quarterly actions such as “be average”, “always raise”, “emulate profit” (do whatever the most-profitable competitor did in the prior quarter), “be unpredictable” (cut, hold, or raise, at random), “follow down” (if a competitor cut its price then cut yours, otherwise don’t change price), and more. ↑
4. That works because each industry’s businesses start from identical positions. ↑
5. For simplicity, I averaged the do-nothing and hold-still strategies. ↑
6. The angle of the dotted line depends on how much you care about the two metrics. The more you care about market share, the closer to horizontal the line should be; the more you care about profitability, the closer to vertical. ↑
7. See “Don’t Let Your Mistakes Go to Waste”, Mark Chussil, Harvard Business Review, March 1, 2016. ↑