Exploring the computational advantage

The decade between 1996 and 2006 was an interesting time for ‘man versus machine’ battle of wits, especially for chess enthusiasts. Within their calculating horizons, the computers seemed to make no mistake. In these games, against a computer, the computer move could be made only by a computer,not by a human.

One famous example is the ‘44th move’ in the first game of the 1997 match between the then World Champion Garry Kasparov and Deep Blue, IBM’s chess machine, where the computer played an apparently random move (Rd1) before resigning. Deeper analysis later revealed that the move would have postponed the much later checkmate. It was reported that when Kasparov learned of this, he was so deeply shocked by Deep Blue’s capabilities that he resigned game 2 in a draw position.

Humans don’t make computer moves, because the benefits materialize much later and are not immediately apparent to human heuristics.

The strategy to, for instance, “connect your rooks and place them on open files” is a foresighted decision many players cannot easily make.” However, in many situations of life these heuristics help human players understand a position. They don’t necessarily lead to the best results, but reliably to decent ones. Computer moves differ substantially in their characteristics from human moves. For example, Artificial Intelligence (AI) chess engines like Alpha Zero sacrifice material much more often than humans.

What Chess Computations Teach Us About Pricing?

Like playing against the computer in chess, to optimize prices, pricing managers also need to cope with substantial complexity. Most often than not, they resort to a collection of pricing heuristics.

One common interrogative states that to price a good-better-best portfolio, you need three things: 

  • a low entry price to attract customers;
  • a high price for the best option to increase customers’ willingness-to-pay; 
  • a right-priced middle product that the customer is supposed to buy.

At buynomics, we are building a pricing machine to optimize offer structures and prices. Over the past months, we have conducted several A/B tests of the prices set by the buynomics pricing machine against human-made prices.

The buynomics pricing machine optimizes prices using Virtual Customers that make purchase decisions like their real-life counterparts — and predict very precisely how real customers would react to price changes. Across the A/B test, the machine prices have significantly outperformed the human prices. 

 

How Machine Prices Differ from Human Prices

To illustrate the comparison, we consider a café that offers three sizes of coffee. As a proxy for human prices, we looked around the cafés in the neighborhood outside of our office and found a typical price structure like this:

  • Small (0.2l): €1.99

  • Medium (0.3l): €2.99

  • Large (0.5l): €3.99

Reiterating the logic behind the pricing: The low entry 'small' version to attract customers and the high price 'Large' to make the medium price look reasonable and compel customers go for the one in the middle. Figure 1_Sales with human prices

Figure 1: Sales with human prices

We modeled the purchase decisions of 1,000 Virtual Customers (Figure 1), based on actual preferences in similar situations. When offered the coffee portfolio, 367 out of the 640 who bought a coffee, went for the medium size (57%) — probably confirming to the café owner that his pricing strategy worked.

 

Observation 1: The buynomics pricing machine reduces the price spread in a portfolio


Compared to human prices, pricing machines reduce the price range in a portfolio. 
As we observed, the price of the large coffee was reduced from €3.99 to €3.39 (Figure 2). This moves a large share of customers to the large coffee, who would otherwise have chosen the small or medium size. In sum, this leads to a profit increase of about 6% (from €1,569 to €1,664), that comes mainly from the higher absolute € margin of the large coffee (with lower % margin).

Reducing the price spread in a portfolio requires either increasing the entry price or reducing the top price. Both are risky — unless you can precisely anticipate the volume reaction to price changes (here, -15% from €3.99 to €3.39). This is very difficult with a back of the envelope price elasticity calculation, but effortless for a pricing machine.

Figure 2_Sales with optimized computer prices

Figure 2: Sales with optimized computer prices

Observation 2: The pricing machine identifies areas of very large price elasticity and exploits these situations


Most pricing professionals consider a price elasticity below -4 very high and would not change a price if it required an elasticity below -6 to be profitable. However, in portfolios with close alternatives, price elasticities can be very high. Figure 3 shows the price elasticity of the large coffee in the range between €3 and €5. At the starting price of €3.99, the price elasticity (for a price increase) is -8. The pricing machine can work with such high price elasticities and use them to optimize the portfolio offer.

Figure 3_Price elasticity of the large coffee

Figure 3: Price elasticity of the large coffee (with small at €1.99 and medium at €2.99)

 

Note that actual price reactions can be even more extreme. In a recent pilot, our pricing machine reduced one price in a portfolio by 36%, and this price change increased sales (as predicted) by a factor of 25! That is, not +25%, but +2400%, which puts the actual price elasticity at about -67.

Conclusion

These are exciting times to be in pricing! As the two observations indicate, machines have a lot to contribute — and they will soon make many established heuristics obsolete. These intelligent tools enable a highly efficient and robust replacement of complex computational operations which can make companies more profitable. At buynomics, we are just getting started. Follow us on our journey as we explore and share many more observations. 

For now, however, we want to leave you with a thought: Alpha Zero, the AI-based chess engine, surely sacrifices material in exchange for a positional advantage more often than humans. However, that does not necessarily mean that it will make it a stronger player. Similarly, in pricing, simply applying the observations will not work - simply reducing the price spread in a portfolio may not necessarily increase profits - no machine can replace a human, it can only provide humans the right tools to improve



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