For the following case study, let us assume we are in an innovation-driven industry, which regularly develops new products. The current sales forecasts for product innovations have been done based on model assumptions and market research. Controlling has shown significant, unexplained discrepancies between planning and actual sales developments.

There is a variety of methods available to forecast product innovation sales. For development products that are advanced enough to be presented to potential customers, conjoint analysis offers a tool to gauge perceived product advantage. While that product advantage is quite useful to determine what might be seen as a fair price, its connection to the achievable market share is obvious as a fact but not trivial in numbers. The Dirichlet Model of Buying Behavior links market penetration to market share and can thus be used to estimate the impact of marketing activities. It assumes market shares to be constant over the relevant period of time, but appears sufficiently tested to be considered valid at least for the peak market share to be reached by a product. Regarding the development of market share over time, the Fourt-Woodlock model differentiates between product trials and repeat purchases, whereas the Bass diffusion model describes the early phases of a product lifecycle in more mathematical terms, claiming to model the share of innovators and imitators among customers. For high repeat purchase rates and a vanishing share of imitators, both models are more and more similar.

The problem with all of these models is that in spite of all their assumptions, they still contain quite a few free parameters. In practical use, these parameters have to be derived from market research, taken from textbooks or guessed, introducing a significant degree of arbitrariness into the forecasts. The problem becomes apparent in this quote attributed to mathematician John von Neumann: “**With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” In fact**, **we will do just that, and the trick will be to find the proper elephant.**

A totally different approach from these models would be to go by experience. What has been true for previous product launches, by one’s own company or by others, should have a good chance of being true for for future new products. Obviously, while having personal experience with the introduction of new products will help in managing such a process, a realistic forecast will have to be based on more than the experience of a few products and, therefore, individual managers. Individuals tend to introduce various kinds of bias in their judgements, which makes personal experience invaluable for asking the right questions but highly problematic for getting unbiased, reliable answers.

On the other hand, there is usually plenty of “quantitative experience” available. The company will have detailed data about its own product launches in the target market and in similar markets, and market research should be able to provide market volumes and market shares for competitors’ past innovations. Aligned, scaled to peak values and visualized in a forecast tool, the market share curves from past data could, for example, look like this:

The simplest way to estimate new product sales would be to find a suitable model product in past data and assume the sales of the new product will develop in roughly the same way. That is relatively close to what an experienced individual expert asked for a judgement would probably do, with or without realizing it. Unfortunately, this approach can be thwarted by a variety of factors influencing the success of new products:

The varying influence of all these factors will make it, at best, difficult to find and verify a suitable model in past data. Besides, judging from one model product yields no error bars or other indication of the forecast’s trustworthiness.

Apparently, to get a reasonable forecast, we need a more complex system, which should be able to learn from all the experience stored in past data. The term “learn” indicates artificial intelligence, and in fact, AI tools like a neural network could be used for such a task: It could be trained to link resulting sales or market share curves to a set of input parameters specifying the mentioned influences. The disadvantage of a neural network in this context is that the way it reaches a certain conclusion remains largely intransparent, which will not help the acceptance of the forecast. Try explaining to your top-level management that you have reached a conclusion with a tool without knowing how the tool came to that conclusion.

On the other hand, there is no need to model a new product exclusively from past data without any further assumptions. All the more analytical models and forecast tools cited above have their justification, and they define a well-founded set of basic shapes, which sales of new products generally follow. New product market shares will usually rise to a certain peak value in a certain time, after which they will either decrease or gradually level off, depending on market characteristics. The uptake curve to the peak value will be either r- or s-shaped, and can usually be well fitted by adjusting the parameters of the Bass model. The development after the peak is usually of lesser importance and depends strongly on future competitor innovations, which are more difficult to forecast. Often, relatively simple models will be able to describe the data with sufficient accuracy – if they use the right parameters.

Generally, all published sales forecast models use market research data from actual products to verify their validity and to tune their parameters. The question is to what extent that historical data actually relates to the products and markets we want to forecast. In this case, we are simply using model parameters to structure the information we will derive from recent market data from our own markets. Based on an analysis of the available data, we have selected the following set of parameters to structure the forecast:

- Peak market share
- Time from product launch to peak market share
- Bass model innovation parameter p
- Bass model imitation parameter q
- Post-peak change rate per time period

The list may look slightly different depending on the market looked at. Tuning these parameters to the full set of the available data would lead to the average product. On the other hand, we have to take into account the influencing factors displayed in the graph above. These influencing factors can be quantified, either as simple numbers by scoring or by their similarity to the new product to be forecasted. This leads us to the following structure of influence factors, forecast parameters and forecasted market share development:

If the parameters were discrete numbers, this graph would describe a Bayesian network. In that case, forecasting could take the form of a probabilistic expert system like SPIRIT, which was an interesting research topic in the 1990s.

In our case, however, the parameters are continuous functions of all the influencing factors, which we approximate using simple, mostly linear, dependencies. These approximations are done jointly in a multidimensional numerical optimization. For example, rather than calculating peak market share as a function of product profile scoring, everything else being equal, we approximate it as a function of product profile, order to market, marketing effort and the other influencing factors simultaneously. The more market research data is available, the more detailed the functions can be. For most parameters, however, linear dependencies should be sufficient. As the screenshot from the case study tool shows, the multidimensional field leads to reasonable results, even if research data is missing in certain dimensions (right hand side graph).

In addition, confidence intervals can be derived in the fitting process, leading to a well-founded, quantitative market share forecast implemented in an interactive model that can be used for all new products in the markets analyzed. Implemented in a planning tool, forecasts from that model could look as follows:

Forecast numbers will depend on the values of the different influence factors selected for the respective product innovation.

This approach presented can be implemented for a multitude of different markets and products, provided there is sufficient market research data available. While using known and well-researched models to structure the problem, the actual information used to put numbers in the forecast stems entirely from from sales data on actual, marketed products. Besides this pure form, it can also be combined with more theory-based approaches, depending on the confidence decision makers in the company have in different theories.

Dr. Holm Gero Hümmler

Uncertainty Managers Consulting GmbH

Whereas *Ego* is quite obviously meant to be an entertaining sensation story rather than a textbook, no business school lecture or book on strategic planning would be complete without a chapter on game theory. Already in their 1944 classic *Theory of Games and Economic Behavior*, the developers of game theory, John von Neumann and economist Oskar Morgenstern, pointed out the concept’s applicability to corporate strategic decisions.

To estimate the impact game theory can actually have in corporate strategy (to be discussed in part 2 of this article) or in the steering of whole economies, let us take a very brief look at what game theory actually does. Here is hardly the place for a complete introduction to rather large field of game theory. Therefore, we will simply recall some important aspects needed to outline the capabilities and limitations of the concept. To refresh your knowledge in more depth, there is a multitude of resources on the web, from articles or videos to presentations or whole books. The Wikipedia article also is a good starting point on various types and applications of game theory for readers with some memory of the basics.

Game theory models a decision in the form of a game with clearly defined rules, which can be mathematically modeled. The games consist of a specified number of players (typically two players in the games cited as examples) who have to make decisions (typically just one per game), and there are predefined payoffs for each player, which depend on the decisions of all players combined. Two-player games with only one decision can be described in the form of a payoff matrix, in which columns describe the options of one player, rows the options of the other. Each matrix field contains payoffs for each player. Game theory then derives each player’s decision leading to the highest payoffs. Commonly cited examples of games are the prisoner’s dilemma, the chicken game or battle of the sexes.

Various types of complexity can be added to such a game. There can be more players who may or may not have previous knowledge of the other’s decisions. Players can have the aim of cooperating and achieving the highest total payoff, or they can compete and even try to harm each other. There can be different consecutive or simultaneous decisions to make, and the game can be played once or repeatedly. Payoff chances can be the same for each player or different; they can be partially unknown or depend on probability. For games with several rounds, complex strategies can be derived. If a strategy only specifies probabilities for each option, while the actual decisions are made randomly according to these probabilities, it is called a mixed strategy. With the complexity of the game, analytically optimizing strategies becomes increasingly difficult.

Based on these principles, can game theory really deliver what is attributed to it? How powerful is this tool? Starting with Schirrmacher’s book, can game theory be the decision machine for a whole economy he describes?

First of all, Schirrmacher ascribes the economic collapse of the Soviet Union and the whole communist block to the superior use of game theory by the US. That would, however, mean that the Soviet Union’s dwindling economic strength should have been caused by at least some kind of influence from a methodically acting outside competitor. In fact, the omnipresent problems of socialist economies around the world – misallocation of resources, inefficiency, lack of motivation, corruption and nepotism – come from within the system. Trade restrictions were limited to goods with a potential military significance, and at least the East German economy was even kept alive with credits from the West.The only factor in which American influence really massively impacted the Soviet economy was the excessive transfer of resources to the military sector in the nuclear arms race. But did the United States really need intricate decision models to try to stay ahead technologically while maintaining at least a somewhat similar number of weapons as the potential enemy? Obviously not. Did it take game theory to understand the Soviet concept of outnumbering any opponent’s weapons by roughly a factor of three? That was simply the Red Army’s success formula from World War II and easily observable from the 1950s onward. Game theory has to quantify outcomes as payoffs, often in the form of money, at least in terms of utility. Can such a model help to predict the secret decision processes, more often than not driven by personal motives, in the inner circles of the Soviet leadership? Does it contribute anything more valuable than the output of classical political and military intelligence? There is a reason why the military was much more interested in game theory as a tool for battlefield tactics than in terms of global strategy.

So if game theory contributed little or nothing to the end of communism, how about Schirrmacher’s second hypothesis? Has game theory turned our decision makers into greedy rational egoists ignoring all social responsibility? Indeed, game theory works for decisions to be made based on the payoff matrix, and in the simplest form, the payoffs just correspond to profits. Commentators point out that game theory can lead to cooperative as well as competitive strategies, but cooperative strategies will also be aiming at maximizing individual or shared payoffs.

The actual point is that game theory in no way implies that a decision maker must or even should aim to maximize profits (although if the decision maker is a manager paid by his company’s shareholders waiting for their dividends, there are good arguments that he should, with or without game theory). Game theory attempts to show to a decision maker which strategy should lead to maximizing an abstract payoff. That payoff may be profit, or it may result from any other utility function. For military officers, the payoff may for example correspond to minimizing the loss of own casualties or to the number of civilians evacuated from a danger zone. For a sales manager, it may be the number of products sold or customer satisfaction.

Even if game theory derives a stategy as leading to the maximum payoff, it still does not mean that the decision maker has to follow that strategy. For example, even if the payoff is identical to profit, game theory can for example be used to estimate how much short term profit must be sacrificed to follow a more socially accepted strategy.

In short, game theory is simply one of many decision support tools available to managers and as firmly or loosely linked to profit maximization as any other of these tools.

Where game theory, however, always relies on maximization of the assumed (monetary or other) payoff is to guess the probable decisions to be made by other parties involved, be they competitors or cooperation partners. Without further information on the other parties’ intentions, game theory has to assume they will maximize payoffs – otherwise there will be no basis for any calculation. In a situation where everyone uses game theory, maximizing payoffs should therefore even help the competitors because it makes one’s actions predictable. What that implies for the applicabilitiy of game theory in actual strategic planning will be discussed in part 2 of this article.

Dr. Holm Gero Hümmler

Uncertainty Managers Consulting GmbH