Game Theory for Managers

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According to Hagen Lindstädt and Jürgen Müller, both consultants for the McKinsey Company, “In times of uncertainty, game theory should come to the forefront as a strategic tool, for it offers perspectives on how players might act under various circumstances, as well as other kinds of valuable information for making decisions. Yet many managers are wary of game theory, suspecting that it’s more theoretical than practical. When they do employ this discipline, it’s often misused to provide a single, overly precise answer to complex problems.”

It is pretty safe to say that we do live in uncertain times and perhaps it’s a wise thing to review all of the possible tools to help managers be proactive and make the most informed decision (not necessarily the “right decision).

Game theory as a management tool has been around for more than 50 years. Today, most university business students are introduced to the idea through the classic “prisoner’s dilemma.” In academic settings, game theory focuses on logically deriving predictions of behavior that are rational for all players and seem likely to occur with an estimated probability. But the real world is messier than the neat environment of the prisoner’s dilemma, and game theory loses some credibility when faced with practical, dynamic, and evolving business problems.

Game Theory for Managers

In the December 2009 (deep into the financial meltdown) McKinsey Quarterly Review, both authors came out with a new model to address those objections to practicality. Instead of predicting a single outcome, with all factors balanced, their model first generates a narrow set of strategic options that can be adjusted to account for changes in various assumptions. Instead of solving an individual game, the model automatically involves a sequence of several games, allowing players to adjust their actions after each of them, and finds the best path for different combinations of factors. As one result, it supports executive decisions realistically by presenting managers with the advantages and disadvantages of the strategic options that remain at each stage of the game progression. In a second step, the model finds the “best robust option,” considering its upside potential and downside risks under all likely scenarios, assumptions, and sensitivities as time elapses. This approach is different from attempts to look for equilibrium in an artificially simplified world.

The Lindstädt-Müller model seeks to balance simplicity and relevance by considering a likely set of actions and their effect on important metrics such as demand and profit.  By considering only the most relevant factors, the model manages complexity and, at the same time, creates transparency around important break points for the key drivers.

These initial steps in setting up a game theory model are straightforward. The crucial element is to create a list that is both exhaustive and manageable. But the world is dynamic, and the payoffs for each player depend heavily on the details. Four factors, which must also be included in the rail model, can significantly affect the outcome.

For their example, the authors used a scenario where a new cross-border passenger rail service is to be fully open to European competition. The relevant variable conserved were:

  • Change in Total demand. The question is asked: “What will happen to demand with each move by an attacker and response by an incumbent?” When offered a broader, more comprehensive choice of rail links, passengers could change their behavior—for instance, traveling by train instead of car or plane.
  • Cost differences. New players typically have significantly lower operating costs than incumbents, which, however, generally enjoy economies of scale. But a higher degree of complexity and public-service obligations, such as maintaining uneconomical routes, often negate this advantage.
  • Network advantages. Incumbents almost always have a network advantage, since attackers rarely replicate an incumbent’s entire system. (Many routes, intrinsically unprofitable by themselves, are valuable only as feeders to the larger network.) Passengers prefer seamless connections—a preference that plays to the incumbents’ strengths, especially to and from points beyond the major routes.
  • Price sensitivity.Attackers typically charge lower fares, and the degree of difference needed for passengers to switch lines or modes of transport (from cars to trains, for instance) is critical to the outcome.

This model suggests that although the attacker enjoys lower costs and seems to have a favorable starting position, it will probably take only a sliver of market share and that thanks largely to a general increase in rail use. The incumbent will remain dominant. Seeing the likely outcome of the attacker’s specialized or niche entry, the incumbent’s executives should conclude that a strategy of tolerance would be best. Only a small share of the market is at stake, and the incumbent could lose much more if it engaged in a costly battle for this thin slice of the market. For instance, by waging a destructive price war or using other expensive tactics. If the attacker is more aggressive the incumbents, the incumbent’s best answer would be to fight back with tactics including aggressive price competition, targeted marketing activities, and more frequent and better service on the routes under attack. Note, however, that this would substantially lower profits for both players.

Indeed, the above example is what we have seen when disruptors have come into markets. Actual disruption requires the complete disappearance of the incumbents for the disruptors. However, during airline deregulation in the USA, we did see the extinction of a large segment of the “legacy” carriers such as Pan American, Eastern, National, TWA and others which were absorbed in a massive consolidation of the industry. (However, in the case of the deregulation of airlines, the rules of the game were changed leaving the legacy carriers with too much debt from the pre-deregulation stage.)

Three scenarios below depict the interrelatedness of customer demand, the incumbent’s cost disadvantage, and the strength of network effects.