The Anatomy of a Game Model

This is the fourth in a series of blog posts on game theory.  Hopefully, you’ve read those posts and understand game theory has great potential in business and decision making, and that it is different from game studies, the science behind Farmville, Foursquare, and video games.

If you attempt to learn game theory using the excellent textbooks available, you’ll probably get a headache.   I usually recommend “Games, Strategies, and Decision Making” by Harrington because it presumes no knowledge of math, econ, psychology, etc.  Yet I still get a headache reading it.  My headache sets in when values are assigned to all the possible outcomes in the game.  This is called the payoff table or payoff matrix.

Without payoff tables, applying game theory stops dead in its tracks.  Payoff tables in simple 2×2 games like the classic Prisoner’s Dilemma, are manageable.  But in more complex games of market strategy, they are unwieldy.  Payoff tables are, in my opinion, the biggest obstacle holding back game theory as a management discipline.  Firms like Priiva Consulting provide services that hide the complexity of payoff tables so that a client gets all the benefits but without getting bogged down in the mathematical science and its complexity.

The Three Inputs to a Game Model

Recall the reason for constructing a game model is to predict behaviors and optimize your outcome.  Formulating a game model requires three inputs:  Players, Options, and Preferences.

• Players. Players are the stakeholders in the issue who act in their own self-interest.  Not every conceivable player needs to be included.  Shortcuts are available to eliminate weak players, or construct composite player definitions.
• Options. Options are the set of options available to each player.  Think – “how many prongs exist on the proverbial fork-in-the-road?”  Note that players may, but don’t necessarily have the same options.
• Preferences. And finally preferences.  For each player, what are the most important options, of all options available to all players, expressed either as fear (meaning the player doesn’t want an option to occur) or desire (meaning the player wants the option to occur).

This process of identifying players, constructing their options, and role playing their preferences forces a level of discussion and insight about your market that few organizations ever achieve.   Its like being a fly on the boardroom wall of each of your current and future competitors.

The Analysis

For example, lets say your game model has ten players and (for simplicity), three options per player.  That is thirty total options – each of which are binary – each one either happens or not.  So there are just over one billion (2**3oth) possible outcomes to be analyzed.  That’s a big payoff table even though the vast majority of these billion outcomes are unstable, meaning they will never occur.

Priiva has developed proprietary software to crunch through the billions of possibilities, eliminate the unstable outcomes, analyze the stable ones, and calculate the payoff tables.  There are three primary outcomes of interest – the Natural Outcome, meaning the outcome that occurs naturally; the Best Achievable Outcome, meaning the best possible outcome for our client; and the Worst Achievable Outcome, meaning the worst possible outcome for our client.

Ah Ha!  Outcomes are an Output

In traditional strategy or decision-making, an outcome is a selected goal and an input to the overall strategy process.  All your energy is about the tactics to achieve the selected goal.  When you apply game theory to strategic decision-making, the process is reversed.  That is, the outcome is an output of the process!

Your energy is first spent debating importance, not tactics.  Once you have settled on importance, the mathematics behind game theory will determine your best possible outcome.  Then all of your energy is spent on the execution and tactics to make that occur.  This is all leads to a more repeatable, structured, and accurate decision making process.

Intrigued?  Here are some more thoughts on my experiences applying game theory to decision making.