A Brief Introduction to Game Theory

Everyone has a natural negotiating style. These styles have analogues that can either work well or poorly in trying to achieve a negotiated result. It's important to understand how certain styles work well together, how some conflict, and how some have inherent advantages over one another.

Before we delve into that, let's spend a little time on basic game theory. Game theory is a mathematical theory that deals with strategies for maximizing gains and minimizing losses within prescribed constraints, such as the rules of a card game. Game theory is widely applied in the solution of various decision-making problems, such as those of military strategy and business policy.

Game theory states that there are rules underlying situations that affect how these situations will be played out. These rules are independent of the humans involved and will predict and change how humans interact within the constructs of the situation. Knowing what these invisible rules are is of major importance when entering into any type of negotiation.

The most famous of all games is the prisoner's dilemma, which you've seen many times if you've ever watched a cop show on television. The simple form, as described in the Stanford Encyclopedia of Philosophy, follows:

Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. “You may choose to confess or remain silent. If you confess and your accomplice remains silent, I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess, I get two convictions, but I'll see to it that you both get early parole.

The classic prisoner's dilemma can be summarized as shown in the following table.

Classic Prisoner's Dilemma

What's fascinating about this is that there is a fundamental rule in this game that demonstrates why two people might not cooperate with one another, even if it is clearly in their best interests to do so.

If the two prisoners cooperate, the outcome is best, in the aggregate, for both. They each get eight months of jail time and walk away. But the game forces different behavior. Regardless of what the co-conspirator chooses (silence versus betrayal), each player always receives a lighter sentence by betraying the other. In other words, no matter what the other guy does, you are always better off by ratting him out.

The other rule to this game is that it is a single-play game. The participants play the game once and their fate is cast. Other games are multiplay games. For instance, there is a lot of interesting game theory about battlegrounds. If you are in one trench fighting and we are in another, game theory would suggest that we would not fight at night, on weekends, on holidays, and during meals. Why not? It would seem logical that if we know you are sleeping, it's the absolute best time to attack.

Well, it's not, unless we can completely take you out with one strike. Otherwise, you'll most likely start attacking us during dinner, on holidays, or while we are watching Billions. And then not only are we still fighting, but now we've both lost our free time. This tit-for-tat strategy is what keeps multiplay games at equilibrium. If you don't mess with us during our lunch break, we won't mess with you during yours. And everyone is better off. But if you do mess with us, we'll continue to mess with you until you are nice to us again.

When you are considering which game you are playing, consider not only whether there are forces at work that influence the decisions being made, like the prisoner's dilemma, but also how many times a decision will be made. Is this a one-shot deal? Or will this game repeat itself, lending increased importance to precedent and reputation?