Game Theory: An Application in Organizational Behaviour
                                                                                        A hypothetical but original concept by Andy Pan

What is Game Theory?

Game Theory is a mathematical concept that was made popular by actor, Russell Crowe, in the hit film “A Beautiful Mind” that was screened in 2002. Some of us might have even studied this particularly interesting theory while in school. While some of us may even be practicing and/or applying it right now at work without us knowing. It is a theory that can hide it conspicuous head in the everyday things that we do, from strategic planning to even the making of simple daily choices. So what exactly is Game Theory?

A Game Theory can be defined as a means of analyzing strategic actions that, more often than not, result from the consideration of the expected behaviour of others; or simply, the decisions that is made by one, taking into account the response from a would-be affected party by one’s decision. Got it? I know this sounds a little confusing but many of the current global economic policies and even between rival companies, game theories have often been used to make effective, calculated decisions. A game, in economics, is defined as a situation whereby rules, strategies and payoffs are involved for parties to make beneficial decisions. In this context, of course, “beneficial” is subjective. Why? Let’s take a look at the following example.

The Prisoners’ Dilemma

This classic illustration has been widely used as a simple yet effective explanation of a game theory.

Once upon a time, there were 2 thieves who were caught while trying to steal a car. The Judge decides to sentence them to a 2-year jail term each. However, the Prosecutor suspects that these men were also responsible for an unsolved bank robbery some years back but he lacks concrete evidence that can tie the men to the case. The Prosecutor then devised a plan with the Judge which he hopes would make the thieves confess to their previous crime.

The Prosecutor first places the 2 prisoners in separate rooms so that they cannot communicate with each other. Each is told that they are suspected of an earlier crime and are also told the following:

If you are one of the prisoners, what would you do?

The payoff matrix is as shown:

Now if I were any of these prisoners, I would be either trying to maximize gain for myself independent of my accomplice’s decision or I would have to make my decision based on how much I trust him. Do I anticipate him to deny so that I can confess and enjoy the shortest of the jail terms? But what if he confesses and I confess as well and my jail term increases to 3 years? So in that case, shall I deny and hope that he denies as well so that we both need only to serve 2 years in jail? But what if he confesses and now I get a 10-year sentence?! Tricky, isn’t it? Hence, the Prisoners’ Dilemma.

The optimum solution to this problem is actually to find its equilibrium. The equilibrium in a game is also known as the Nash equilibrium, named after John Forbes Nash (the character portrayed by Russell Crowe in the movie). This balance occurs when one takes the best possible action given the action of the other party and vice versa. In this example, a dominant strategy exists for each prisoner. This means that in this dilemma, no matter what the other prisoner decides, one would choose to confess because it is the best course of action. Thus, the equilibrium of the prisoners’ dilemma is that each prisoner confesses.

Yes, I know what you’re thinking. Why shouldn’t the equilibrium be the situation if each prisoner denies? If so, both would only serve a 2-year jail sentence compared to a 3-year one right? Take note that the Nash equilibrium is not achieved with actions that would generate the best payoff. Remember the prisoners are kept in separate rooms and trust is an issue here because if I trust that my accomplice would deny along with me, but if he doesn’t, then I am in for a decade behind bars.

This game model is essentially a non-zero sum game, which means that a gain by one player does not necessarily cause a loss in another player. In other words, win-win scenarios exist. On the other hand, there are also zero-sum games, whereby a player gains at the equal expense of other players. An example would be Poker. If I win with a good hand, then I would gain all bets that the other party has made at the table. So with all these “mambo jumbo” about a less-than-interesting economic theory (for some), what does it have to do with organizational behaviour?

Internal Strife

Game theories have been used extensively to study the behaviours of companies in an oligopoly. An oligopoly is a market or industry that is dominated by a few firms. More often than not, the price strategies of these firms are heavily influenced by that of rival firms. An obvious example would be the local petroleum market that is dominated by the likes of Shell and Caltex. Ever noticed that when one of these companies decides to lower its price of petrol, the rest would follow suit? However, the reverse would never happen. Why would any company in an oligopoly be in the right mind to raise prices? Would its rivals follow suit? However, you can try working out a payoff matrix for a hypothetical scenario and you would be able to appreciate the effectiveness of a game theory.

Although several other real-world applications exist, another of a game theory’s application is present as well. One that does not involve comparison between firms but it is one that can help explain the rise of conflicts within an organization.

Have you ever heard or even witness business functions of an organization “backstabbing” one another? Maybe it could be the sales department having constant arguments and disagreements with the production department? Maybe it could also be a case whereby the management fails to work in line with its ground staff? Ever since I became a facilitator, I, personally, have had corporate clients complaining about the friction between one department and another and in some cases, internal competition seems to be the norm as department heads contest with one another, thus putting a huge strain on the entire organization. It has almost gotten pretty cliché with regards to the common troubles that these organizations face. Maybe with an understanding of game theory, “rival” functions within any organization can learn that such conflicts arise from familiar roots.

Let’s say we have a scenario where the product department and the marketing department of a fictitious organization are at loggerheads which each other. The product people are in charge of creating new products while the marketing folks are responsible for selling whatever the product people came up with. However, perhaps due to some misunderstandings and accusations between the two, relationships start to break down and internal strife ensues. The situation gradually escalates to a point whereby both teams must make a decision on whether, they want to cooperate or refuse cooperation with each other. Cooperation here can refer to information-sharing, effective communication etc. Hence the following scenarios, with regards to probable effects each decision has on the organization’s performance as a whole, might just turn out.

The payoff matrix is as follows:

So in this case, what do you think is the Nash equilibrium? In terms of game theory, the Nash equilibrium in this situation would, of course, be the point when both departments cooperate. This is so because no matter what choices that the other department makes, one would choose to cooperate in order to maximize one’s gains. In addition, the organization benefits from the highest total revenue with mutual cooperation, as compared with the rest of the other scenarios. However, would this be the dominant strategy for both departments?

In theory, any business functions within the same organization would decide to cooperate to avoid conflict and at the same time, generate win-win results. However, how often have we witness Scenario D as the eventual outcome? Simply because Scenario B and C, more often than not, do not exist in the real world and the fact is that we live in a “tit-for-tat” society. This is what I call the Pan Disequilibrium. Okay….I’m just kidding. Let’s just name this point as the Organizational Disequilibrium.

Firstly, any CEO would tell you that in situations like this, product folks have to learn to co-exist and collaborate with their marketing counterparts because these two key departments are interdependent with each other. However, if one department refuses to cooperate, do you think the resulting party would not follow suit? Assuming ceteris paribus (all things remaining the same), any person would retaliate in response to hostility towards him or her. Eventually, a “bloodbath” begins, leaving both parties crippled, whilst generating negative results.

Why then do teams degenerate to such a state? We will find the answers in the deeper roots of such organizational relationships. These answers lie with two very tenuous components in relationship-building and you can find them in my earlier pages. The words are highlighted and I’m sure anyone can spot them.

You got them? If you did, then scroll down to the next page to verify your answers. No prizes for getting them correct though.

BINGO!

The two critical factors that determine any positive relationships are:

In the Prisoners’ Dilemma, communication was cut off between both prisoners and thus, trust became an issue. This setting then led us to the Nash equilibrium of when both prisoners confess. In the product/marketing analogy, wouldn’t communication be readily available to allow both departments to produce win-win results? Strange isn’t it? In today’s organizational environment, with the widespread availability of communication technologies, why should communication be of any concern? Why, even with communication, our product and marketing teams would still end up in Scenario D?

What is communication?

First of all, let us define communication. According to Dictionary.com, the word “communication” is defined as the imparting or interchange of thoughts, opinions, or information by speech, writing, or signs. However, do you think that communication would be more of an “interchange” instead of an “imparting”? In this case, is sending an e-mail message or posting a notice a form of communication? Is holding an “informative” meeting a form of communication? The answer: no. These are mere forms of notification. Why? Let us take a look at the following model which illustrates the Communication Cycle.