Game theory: Lighthouse for finance

  “I think game theory creates ideas that are important in solving and approaching conflict in general” –Robert Aumann

In an African jungle, there are thousands of ravenous animals, each striving every moment to attack their prey whilst keeping themselves safe. Amidst this chaos of survival, some predators are lucky enough to get their desired prey while others continue to search for another hunt.

When an animal, say a cheetah, hunts for a deer as its prey, it has to apply a set of techniques, skill and precision in order to get his way. He has to wait for hours and hours at the right place before it can catch the deer and have a sumptuous feast.  But sometimes this attack involves decision making, as in the wilderness there will always be predators waiting for an opportunity to strike. In this case, consider there is a pack of hyena right behind the lone cheetah. At this point, the cheetah and the hyena have to make a decision- either they need to cooperate with each other and negotiate on their share of deer or they fight until one survives.  Additionally, this decision has to be made quickly, as behind the bushes a lion awaits, looking for the right opportunity to kill.

If the cheetah and hyena decide to fight for their right over the feast, there are four possibilities:

1)  The only one will get to eat the whole deer.

2) At the time of their fight, the lion would bust in and would eat the whole deer while both fight, thus leading them back to square one.

3) The cheetah and the hyena both die fighting each other.

4) Both the animals get killed by the Lion.

This shows how uncertainty is situations leads to a pool of possible outcomes. In such uncertain and competitive situations, just like animals, human beings too have to make need-based decisions.

Knowing that there is another animal waiting to eat that deer, the only optimal choice for the cheetah is to share the deer with the pack of hyena equally. Similarly humans, at the time of their vulnerabilities, often need to make optimal choices. A wonderful example of the same is seen in the movie- A Beautiful Mind, based on the life of John Nash, who came up with the Game Theory. It portrays how, in a bar, when any guy sees a beautiful girl, he thinks that he has all the opportunity to date that girl, but he neglects the fact that his friends must also have checked out that girl. If all of them go for the same girl, they will block each other and none of them will eventually get her. So, the only best choice is to approach the friends of the hot girl, so that everyone gets to go on a date.

For an economist, this survival decision is just another “game” to prove their thesis: “Uncertainty persists in every event that has the probability of occurrence, and the best way to approach uncertainty is using Game theory.”

Game theory

Game theory is the study of strategies between players based on different payoffs so as to maximize the combined outcomes of the “game” in uncertainty. For John von Neumann and Oskar Morgenstern, the two economists who developed the idea, a strategy was “a complete plan: a plan which specifies what choices [the player] will make in every possible situation”. Game theory, in simplistic form, is used to study scenarios in which there are set players and objectives and as the game progresses, each player has to make a certain choice to get to the individual “optimal strategy”. Each objective is set off as a future payoff and a measure of equilibrium. This method is not a new rule in the investment business and many erudite investors might be aware of few examples of the Prisoners Dilemma or Zero-sum game.

In game theory, uncertainty is choices made by rational decision rather than unpredictable events we cannot influence. For example, a pharmaceutical company faces choices all the time, whether to market the product promptly and gain competition over rival firms or expand the testing period of the drugs. If a bankrupt company is being liquidated and its assets auctioned off, what is the ideal approach for the auction? What is the best way to structure proxy voting schedules? Since these decisions involve numerous parties, game theory provides the base for rational decision making.

Let’s understand game theory using a simple example;

Game theory

Consider the case of Pepsi versus Coca-Cola. Coca-Cola might assume that Pepsi is thinking of cutting the price of its iconic soda. If it does so, Coca-Cola may have no choice but to follow in suit, i.e. to reduce prices, to retain its market share. This may result in a significant drop in profits for both companies. A price drop by either company may, therefore, be inferred as defecting, since it breaks an implicit agreement to keep prices high and maximize profits as a part of a cartel. Thus, if Pepsi drops its price but Coca-Cola continues to keep prices high, the former is defecting while the latter is cooperating (by sticking to the spirit of the implicit agreement). In this scenario, Coca-Cola may win market share and earn incremental profits by selling more Colas.

Recommended Read:- INVESTMENT-SEEKING ALPHA: THE HOLY GRAIL OF INVESTING

In this case, there are two players, Pepsi and Coca-Cola; and each player’s role is dependent on a personal decision. Economists use “Payoff” matrix to find an optimal strategy in such scenarios.
In this game of cooperation, if Pepsi wanted to reduce a price of a product, what might Coca-Cola do in response? Would Coca-Cola also reduce the price of the product?

By definition, a Payoff is “the payout a player receives from arriving at a particular outcome.”

In the dispute over profits and market share, companies tend to create an atmosphere of competition, or even sometimes form a cartel to gain larger market share. By forecasting profits and losses of the product in different scenarios, we can set up a game to predict how events might unfold. Below is an alter-example of how one might model such a game.

Game theory

The above model implies that each decision made by every player has a resulting effect on their market share and profits. Let’s assume that the incremental possible profits that accrue to Coca-Cola and Pepsi are as follows:

  • If both Pepsi and Coca-Cola keep prices high, profits for each company will increase by $500 million.
  • If Pepsi decides to reduce its price but Coca-Cola doesn’t, then Pepsi would acquire an increase in profits by $750million because of greater market share and vice- versa.
  • If both companies reduce prices, the increase in soft drink consumption offsets the lower price, and thus, profits for each company increases by only $250 million.

This game of price stability and mutual cooperation can also be referred to as Prisoner’s Dilemma, accruing to a story of 2 prisoners caught up in a similar situation, where it shows us that mere cooperation is not always in one’s best interests. In here the optimal strategy for each individual is to choose the best option to reach to equilibrium that could be beneficial for both.

How can we use game theory in everyday life?

Game theory, being a pervasive economic concept, can be used for making several real-life decisions such as buying a car, salary negotiation and so on.

Suppose, you want to buy a new car and you walk into a car dealership store. You want to get the best possible deal in terms of price, car features, etc. while the car salesman wants to get the highest possible price to maximize his commission.
What does this “game” tell us? If you push for a hard bargain and get a quiet reduction in car price, you will be more satisfied with the deal, but the salesman is likely to be unsatisfied because of the loss in commission. Conversely, if the salesman sticks to his guns and does not budge on price, you are likely to be unsatisfied with the deal while the salesman would be fully satisfied. Here, the optimality depends on satisfaction between buyer and seller.

The Bottom Line:

Just like the choices made in the beverage industry or car dealership, game theory can predict many other choices for everyday decisions. This system is used widely and efficiently can help a lot of financial advisors to predict new methods to invest in different situations.

All in all, game theory is the study of how and why a person makes a decision. It is not just another game but involves valuing a decision on the basis of likely outcome. This decision making is highly valued in financial market; therefore, choosing an optimal strategy would be referred as pure Nash equilibrium (named after John Nash) i.e. choosing best option at the time of uncertainty that would give the highest payoff, for anyone playing the game. This simple method of game theory can solve an array of confusing outcomes of worldly situations.

Recommended Read:- The prisoner’s dilemma

Jobby Thadicaran
Economic Associate
Mudraksh and McShaw Asset Management Analytics

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