GAME THEORY AND STRATEGIC DECISION MAKING

Game theory is a field of study that helps us understand decision-making in strategic situations. In addition to being an important methodology within the economics discipline, it also gives insights into pricing and management strategies used by a business.

Furthermore, game theory has wide-ranging applications in areas such as international relations, political science, and military strategy. Much of game theory involves the interaction of decision-makers where there is an asymmetry of information. Thus, the study of game theory can provide insights into how decision-makers act when there is some important information that they cannot directly observe.

Classification of Game Theories

1. Cooperative vs. Non-Cooperative Games

Although there are many types (e.g., symmetric/asymmetric, simultaneous/sequential, etc.) of game theories, cooperative and non-cooperative game theories are the most common. Cooperative game theory deals with how coalitions, or cooperative groups, interact when only the payoffs are known. It is a game between coalitions of players rather than between individuals, and it questions how groups form and how they allocate the payoff among players.

Non-cooperative game theory deals with how rational economic agents deal with each other to achieve their own goals. The most common non-cooperative game is the strategic game, in which only the available strategies and the outcomes that result from a combination of choices are listed. A simplistic example of a real-world non-cooperative game is rock-paper-scissors.

2. Zero-Sum vs. Non-Zero-Sum Games

When there is a direct conflict between multiple parties striving for the same outcome, this type of game is often a zero-sum game. This means that for every winner, there is a loser. Alternatively, it means that the collective net benefit received is equal to the collective net benefit lost. Almost every sporting event is a zero-sum game in which one team wins and one team loses.

A non-zero-sum game is one in which all participants can win or lose at the same time. Consider business partnerships that are mutually beneficial and foster value for both entities. Instead of competing and attempting to "win", both parties’ benefit.

Investing and trading stocks is sometimes considered a zero-sum game. After all, one market participant will buy a stock and another participant sells that same stock for the same price. However, because different investors have different risk appetites and investing goals, it may be mutually beneficial for both parties to transact.

3. Simultaneous Move vs. Sequential Move Games

Many times, in life, the game theory presents itself in simultaneous move situations. This means each participant must continually make decisions at the same time their opponent is making decisions. As companies devise their marketing, product development, and operational plans, competing companies are also doing the same thing at the same time.

In some cases, there is an intentional staggering of decision-making steps in which one party can see the other party's moves before making their own. This is usually always present in negotiations; one party lists their demands, then the other party has a designated amount of time to respond and list their own.

4. One Shot vs. Repeated Games

Last, game theory can begin and end in a single instance. Like much of life, the underlying competition starts, progresses, ends, and cannot be redone. This is often the case with equity traders that must wisely choose their entry point and exit point as their decision may not easily be undone or retried.

On the other hand, some repeated games continue and seamlessly never end. These types of games often contain the same participants each time, and each party has knowledge of what occurred last time. For example, consider rival companies trying to price their goods. Whenever one makes a price adjustment, so may the other. This circular competition repeats itself across product cycles or sale seasonality.

In the example below, a depiction of the Prisoner's Dilemma (discussed in the next section) is shown. In this depiction, after the first iteration occurs, there is no payoff. Instead, a second iteration of the game occurs, bringing with it a new set of outcomes not possible under one shot games.

How do you find Nash equilibrium?

To find the Nash equilibrium in a game, one would have to model out each of the possible scenarios to determine the results and then choose what the optimal strategy would be. In a two-person game, this would take into consideration the possible strategies that both players could choose. If neither player changes their strategy knowing all of the information, a Nash equilibrium has occurred.

Why is Nash equilibrium important?

Nash equilibrium is important because it helps a player determine the best payoff in a situation based on not only their decisions but also the decisions of other parties involved. Nash equilibrium can be utilized in many facets of life, from business strategies to selling a house, from war to social sciences, and so on.

How do you calculate Nash equilibrium?

There is not a specific formula to calculate Nash equilibrium. It can be determined by modeling out different scenarios within a given game to determine the payoff of each strategy and which would be the optimal strategy to choose.

What are the limitations of Nash equilibrium?

The primary limitation of Nash equilibrium is that it requires an individual to know their opponent’s strategy. A Nash equilibrium can only occur if a player chooses to remain with their current strategy if they know their opponent’s strategy.

DOMINANT STRATEGIES

What is Dominant Strategy?

The dominant strategy in game theory refers to a situation where one player has superior tactics regardless of how their opponent may play. Holding all factors constant, that player enjoys an upper hand in the game over the opposition. It means, regardless of the strategies employed by the opponent, the dominant player will always dictate the outcome.

Understanding Dominant Strategy

-    In game theory, players employ different independent strategies to optimize their decision-making with the goal of beating the opponent. Players in an oligopolistic market, military, managers, consumers, or games like the chase, often use game theory as a strategic tool.

- In game theory, the outcomes of the actors are different depending on their actions. Some players enjoy the upper hand, while others are less fortunate. The dominant strategy describes a state where one of the players has a superior tactic that always leads to a winning outcome, despite the opponent’s employed choice of strategy.

2. Weakly Dominant Outcome

-    In a weakly dominant outcome, the dominant player dominates the game but against some strategies, only weakly dominates.

3. Equivalent Outcome

-    In an equivalent outcome, none of the actors benefit or lose against each other. They each choose the one optimal result that is fair for both players. In case one of the players selects the alternative, it would mean an outlandish gain or loss.

4. Intransitive Outcome

- In an intransitive outcome, none of the above three outcomes are experienced – no equivalent, strictly, or weak dominant outcome results. The available outcome happens by chance. Either player can win, while the other loses depending on the strategy employed. Therefore, in this outcome, there is no well-defined approach to point to the dominance strategy.

MECHANISM DESIGN

What Is Mechanism Design Theory?

Mechanism design theory is an economic theory that seeks to study the mechanisms by which a particular outcome or result can be achieved.

Mechanism design is a branch of microeconomics that explores how businesses and institutions can achieve desirable social or economic outcomes given the constraints of individuals' self-interest and incomplete information. When individuals act in their own self-interest, they may not be motivated to provide accurate information, creating principal-agent problems.

In particular, mechanism design theory allows economists to analyze, compare, and potentially regulate certain mechanisms associated with the achievement of outcomes that focuses on how businesses and institutions can achieve desirable social or economic outcomes given the constraints of individuals' self-interest and incomplete information.

Mechanism design theory is thus used in economics to study the processes and mechanisms involved with a particular outcome. The concept of mechanism design theory was broadly popularized by Eric Maskin, Leonid Hurwicz, and Roger Myerson. The three researchers received a Nobel Memorial Prize in Economic Sciences in 2007 for their work on the mechanism design theory and were branded as foundational leaders on the subject.

CONSIDERATIONS IN MECHANISM DESIGN THEORY

Mechanism design theory built on the concept of game theory, which was broadly introduced by John von Neumann and Oskar Morgenstern in their 1944 book, Theory of Games and Economic Behavior.3 Game theory is known in economics for the study of how different entities work together both competitively and cooperatively to achieve outcomes and results.

Various mathematical models have been developed to efficiently study this concept and its results. Game theory has also been recognized throughout the history of economic studies with more than a dozen Nobel Prizes going to researchers in this area.

Both game theory and design theory look at the competing and cooperative influences of entities in the process towards an outcome. Mechanism design theory considers a particular outcome and what is done to achieve it. Game theory looks at how entities can potentially influence several outcomes.

EXAMPLE NO. 1:

The prisoner’s dilemma is a well-known example used to depict the predicament of two criminals, A and B, when facing persecution – i.e., car theft. During the trials, the prosecutor believes the two suspects might have committed an earlier crime but were not convicted – i.e., burglary. Since there is no hard evidence, the DA employs game theory to force a confession out of the two. They are offered a deal to rat each other out. The following are the terms:

• For the car theft crime, of which there is hard evidence, they will face a jail term of two years.

• If A rats out B by confessing to the burglary crime, the sentence will be reduced to one year, while B gets seven years for being uncooperative. On the flip side, if A denies, but B confesses, the sentence for A will be seven years, while B gets only one year.

• A similar deal is offered to Suspect B.

• However, if they both confess to the burglary crime, the jail term will be reduced to three years.

The above information can be plotted in a payoff matrix as below:

EXAMPLE NO. 2:

Imagine two competing companies: Company A and Company B. Both companies want to determine whether they should launch a new advertising campaign for their products.

If both companies start advertising, each company will attract 100 new customers. If only one company decides to advertise, it will attract 200 new customers, while the other company will not attract any new customers. If both companies decide not to advertise, neither company will engage new customers. The payoff table is below: