# Game Theory and Its Implication in Decision Making Process

`By: Flabia Maharjan`

## Key Terms

To comprehend the concept of game theory, it is essential to know the following terms and what they mean in this context.

1. Game – Game refers to any interaction that brings about an outcome depending upon the actions of two or more people.
2. Players – Players refer to the decision-makers involved in the game.
3. Strategy – Strategy refers to all the possible actions that the players can undertake during the game.
4. Payoff – Payoff refers to the outcome obtained by each player involved in the game.

## Game Theory

The development of game theory has been attributed to John von Neumann and Oskar Morgenstern, two mathematicians at Princeton University during the 1940s. The game theory incorporates the strategic interaction between two or more competing players in a variety of situations. It is based on the assumption that all the players make rational decisions in their own self-interest and that they all see the game structure in the same way. By understanding the choices available to the players in a given situation along with the outcomes derived from each choice, players are deemed to make rational decisions.

Game Theory, the theory of independent or interdependent decision making, is concerned with decision making where the outcome depends upon two or more autonomous players. One of them can be nature itself. However, neither will have full control over the outcome.

Classical models neglect the fact that most people make decisions based on the preceding player’s choice. Conversely, the game theory model believes that the decisions of players are highly influenced by the opponent player’s choices and thus lays down all the strategic choices available to the players along with the outcomes of each of the accessible choices.

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## Game Theory in Decision Making

Game Theory principles are implemented through the use of strategy games. These games are mathematical scenarios that involve a set of players (individuals or firms), a set of strategies accessible to those players, and a payoff specification for each combination of strategies.

Game Theory acts as a dominant tool for forecasting the outcomes of a set of interacting firms where the actions of a single firm have a direct impact on the payoff of other players. The interconnection between the firms makes decisions or choices made by a firm influence multiple entities that interact with the firm, and vice versa. Every player must consider the potential choices and payoffs of other players while making a decision or selecting a strategy. Along with that, they have to be aware that other players are likely to think about their strategy while making their decisions as well. This knowledge, which may be quantified through payoff calculations, helps a corporation develop its best strategy.

We see the application of game theory in several fields, including economics, finance, business, politics, science, and psychology. Adequate knowledge of game theory strategies is said to improve one’s decision-making abilities.

## Game Theory Strategies

### 1. The Prisoner’s Dilemma

The Prisoner’s Dilemma Strategy lays down the foundation for all the other game theory strategies. According to this strategy, when two individuals act in their self-interest, they end up with the worst outcomes, while the situation would have been quite different if they had cooperated.

Here, we assume two crime suspects have been summoned and separated so that they cannot communicate with each other. They’re both offered a deal individually. If both of them confess, they will go to jail for five years. If no one confesses, they will be sentenced to two years in prison, and if one confesses and the other one chooses not to, the one who confesses will be set free while the other suspect suffers in jail for eight years.

In such a situation, it would have been best for both of them if they had remained silent. But, as self-interest kicks in, people become selfish and research shows that most rational people confess and testify against the other party rather than remain silent and come to know that the other party has confessed against him/her.

Hence, the prisoner’s dilemma conceptualizes a situation where decision-makers have an incentive to make a choice that has a less optimal outcome for individuals as a group.

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### 2. Cournot Competition

Companies operating in an oligopolistic market, which is a market with limited competition, often compete for the market share of their competitors. One way of doing so is by altering the number of goods sold.

 Company B Company A Co-operate Defect Co-operate (a)    5,5 (b)   0, 10 Defect (c)    10,0 (d)    2,2

Let us assume two dominant players in the market, Company A and Company B, produce identical products. They both have the choice of producing low quantities or high quantities of their product. If both cooperate and produce at low levels, then limited supply would result in high prices, leading both companies towards high profits, as in cell (a). Conversely, if both produce at high levels, greater supply would result in lower prices, translating to lower profits for both the companies, as in cell (d). However, if one produces at low levels and the other produces at high levels, the former will break even while the latter will benefit from maximum profit due to affordability, as in cell (b).

### 3. Matching Pennies

Matching Pennies involves two players who will simultaneously place a penny on the table. The payoff depends upon whether the pennies match or not. If both the pennies are either heads or tails, then the first player wins and gets to keep the other player’s penny. Conversely, if the pennies do not match, the second player wins and gets to keep both the pennies.

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### 4. Peace-War

 Company B Company A Peace War Peace (a)    4,4 (b)   0, 5 War (c)     5,0 (d)   2,2

In the prisoner’s dilemma, the players have either “cooperate” or “defect” choices. Here, those choices are replaced by “peace” or “war”. Given that two companies could engage in a price war but both avoid price-cutting mechanisms, then both Company A and Company B will enjoy higher payoffs as shown in cell (a). However, if they indulge in a price war, this would drastically reduce the payoffs, as demonstrated in cell (d). In a case where Company A indulges in price-cutting and Company B avoids doing so, then Company A would achieve a greater payoff as it would be able to capture considerable market share through its low price strategy, as shown in cell (b).

### 5. Coordination Game

 Company B Company A New Technology Revised version New Technology (a)    50, 50 (b)   10, 0 Revised version (c)     0, 10 (d)   20,20

If players select the same course of action, they can earn higher payoffs. This is the coordination game strategy. The above table represents the payoff of Company  A and Company B for selecting a strategy. Firstly, we assume all the figures in the above table to be the profit of the respective companies in millions. The courses of action that they can choose are either introducing a new technology that will help them earn millions or, a revised version of the old technology that wouldn’t yield much profit. If both companies decide to introduce the new technology, they will earn 50 million each, as shown in cell (a). If they end up introducing the revised version of the old technology, they will end up earning 20 million, as illustrated in cell (d). Lastly, if they have contradicting choices, they will end up earning the least. For example, Company A chooses to introduce the new technology while company B introduces the revised version of the old technology. If we refer to cell (b), Company A earns 10 million assuming that the rate of adoption would be lower, while Company B’s payoff would be 0 assuming that consumers wouldn’t be willing to pay for the outdated technology. This shows that companies are earning far less than what they would have if they had coordinated their decisions.

## Criticisms of Game Theory

Game Theory is based on a couple of assumptions that do not always hold in reality. Game theory assumes that players are rational decision-makers who act in their self-interest. It also assumes that players are strategic and consider the competitive responses of their actions. However, this isn’t always the case. Game theory is believed to be the most effective when managers understand the positive and negative payoffs of their actions as well as their competitors. In truth, most businesses lack sufficient knowledge about their payoffs, so knowing the payoffs of their competitors is far from happening. All these arguments portray the shortcomings of game theory.

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