Application of Game Theory to Business Strategy

Abstract

Game theory is the most popular mathematical tool, the spheres of application of which are economics, finance, management, politics, and military science. The game theory is a multifaceted phenomenon, which, despite being theoretical in nature, highly affects real-life business situations. This article briefly reviews the literature regarding game theory and business and introduces the basic concepts of game theory within the context of business strategy. The authors seek to provide insights into the winning business strategy which includes the elements of competition and cooperation. They determined the main rules of the sequential and parallel interaction in the game. Likewise, the authors focused on the prisoners’ dilemma and highlighted two obvious alternatives that managers can use to ensure compliance with agreement. The four characteristics of a successful business strategy were presented as a prerequisite for decision-making using game theory.

1. Introduction

Nowadays game theory attracts particular attention in terms of its use as a strategic tool for conducting business. However, many business leaders underestimate this theory and believe that it is more theoretical than applied. But nevertheless experience shows that the higher manager’s level is the more important for him to develop strategic thinking and the ability to apply game theory methods in practice.

During the last years, the importance of game theory for making strategic management decisions has increased significantly in many areas of economic science. In economics, it is applicable not only to solve general economic problems but also to analyze the strategic problems of industries, markets, enterprises, development of organizational structures, management accounting systems, and forms of effective activity stimulation. Examples include decisions on pricing policy, access to new markets, cooperation and joint ventures, identifying leaders and executive agents in innovation, vertical integration, and so on. Generally, game theory can be used for all types of decisions if their decision-making is influenced by other actors. These persons or players are not necessarily market competitors; sub-suppliers, main customers, employees of organizations, and work colleagues may act as them. Due to game theory, the company’s management has an opportunity to predict its partners and competitors’ moves. The practical significance of game modeling is also evidenced by the fact that researches conducted in this area have been awarded the Nobel Prize in Economics twice in the past 20 years.

2. Literature review

Game theory is the most popular mathematical tool, the spheres of application of which are Economics, Finance, Management, Politics, and Military Science. It is an economic and mathematical tool for modeling by different persons their optimal performance under competitive (conflict) conditions or cooperation with other persons. The form and applied methods of this theory are mathematical, but by nature of the tasks resolved it refers to the economic analysis. Game theory is a branch of mathematics, but its conclusions have long been applied to economics and business. It studies decision-making processes under conflict conditions, i.e., game theory provides a mathematical prediction of a conflict situation [1].

In any market situation, there is an opportunity to act differently and get the answer to the question—which option will lead to the desired goal with the lowest cost? If you can simulate the player companies’ actions, you will get an answer. Has the competitor lowered the price of a product that is already sold at cost again? Has the supplier company made shipments to a noncore retail chain, and now they go to the supermarket to buy a hammer and nails instead of to you? Why do competitors and suppliers destroy the market? And what company strategy is appropriate in this situation? These are the questions that game theory answers. Until the mid-twentieth century, all existing models of decision-making in economic systems considered a participant in a vacuum, who was only interested in increasing their own profits and did not take into account the activities of other economic system participants when your steps affect other participants (players), and their actions affect you. It contradicted the market economy realities, because one of the main factors affecting market participants’ performance—competition—was not taken into account. In 1944, John von Neumann and O. Morgenstern published the book “Theory of Games and Economic Behavior,” which revealed the idea to consider the economic model as a special case of the game, and its participants—as those who compete with each other, the players, and using mathematics scientifically substantiated the behavior of players in any games designed to cause competition between players (noncooperative games). They mathematically described a way to find optimal strategies in such a game.

They saw the main purpose of game theory as an attempt to accurately describe the individual’s desire for maximum utility, or, in the case of the entrepreneur, for maximizing possible profit. In the game theory, the tougher decisions call for the use of the more effective approaches such as game trees. Decision trees are important for the optimization of one player without necessarily indigenizing the other players in the market. For instance, when determining the feasibility of entering a new market where only one firm is operational, the issue of market profitability is considered first which also depends on the reaction of the incumbent firm toward the new entrant ([2], p. 708). On the positive side, the incumbent firm could welcome the new entrant and allow them to take a share in the market or otherwise react negatively through aggression.

A precondition for using game theory and building mathematical models of conflicts is the presence of antagonistic interests between the participants. First of all, this is true for the economic sphere, where the efforts of each participant are aimed at obtaining optimal financial results. Achieving this goal requires effective interaction with other participants (partners, contractors, etc.). That’s why, the result of an individual’s actions in a business environment depends not only on their own efforts but also on the these persons’ actions.

In 1949, John Nash significantly extended the theory of games, allowing situations where players do not compete with each other but cooperate to achieve a common goal (cooperative games). He also introduced the concept of nonzero-sum games, where the payoff was not a constant (zero-sum games), but could change from the players’ actions. It was a real breakthrough in the study of game interaction, which clearly showed obsolescence of the classic competition concept (when every man is for himself).

He developed analysis methods according to which all participants either win or lose. These situations are called Nash equilibrium. According to his theory, the participants should use the optimal strategy, which leads to the stable equilibrium creation. It is advantageous for players to maintain this equilibrium, because any change will worsen their situation. These Nash’s works made a serious contribution to the development of game theory, and the mathematical tools of economic modeling were revised. John Nash has shown that the classic Adam Smith approach to competition, where every man is for himself, is suboptimal. More optimal strategies are when everyone tries to do better for themselves by doing better for others. In the Nash equilibrium, the egoistic thinking of each player in the long-term (strategic) perspective leads to a general loss. The result is optimal when each member of the group does better for themselves and for other players. A player’s decision that contradicts Nash equilibrium results in their loss. Moreover, Nash equilibrium requires each player to trust others in their rational actions regarding gaining their own benefits, and if one of the players receives information about Nash equilibrium, they must inform other players about the strategies to be followed to increase their payoffs.

Since each organization is one part of a conglomerate of interactions, any decision or action taken by companies will affect several entities that are in direct or indirect contact with the organization. In this regard, the ideal scenario in any industry is the one that entails interactive decision-making where each player’s actions depend on the decisions of others. Organizations not only utilize different strategies when handling competitors but are also keen when dealing with suppliers ([3], p. 59). Each supplier will always act based on self-interest, and the collective decisions of the players will not always lead to an optimal outcome for the chain. Shareholders are also an important part of the game, since the actions of the managers will determine the organization’s performance and hence the value of shareholders. Notably, there have been numerous companies that sought to increase their profits through malpractices, which were disadvantageous for the shareholders in the long run ([4], p. 101). In this regard, this article argues that the practice of organizational decision-making is a process that necessitates serious consideration of all stakeholders to ensure that the payoffs work in the best interests of all parties.

In 1996, Adam M. Brandenburger and Barry J. Nalebuff published a book called “Coopetition,” where they applied game theory conclusions as a branch of mathematics to economics and business. They created a classification of business games and their elements and rules. The proposed principle of “co-competition” allows you to leave the game as a winner without ruining your competitors.

As a revolutionary and interdisciplinary phenomenon, the game theory utilizes mathematical, philosophical, psychological, and a wide range of knowledge in other fields. In the business context, the theory is commonly used to conduct economic analysis for the highly competitive market such as the oligopolistic market. As a result, the game theory is a particularly useful tool in identifying high-risk versus high-reward strategic decisions in which strategy games are utilized. The game theory has indeed enables many organizations to grow into veterans in their respective industries and consequently maintain their influence in the long term.

The game theory is an ideal approach where competitive modes can be easily remodeled. In this regard, multiple strategy games will be played for the purposes of averting the different pressures caused by different competitors. The games are aimed at recommending multiple strategic decisions to guide competitive processes and analyzing how the possible strategies can aid in predicting competitive outcomes. The involved strategic decision, number of players, and the available information will hence help to determine the type of game that is best suited for the organization’s immediate needs ([5], p. 121). The concerned organization must also consider that the methodologies tend to have several shortcomings. In this regard, the game theory is based on the assumption that: the players will act in a rational manner and only pursue personal interests; the players conduct themselves strategically; and that the outcome is only desirable if managers fully grasp the anticipated positive and negative outcomes of the targeted decision. In reality, however, humans do not always act rationally, managers do not always think strategically, and companies often neither understand their payoffs nor that of competitors.

Since its roll-out, the game theory has grown tremendously. The approach has helped organizations optimize their marketing strategies, roll out decisions that wage war with competitors, develop tact in auctioning activities, and establish authentic styles of voting. For instance, the Nash equilibrium that was developed by John Nash has helped organizations plan and strategize their decisions ([4], p. 104). The equilibrium assumes that the market is operating at a stable state, and hence no organization is advantaged over the other whether or not it changes its strategy unilaterally. Through such an assumption, companies can engage in a noncooperative game when implementing their strategies.

The theory is an imminent part of modern decision-making practices. Through the simultaneous strategies, for instance, rivals need not inform their competitors about their decisions before taking them. For example, if two airline companies are required to submit sealed bids for the price of several jet airliners to a foreign national airliner. Both organizations will be free to set either low or high prices, in which case, the lower bidder will be awarded the order. However, should both companies bid the same amount, and then they will share the bid especially if both have the capacity to build all 10 airplanes. The benefits realized for both firms are therefore dependent on the choices of each company ([4], p. 106). The dominant strategy is also a well-known approach that was developed as part of the game theory. The dominant theory is applicable in situations where the only means of achieving optimization is through a specific strategy regardless of the rival’s actions ([5], p. 123). In such a case, the equilibrium is attained when each player settles for their own dominant strategy.

Indeed, with the dominant strategy, the payoffs could involve profit or loss. According to [6] (p. 158), the preferences and needs of the end user (dimensions of value) can be used as a means of beating competitors. One form of aggression is a cut-throat price war ([3], p. 62). To cut down on operational costs, the new entrant can venture into moderns technology or otherwise settle for the high cost case by using existing technologies. In such a case, the game theory dictates that the incumbent would benefit more by accommodating the new entrant. In this regard, the theory discourages indifference and irrationality among firms, as doing so can thwart optimization [7].

The game theory is a multifaceted phenomenon, which, despite being theoretical in nature, highly affects real-life business situations [8]. The principles thereof account for the different forms and sizes of organizations regardless of the industry in which they operate. For instance, the emphasis the theory puts in the concepts of equilibriums offers a clear-cut depiction of the need for organizations to pay attention to the potential impact of their short-term and long-term decisions. The theory is also rich in perspectives and allows for real-life investigation of decisions before embarking on them [9]. Doubtlessly, the game theory has had a revolutionary effect on the business world since its inception.

3. Main part

From the game theory point of view, economics is identified with the strategic game. Each participant in this game tries to maximize some function (result). In order to obtain this payoff (optimal financial result), the participant needs to make a choice in favor of such a behavior strategy that minimizes influence of the opponents’ strategies. A good strategy is not just a way to win a competitive war. Avinash K. Dixit [10] and Barry J. Nalebuff are sure that winning strategy should combine elements of competition and cooperation. And the manager needs to have a special type of thinking that will allow him to create good strategies and act correctly in difficult situations.

Strategic thinking, according to Dixit [10] and Nalebuff, is the ability to outperform the opponent, knowing that he is also trying to outperform you. It is also the ability to find ways to cooperate, even if others are guided only by their own interests. This is the ability to convince others (and even yourself) to do what you have promised. This is the ability to interpret and disclose information. This is the ability to put yourself in the other person’s place in order to predict their actions and influence them.

They claim that strategic thinking is based on the principles of a science called game theory. Although people sometimes tend to behave irrationally, their behavior can still be predicted using this knowledge.

One of the principles to keep in mind when playing the “strategy game” is that you are not acting in a vacuum. Your moves affect other players, and their actions affect you. This game provides two main types of interaction (Figure 1):

• sequential, when decisions are taken in succession and players in this case need to look ahead to try to calculate what their actions will lead to, what the responses may be, etc.

• parallel, when players act simultaneously, not knowing what moves are made by their opponents. In this case, in order to win, you need to think about how the competitor can act, because you must not forget that you are not alone in this game.

Figure 1.

Types of interaction between participants in the game.

Your steps affect other players, and their steps affect you. That’s why, before forming your strategy, you need to understand what type of interaction you are dealing with. Sometimes, it happens that there are both parallel and sequential interactions in the game.

The main rule of games with sequential steps is the following: to look ahead and think in reverse order. In other words, you need to analyze what your opponents will do next and use your conclusions to make a decision right now.

This allows you to resolve problems correctly and choose a strategy in situations where players take turns at making their steps. Those who do not do this (whether consciously or not) are impeding their own goals achievement. However, sometimes unexpected difficulties occur. In particular, if the opponent “plays an ultimatum,” it becomes very difficult to predict the results.

One of the basic game theory concepts is the prisoners’ dilemma. That’s the name of a situation when both opponents are forced to act in a way that is not in their mutual interests, i.e., the players will not always cooperate with each other, even if it is in their interests.

Two prisoners, for example, A and B, are accused of committing a joint crime, which is punishable by deprivation of liberty for a period of 10 years. However, if one of them confesses to what they have done and blames the initiative of the crime on the other one, his prison term will be reduced to 3 years, and the other prisoner will get the full term (10 years). If both prisoners confess to the crime, they get 5 years each. It is possible that both prisoners will deny their involvement in the crime, and then they will be released for failure of guilt evidence (Table 1). However, to do so they need to agree to remain silent. But prisoners are kept in different cells and cannot coordinate their behavior during interrogation.

	Prisoner B remains silent	Prisoner B testifies
Prisoner A remains silent	0, 0	10; 3
Prisoner A testifies	3; 10	5; 5

Table 1.

Game matrix of prisoners’ dilemma.

Of course, everyone wants to be free from restrain, but to achieve this goal both prisoners must not confess to the crime. At the same time, those who do not confess to the crime risk to stay in prison for 10 years if their partner does. To confess or not, that’s the question. It is obvious that in noncooperative behavior conditions, everyone will choose the least risky option. The rational assumption in this case is the worst option scenario (the partner in crime confesses to the crime). According to this strategy, both criminals will confess and get 5 years each.

In any case, the strategy of testifying for each prisoner (player) is dominant. The dilemma is that payoff in the dominant strategy for each player is smaller than for option that takes into account all players’ interests. The situations described by the term “prisoners’ dilemma” include a very common situation in business—price wars between competitors. In this situation, the best result for one company does not always mean the worst result for another one. In addition, this kind of game does not mean that somebody will be the loser and somebody—the winner. In many games, such as prisoners’ dilemma, the main issue is how to avoid losing or achieve a payoff for both participants. If in a game with parallel steps, the optimal player’s choice does not depend on other players’ choices, and it is said that the player has a dominant strategy—both Dixit and Nalebuff recommend to use exactly this one. In the prisoners’ dilemma, each player has a dominant strategy.

People or companies that found themselves in the prisoner’s dilemma can achieve better results if they reach agreement and cooperate. In reality, however, it’s not so easy to do. Each participant has a serious temptation to break the agreement (betray) and get even more. For example, to preserve the fish population, fishermen may decide to set a certain catching quota. However, how can we ensure compliance with this agreement? There are two obvious alternatives: either promise the participants a reward for sticking to the decision or determine the penalty for violating the agreement. Of course, the reward can be given to players only after they have made a step (otherwise, the temptation to betray might turn out to be stronger). It means that the player may not believe the promise.

However, despite all these difficulties, the reward can be effective and useful. For example, you can entrust the reward to a neutral third party. In real life, the situation is often different: since players interact in several directions, cooperation in one of them is rewarded with a corresponding favor in something else. The option of punishment for breach of the agreement is more common. Because, many games are part of a long-term interaction between the players. And if someone cheats, they will get only short-term benefits. Cheating will damage relationship with the other player, which means that in the long-term outlook it will turn out to be a loss. Punishment is often quite an effective way to achieve cooperation which benefits the participants in the game. However, to achieve the result, the punishment system must meet several criteria: deception detection, punishment form, comprehensibility, inevitability of punishment, scale of punishment, and repeatability. So, deception detection is the first necessary prerequisite for adequate punishment, then it is necessary to determine the punishment nature before the agreement comes into force, and it is also important for the participants to realize what is acceptable behavior in this game conditions, and what is not, and understand possible consequences of deception. It is important for the participants in the game to understand: deception will necessarily be disclosed and punished, and cooperation—rewarded; the participants must know that a serious punishment is more likely to keep them from deception—opponents simply will not want to risk, while deception and destruction of confidence that follows it must cost more than the potential profit it can deliver. Unfortunately, the prisoner’s dilemma very accurately describes the situation in business, namely, market competition, when competing companies lower prices, not trusting each other. Although there is a solution, you need to negotiate and maintain the price level. However, as part of the strategy of fighting for the consumer, based on a low price, companies are forced to focus primarily on their competitors’ moves. As an example, let us consider the following game model, namely the prisoners’ dilemma application in a duopoly. Let us assume that there are two light industry products companies A and B in the market, competing with each other. These companies’ price reduction strategy is considered. If company A starts to reduce prices and company B does the same, none of them will increase their market share, and their profits will be reduced by UAH 1000 thousand. However, if company B reduces the price, and company A leaves the price unchanged, company A’s profit will increase by UAH 1500 thousand, and company B’s profit will be decreased by the same amount and vice versa. If both companies leave their prices unchanged, their profits will not change. While developing its price strategy, company A calculates possible company B’s responses (Table 2).

Company strategy	Company B reduces the price	Company B leaves the price unchanged
Company A reduces the price	−1000, −1000	1500; −1500
Company A leaves the price unchanged	−1500; 1500	0; 0

Table 2.

The winning matrix the prisoners’ dilemma application in a duopoly.

Which strategy will company A choose? The best option for it is to reduce prices when company B’s policy is stable because in this case the profit increases by UAH 1500 thousand. However, this option is the worst from the point of view of the company B. For both companies, it would be reasonable to leave prices unchanged. At this, profits would remain at the same level. At the same time, fearing the worst possible scenario, companies will reduce their prices, while losing profits in the amount of UAH 1000 thousand each. Company B’s reduction price strategy will be the strategy of the minimum losses.

Achieving high profits remains the most important goal of any company. That’s why, along with competition, they tend to strive for cooperation and coordination of actions, maintaining price stability. Even when demand changes, these companies tend to try maintaining prices at the same level, fearing to be misunderstood by competitors. Oligopolies closely monitor each other’s behavior, and if one of them changes prices, others may perceive this decision as the beginning of a price war that is not profitable for everyone. Although many researches have been written about the prisoners’ dilemma, there are only a few its solutions (Figure 2).

1. Create a punitive rule that will remove the betrayal strategy. That is, reducing prices from the dominant ones. For example, each time after another price reduction made by some competitors, the others can influence them in some way. Options for suppliers: stop shipments, marketing support deprivation, or purchase discount reduction.

2. Get out of the dilemma. That is, simply leave the consumer no choice. This strategy was once used by GM in the automotive market. Tough competition in the market has led to a sharp drop in car prices. Customers increasingly focused on discounts and sales. Then GM issued a credit card that accumulated annual bonuses from purchases. They could spend bonuses on GM car or service only. The company canceled all promotions and directed its efforts to promote the bonus program. As a result, the cards were very popular. The holder could accumulate up to $3500 bonuses during the year, and the issue of choosing a car brand is resolved. By the way, then other car companies followed this way.

3. Correct the strategy in terms of time. Before that, when describing the prisoners’ dilemma, we assumed that the game develops within a short time frame. However, when companies already have experience of previous games, this situation better responds to the reality and is more interesting in terms of the result options.

Figure 2.

Solutions to the dilemma are coherent in business.

The research of R. Axelrod showed that when conducting repeated games at a larger number of players, the strategy to give up, that is, to reduce the price, gives a lower result. The optimal is an “eye for an eye with forgiveness” strategy. Analyzing the strategies that gave the best results, Axelrod named several conditions necessary for the strategy to get a high result (Figure 3):

1. Virtue. Never be the first to reduce prices, that is, the most important condition is that the strategy must be good, that is, not betray until the opponent does so. Almost all of the strategy leaders were kind.

2. Vindictiveness. A successful strategy should not be a blind optimist, and it should respond with a stroke to the competitors’ stroke, not to give them a break, maintain control over prices.

3. Forgiveness. After taking revenge on the competitor, return to cooperation if the opponent does not continue to betray. This prevents endless revenge on each other and maximizes your payoff.

4. Unenviousness. Not to try to destroy a competitor at any cost. To look less at other people’s business, and more at your own one.

Figure 3.

The characteristics of successful business strategy (Axelrod).

In the modern business, company orientation on unilateral advantages is strategically unjustified as a benefit can and should be provided to all partners.

Based on the fact that many participants can simultaneously win in the market, they proposed to conduct an effective business policy that is based on game theory: to change, in accordance with the company’s goal, the composition of players and the added values made by players (business participants), to determine the rules and tactics of the game, its scope and framework. For example, in the fighting for a customer, two companies are competitors, and in issues concerning equipment purchase it is desirable for these companies to cooperate. If they order several identical models of equipment, they can have profit, which will be acceptable for the supplier itself. Thus, the concept of A.M. Brandenburger and B.J. Nalebuff called for a flexible competitive policy that would combine the struggle for leadership with cooperation, and as a result, the company’s competitive position would be formed. It will help businessmen successfully conduct business by playing a game that is beneficial for their company.

4. Conclusion

In this article, the authors concluded that game theory is the most popular mathematical tool, the spheres of application of which are Economics, Finance, Management, Politics, and Military Science. The authors conclude that the winning strategy for companies should combine elements of competition and cooperation. The identified two main rules of games are sequential and parallel interaction. Based on this, the main rule of games with sequential steps is the following: to look ahead and think in reverse order. This allows to resolve problems correctly and choose a successful strategy in situations where companies take turns at making their decisions. For parallel interactions, the main rule is to decide if it’s better to cooperate or compete. One of the basic game theory concepts is the prisoner’s dilemma. The situation described by this term includes a very common situation in business know as price wars between competitors. In this situation, the best result for one company does not always mean the worth result for another one. The authors highlighted that two obvious alternatives that managers can use in business: either promise the participants a reward for sticking to the decision or determine the penalty for violating the agreement. The game model, namely the prisoners’ dilemma, is also applicable in duopoly. The authors presented three options solution to the dilemma in business such as create a punitive rule, get out of the dilemma, and correct the strategy in terms of time. In addition, the characteristics of successful business strategy by Axelrod were presented as a required condition for successful strategy in business.