5.2 Using Game Theory

[5.3 Classic Game Models] [5.4 Simultaneous Games]

[5.5 Sequential Games] [5.6 Oligopoly] [5.7 Network Effects]

Game Theory and Business

Game theory emerged as a scholarly field of study in the first half of the 20th century. Since that time, it has significantly affected various academic disciplines, such as economics, political science and biology. Although the term "game theory" may suggest a certain frivolity, the concepts underlying it have many real-world applications and offer a structured and logical method of considering strategic situations.

The parallels between competitive games and strategic business situations should be fairly obvious. Consider the game of chess. There are two players, each of whom makes moves in sequence. After observing the move made by the first player, the second player makes a counter move. Then the first player, having observed the first two moves, makes the third move and so on.

Compare this to the business situation of gas stations competing for customers through strategic pricing. (The players in this case are station A and station B.) Suppose, for instance, that station A starts by choosing a new pricing strategy. Given station A's decision, station B decides how it will set its prices. Given station B's response, station A can choose to revise its pricing strategy and so on. The objective of each gas station in this "game" is to maximise its own profit. For each to do so, it must be continually acting and reacting to its competitor in the market as well as anticipating competitive responses when making decisions.

What does game theory have to offer?

First, game theory provides a framework, or formal procedure, for analysing any competitive situation (or "game"). Specifically, it forces you to identify the players in a game (consumers, sellers, input providers, governments, foreign organisations, etc.), their possible actions and reactions to the actions of other players, and the payoffs or rewards implicit in the game.

Game theory models reduce the world in which businesses operate from a highly complex one to one that is simpler but nevertheless retains some important characteristics of the original. By capturing and clarifying the most significant aspects of competition and interdependence, game theory models make it possible to break down a complex competitive situation into its key components and to analyse the complex dynamics between players.

In order for game theory to be truly useful in analysing such complex situations, certain assumptions need to be made. The most significant assumption is that the players in a game are choosing their actions optimally; that is, they are choosing their actions in the hope of maximising their ultimate payoff and they assume that the other players are doing likewise. Without this assumption, game theory cannot successfully model real-world situations.

Because game theory can realistically model business situations, it helps businesses to make optimal decisions and choose optimal actions. In other words, by "solving" a game, a business can identify its optimal actions (assuming, as always, that all the other players are also choosing their actions optimally). This is especially valuable because it helps companies choose the right business strategies when confronted with a complex strategic situation.

In what types of business situations can game theory be applied? Click on the link here to find out.

The nature of the solution(s) in game theory also motivates businesses to analyse how the structure of the game can be altered so that a different (and perhaps a more favourable) game can be played. Because of its systematic approach, game theory allows businesses to examine the consequences of actions that they may not have considered.

It is worth noting here that many games involving business are different from games in other fields. For instance, in business, many players can win (and lose) simultaneously, which obviously is not the case with chess. Additionally, because of the interdependent nature of most business relationships, these games are not always ones of direct competition. Consider a game between manufacturer and supplier — both have incentives to do well, but each also has a vested interest in the success of the other. Furthermore, unlike some other games with fixed rules, the rules of business are continuously in flux. They may be formulated by law, by tradition or by accident. Often, however, players have an influence on how rules are decided.

How does game theory differ from microeconomics?

Because game theory can be used to model almost any economic situation, it might seem redundant to study both microeconomics and game theory. However, microeconomics tends to focus on cases in which there are many buyers and sellers or there is one seller (or buyer) and many buyers (or sellers). Yet there are many instances in which there are a few buyers or sellers. Markets in which more than one but still only a few firms compete are known as "oligopolies." Oligopolists are acutely aware of their interdependence. Each firm's decisions in the market depend on the specific assumptions it makes about how its rivals make pricing and output decisions.

In addition, there are other situations in which there is one buyer and one seller. Microeconomics without game theory does not adequately address these matters.

Consider a market in which the number of producers is small. In aircraft manufacturing, two firms, Boeing and Airbus, control 100 percent of the world market for commercial aircraft. Each firm recognises that its pricing and production decisions have important implications for its rival's profitability. As a consequence, each firm attempts to guess which actions its rival will take. But each must also recognise that its rival will also be guessing as to what it will do. Clearly, such interactions are inadequately represented by classic microeconomic models, which assume that the firms are price takers.

In some other markets, the number of buyers is small. For instance, the wholesale market for diamonds is dominated by a small group of global firms; therefore, diamond producers may find that implicit (or explicit) collusion between buyers makes it difficult for the diamond producers to exercise market power. Once again, classic microeconomic models may be missing a very important feature of actual markets.

Click on each of the links below to read a few real-world examples in which game theory is applicable.

When modelling a game, it is important to consider all fundamentally interdependent players. Obviously, this would include any player actively competing for a game's payoffs. But that is not the only rationale for interdependence. To be fundamentally interdependent, a player can be anyone or anything that can realistically be expected to have an impact on that game — to affect the other players — regardless of whether that player is concerned directly with that game's payoffs. Sometimes a seemingly unimportant player can have a large impact on the optimal strategies and the outcome of the game.

Take, for example, the commercial aircraft manufacturing industry. Most people can correctly identify the two primary players — Boeing, a US aircraft manufacturer, and Airbus, a consortium of several European aircraft manufacturers. But are there other players? The US government and the European Union have an interest in this industry. Greater sales volume by Airbus — at Boeing's expense — is clearly in the interest of the European Union even though the EU would not share directly in Airbus's payoff (profits). In a similar vein, greater sales volume by Boeing — at the expense of Airbus — is in the United States' best interest. This means that often an analysis of the aircraft industry would also account for the interests of the two governments (or, more precisely, one government and one confederation of governments). In addition, labour unions, shareholders, suppliers and others in the United States and the European Union can also have a vested interest in influencing aircraft production.

Strategies and actions

It is important to differentiate between an action and a strategy. An action is the "move" a player makes at a certain stage. On the other hand, a strategy specifies the action a player will take at each stage of the game given what he or she knows about the actions of other players and any other information that a player may learn over the course of the game. For example, consider a firm that is thinking about a price cut. Saying that it will cut its prices by 10 percent is an action in a dynamic pricing game. Cutting prices by 10 percent and then specifying responses to any possible competitive reaction is a strategy. In short, a strategy describes what actions are going to be taken at any point in the game.

In the case of the aircraft industry example, Boeing's and Airbus' strategies would include actions such as how many aircraft to produce, how to price them, what new products to develop, and so on. Additionally, strategies here must include Boeing's possible reactions to any move made by Airbus and Airbus' possible reactions to any moves made by Boeing. Furthermore, both airplane makers have to expect and plan for the actions and reactions of the other players in this game (eg, consumers, the European and American governments, labour unions).

Click on the link here to see how one small airline company used game theory.

Payoffs

A payoff is the reward that a player receives based on the outcome of the game. Game theorists assign a positive or negative number to each possible payoff or outcome. In business terms, positive numbers represent profits, while negative numbers represent losses. Game theory assumes that players will choose to maximise their payoffs. Even if all of a player's possible payoffs are negative numbers, it is still in that player's best interest to choose actions that minimise his or her loss.

In the case of Boeing and Airbus, it is reasonable to assume that their payoffs are greater profits. This is not an essential assumption of game theory; what is essential is that each player has well-defined objectives that can be represented quantitatively. For some other players, such as governments and labour unions, maximising profits is not an appropriate objective. For the United States and the European Union, the incentive may be to maximise the welfare of their citizens by doing everything they can to keep these large companies operating successfully, employing people, and, most importantly, paying taxes. Labour unions are interested in protecting the interests and the paycheques of the companies' workers.

Rules of Games

Most games have rules that specify what players can and cannot do and how disputes will be resolved. In many games of business, there may be few rules (with the exception of contract and customs laws) or the rules may be vaguely defined and in a state of flux. For instance, antitrust laws in the United States provide firms with rules specifying broad parameters of behaviour, but even these are subject to interpretation by courts and, as such, change over time.

In some industries, participants — or to speak in terms of game theory, players — often attempt to manipulate the rules of the game in their favour. If done successfully, it then becomes difficult for others to function competitively in that industry. Hence, one might say that the really important game is the one that determines which rules are accepted and which rules are not.

Sequential and Simultaneous Games

Proponents of game theory have identified several different types of games. This subject concentrates on the dynamics of sequential games, where players move in turn, and simultaneous games, where all players must move at once.

The structure or form of a game determines the way it will be played out. For instance, in chess, the player with the white pieces moves first followed by the player using the black pieces. This sequential pattern continues until one of the players concedes or is checkmated or the players reach a draw. In other games, for instance, participating in a sealed-bid auction, players move simultaneously and, many times, blindly. It is important to note that the moves need not literally be simultaneous; the key feature is that each player must choose his or her action without knowing the decisions of other players.

Distinguishing between sequential games and simultaneous games is important because each requires players to think through the game differently. In sequential games, for instance, players must consider how a rival might respond to their actions, how they would then respond to their rivals' reactions, how their rivals would then respond, and so on. In simultaneous games, the problem is a little more challenging because players must be able to anticipate what action their rivals will choose while choosing their own action. Of course, players know that their rivals face the same dilemma.

In sequential games, it is sometimes advantageous to move first and it is sometimes disadvantageous. Commitment (making your move first and sticking to it) can be valuable in some situations and disadvantageous in others. For instance, when flexibility is important, it may be better to wait for your rival to move if more information (beyond simply the action of the other player) will be available later. However, in other situations, moving first allows a player to dictate the results of the game — as in the Battle of the Sexes classic game (discussed later in this segment).

Equilibrium

In the course of solving a game, a balance is found where all players are satisfied with their chosen strategies given the strategies of all other players. This balance is called "equilibrium". In equilibrium, no player has any incentive to change his or her strategy given the strategies of the other players and given that every other parameter of the game is unchanged. In other words, in equilibrium, each player is using a strategy that is the best response to the employed or anticipated strategies of the other players.

Topic Summary

In this topic, you have learnt how to

· define games by players, strategies and payoffs

· classify simultaneous and sequential games

Now go on to topic 5.3, “Classic Game Models”.