In some respects, game theory is the science of strategy, or at least the optimal decision making of independent and competing actors in a strategic environment. Key pioneers of game theory were the mathematicians John von Neumann and John Nash, as well as the economist Oskar Morgenstern.
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Game theory is a theoretical framework for conceiving social situations between competing players and producing optimal decision making by independent and competing actors in a strategic environment.
Using game theory, real-world scenarios for situations such as price competition and product launches (and many more) can be presented and their outcomes predicted.
Game theory scenarios include the prisoner’s dilemma and the dictator game, among many others.
The foundations of game theory
The focus of game theory is the game, which serves as a model of an interactive situation between rational players. The key to game theory is that one player’s reward depends on the strategy implemented by the other player. The game identifies players’ identities, preferences, and available strategies and how these strategies affect the outcome. Depending on the model, various other requirements or assumptions may be necessary.
Game theory has a wide range of applications, including psychology, evolutionary biology, warfare, politics, economics, and business. Despite its many advances, game theory remains a young and developing science.
According to game theory, the actions and choices of all participants affect the outcome of each.
Definitions of game theory
Whenever we have a situation with two or more players that involves known payoffs or quantifiable consequences, we can use game theory to help determine the most likely outcomes. Let’s start by defining some terms commonly used in the study of game theory:
Game: any set of circumstances that has an outcome that depends on the actions of two or more decision makers (players)
Players: a person who makes strategic decisions in the context of the game.
Strategy: A complete plan of action that a player will take given the set of circumstances that may arise within the game.
Payout: The payout a player receives upon reaching a particular outcome (the payout can be any quantifiable form, from dollars to profits).
Information Set: The information available at a given point in the game (the term information set is usually applied when the game has a sequential component).
Equilibrium: The point in a game where both players have made their decisions and a result is reached.
The Nash equilibrium
Nash equilibrium is an achieved outcome that, once achieved, means that no player can increase the payoff by unilaterally changing decisions. It can also be considered a state of “no regrets” , in the sense that once a decision is made, the player will not regret decisions that take into account the consequences.
Nash equilibrium is reached over time, in most cases. However, once the Nash equilibrium is reached, it will not deviate from it. After we learn how to find the Nash equilibrium, see how a unilateral move would affect the situation. Does it make any sense? It shouldn’t, and that’s why the Nash Equilibrium is described as “remorseless . ” In general, there can be more than one balance in a game.
However, this usually occurs in games with more complex elements than two-player options . In simultaneous games that are repeated over time, one of these multiple equilibria is reached after some trial and error. This scenario of different overtime options before reaching equilibrium is most common in the business world when two companies determine the prices of highly interchangeable products, such as airline tickets or soft drinks.
Impact on the economy and business
Game theory brought about a revolution in economics by addressing crucial problems in earlier mathematical economic models. For example, neoclassical economics struggled to understand business anticipation and could not handle imperfect competition. Game theory shifted attention from steady-state equilibrium to the market process.
In business, game theory is beneficial for modeling competitive behaviors among economic agents. Companies often have several strategic options that affect their ability to make economic profits. For example, companies may face dilemmas such as withdrawing existing products or developing new ones, lowering prices relative to the competition, or employing new marketing strategies. Economists often use game theory to understand the behavior of oligopoly firms. Game theory helps predict likely outcomes when companies engage in certain behaviors, such as price fixing and collusion.
Twenty game theory economists have received the Nobel Prize in Economic Sciences for their contributions to the discipline.
Types of game theory
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 outcomes are known. It is a game between coalitions of players rather than individuals, and questions how groups are formed and how they distribute rewards 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 options are listed. A simplistic example of a real-world non-cooperative game is the game of Rock, Paper, Scissors.
Examples of game theory
There are several “games” that game theory analyzes. Below we will briefly describe some of these.
The prisoner’s dilemma
The prisoner’s dilemma is the best-known example of game theory. Consider the example of two criminals arrested for a crime. Prosecutors do not have compelling evidence to convict them. However, to obtain a confession, officials remove prisoners from their solitary cells and interrogate them in separate chambers. None of the prisoners have the means to communicate with each other. Officials submit four bids, often displayed as a 2 x 2 box.
If both confess, each will receive a five-year prison sentence.
If Prisoner 1 confesses, but Prisoner 2 does not, Prisoner 1 will have three years and Prisoner 2 will have nine years.
If Prisoner 2 confesses, but Prisoner 1 does not, Prisoner 1 will get 10 years and Prisoner 2 will get two years in prison.
If neither confesses, each will serve two years in prison.
The most favorable strategy is not to confess. However, neither man knows the other’s strategy, and without certainty that one will not confess, both will likely confess and receive a five-year prison sentence. Nash equilibrium suggests that in the prisoner’s dilemma, both players will make the move that is best for them individually but worst for them collectively.
The expression “tit for tat” (retaliation) has been determined to be the optimal strategy to optimize the prisoner’s dilemma. Tit for tat was introduced by Anatol Rapoport, who developed a strategy in which each participant in an iterated prisoner’s dilemma follows a course of action consistent with his opponent’s previous turn. For example, if provoked, a player subsequently responds with retaliation; If unprovoked, the player cooperates.
Zero sum games
Zero-sum games are a special case of constant-sum games in which players’ choices cannot increase or decrease the available resources. In zero-sum games, the total benefit to all players in the game, for each combination of strategies, always sums to zero (more informally, one player benefits only at the equal expense of the others). Poker, for example, is a zero-sum game (ignoring the possibility of the house cut), because you win exactly the amount your opponents lose. Other zero-sum games include matching pennies and most classic board games, including Go and chess.
Many games studied by game theorists (including the famous prisoner’s dilemma) are non-zero-sum games, because the outcome has net payoffs greater or less than zero. Informally, in non-zero-sum games, a win by one player does not necessarily correspond to a loss by another.
Constant sum games correspond to activities such as theft and gambling, but not to the fundamental economic situation in which potential profits from trade exist. It is possible to transform any game into a zero-sum (possibly asymmetric) game by adding a fictitious player (often called “the board”) whose losses offset the players’ net gains.
Dictator game
This is a simple game in which Player A must decide how to split a cash prize with Player B, who has no involvement in Player A’s decision.
While this is not a game theory strategy per se, it does provide some interesting insights into people’s behavior. Experiments reveal that approximately 50% keep all the money for themselves, 5% divide it equally, and the other 45% give the other participant a smaller share.
The dictator game is closely related to the ultimatum game, in which player A receives a fixed amount of money, part of which must be given to player B, who can accept or reject the given amount. The problem is that if the second player rejects the amount offered, both A and B get nothing. The dictator and the ultimatum games offer important lessons for issues such as charitable giving and philanthropy.
Volunteer Dilemma
In a volunteer’s dilemma, someone has to perform a task or job for the common good. The worst possible outcome is realized if no one volunteers. For example, consider a company in which accounting fraud is rampant, although senior management does not know it. Some junior employees in the accounting department are aware of the fraud, but are hesitant to inform senior management because this would result in the employees involved in the fraud being fired and likely prosecuted.
Being labeled as a whistleblower can also have some repercussions in the future. But if no one volunteers, large-scale fraud can result in the company going bankrupt and everyone losing their jobs.
The centipede game
The centipede game is an extensive form game in game theory in which two players alternately have the opportunity to take the lion’s share of a slowly increasing stash of money. It is organized so that if a player passes the stash to his opponent who then takes the stash, the player receives a smaller amount than if he had taken the entire stash.
The centipede game concludes as soon as one player takes the stash, with that player getting the larger portion and the other player getting the smaller portion. The game has a predefined total number of rounds, which each player knows in advance.
Limitations of game theory
The biggest problem with game theory is that, like most other economic models, it is based on the assumption that people are rational, self-interested, utility-maximizing actors. Of course, we are social beings who cooperate and care about the well-being of others, often at our own expense. Game theory cannot explain the fact that in some situations we can fall into a Nash equilibrium, and other times we cannot, depending on the social context and who the players are.
General uses and applications of game theory
As a method of applied mathematics, game theory has been used to study a wide variety of human and animal behaviors. It was initially developed in economics to understand a large collection of economic behaviors, including the behaviors of firms, markets, and consumers. The first use of game theory analysis was by Antoine Augustin Cournot in 1838 with his solution of the Cournot duopoly. The use of game theory in the social sciences has expanded, and game theory has also been applied to political, sociological, and psychological behaviors.
Although pre-20th century naturalists such as Charles Darwin made game-theoretic statements, the use of game-theoretic analysis in biology began with Ronald Fisher’s studies of animal behavior during the 1930s. This work predates to the name “game theory,” but it shares many important characteristics with this field. Developments in economics were later applied to biology largely by John Maynard Smith in his book Evolution and the Theory of Games.
In addition to being used to describe, predict, and explain behavior, game theory has also been used to develop theories of ethical or normative behavior and to prescribe such behavior. In economics and philosophy, scholars have applied game theory to help understand good or appropriate behavior. Game theoretical arguments of this type can be found since Plato. An alternative version of game theory, called chemical game theory, represents the player’s choices as metaphorical chemical reactive molecules called “knowlecules.” Chemical game theory then calculates the results as equilibrium solutions for a system of chemical reactions.
Application in Economy and business
Game theory is an important method used in mathematical economics and business to model competitive behaviors of interacting agents. Applications include a wide range of economic phenomena and approaches, such as auctions, negotiations, M&A pricing, fair division, duopolies, oligopolies, social network formation, agent-based computational economics, general equilibrium, mechanism design, and control systems. vote; and in areas as broad as experimental economics, behavioral economics, information economics, industrial organization and political economy.
This research typically focuses on particular sets of strategies known as “solution concepts” or “equilibria.” A common assumption is that players act rationally. In non-cooperative games, the most famous of these is the Nash equilibrium. A set of strategies is a Nash equilibrium if each represents a better response than the other strategies. If all players are playing the strategies in a Nash equilibrium, they have no unilateral incentive to deviate, since their strategy is the best they can do given what others are doing.
Game profits are generally taken to represent the utility of individual players.
A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation. One or more solution concepts are chosen, and the author demonstrates which sets of strategies in the presented game are equilibria of the appropriate type. Naturally, one might wonder what this information should be used for. Economists and business professors suggest two main uses (mentioned above): descriptive and prescriptive.
Uses of game theory in project management
Sound decision making is critical to project success. In project management, game theory is used to model the decision-making process of players such as investors, project managers, contractors, subcontractors, governments, and customers. Very often, these players have competing interests, and sometimes their interests are directly detrimental to other players , making project management scenarios suitable for being modeled by game theory.
Mahendra Piraveenan (2019) in his review provides several examples where game theory is used to model project management scenarios. For example, an investor usually has several investment options , and each option will likely result in a different project, and therefore one of the investment options must be chosen before the project charter can be produced. Similarly, any large project involving subcontractors, for example a construction project, has a complex interaction between the main contractor (the project manager) and the subcontractors, or between the subcontractors themselves, typically having several decision points.
For example, if there is an ambiguity in the contract between the contractor and subcontractor, each must decide how difficult it is to argue their case without jeopardizing the entire project and therefore their own participation in it. Similarly, when launching projects from competing organizations, marketing staff have to decide the best time and strategy to market the project, or its resulting product or service, so that it can gain maximum traction against the competition. In each of these scenarios, the decisions required depend on the decisions of other players who, in some way, have competing interests with the interests of the decision maker and can therefore ideally be modeled using game theory.
Piraveenan summarizes that two-player games are mainly used to model project management scenarios, and based on the identity of these players, five different types of games are used in project management.
- Government-private sector games (games that model public-private partnerships)
- Contractor-contractor games
- Contractor-subcontractor games
- Subcontractor-subcontractor games
- Games that involve other players.
In terms of game types, both cooperative and non-cooperative games, normal and extensive form games, and zero-sum games are used to model various project management scenarios.
Game theory in pricing for retail products
Applications of game theory are widely used in pricing strategies in retail and consumer markets, particularly for the sale of inelastic goods. With retailers constantly competing with each other for consumer market share, it has become quite common practice for retailers to discount certain products, intermittently, in hopes of increasing foot traffic at physical locations (website visits for e-commerce retailers) or increase sales of complementary or complementary products.
Black Friday, a popular shopping holiday in the United States, is when many retailers focus on optimal pricing strategies to capture the holiday shopping market.
In the Black Friday scenario, retailers using game theory applications often ask themselves ” what is the dominant competitor’s reaction to me?” In such a scenario, the game has two players: the retailer and the consumer. The retailer focuses on an optimal pricing strategy, while the consumer focuses on the best deal. In this closed system, there is often no dominant strategy as both players have alternative options. That is, retailers may find a different customer and consumers may shop at a different retailer. However, in the market competition that day, the dominant strategy for retailers lies in outperforming competitors. The open system assumes that multiple retailers sell similar products and a finite number of consumers demand the products at an optimal price.
A blog by a Cornell University professor provided an example of such a strategy, when Amazon priced a Samsung TV $100 below retail value, effectively undercutting competitors. Not counting the price of HDMI cables, as consumers have been found to be less discriminating when it comes to selling secondary items.
Retail markets continue to develop strategies and applications of game theory when it comes to pricing consumer goods. Key insights found between simulations in a controlled environment and real-world retail experiences show that applications of such strategies are more complex, as each retailer has to find an optimal balance between pricing, customer relationships, and suppliers, brand image and the potential to cannibalize the sale of more profitable items
