research topics about game theory

Game Theory Research Paper Topics

This comprehensive guide to game theory research paper topics is designed to assist students and researchers in the field of economics. Selecting a compelling and relevant research topic is a crucial step in the academic journey, and this guide aims to facilitate this process. We provide an extensive list of topics, divided into ten categories, each with ten unique ideas. Additionally, we offer expert advice on how to select a topic from this multitude and how to write a research paper in game theory. Lastly, we introduce iResearchNet’s professional writing services, tailored to support your academic journey and ensure success in your research endeavors.

100 Game Theory Research Paper Topics

Choosing a research paper topic is a critical step in the research process. The topic you select will guide your study and influence the complexity and relevance of your work. In the field of game theory, there are numerous intriguing topics that can be explored. To assist you in this process, we have compiled a comprehensive list of game theory research paper topics. These topics are divided into ten categories, each offering a different perspective on game theory.

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• The role of Nash Equilibrium in game theory
• The concept of Dominant Strategy and its applications
• The Prisoner’s Dilemma and its implications
• The concept of Subgame Perfect Equilibrium
• Zero-sum games and their significance
• The role of Mixed Strategy in game theory
• The concept of Pareto Efficiency in game theory
• Evolutionary game theory and its applications
• The concept of Bayesian games
• The role of Repeated Games in game theory
• The role of game theory in strategic decision making
• The impact of game theory on negotiation strategies
• Game theory and decision making under uncertainty
• The role of game theory in conflict resolution
• The impact of game theory on cooperative decision making
• Game theory and decision making in competitive environments
• The role of game theory in risk management
• Game theory and decision making in auctions
• The impact of game theory on voting strategies
• Game theory and decision making in social dilemmas
• The use of game theory in understanding market competition
• The impact of game theory on economic policy making
• The role of game theory in understanding oligopolies
• Game theory and its role in understanding bargaining situations
• The influence of game theory on economic behavior
• The role of game theory in understanding public goods and free-riding
• The impact of game theory on understanding market failures
• Game theory and its role in understanding strategic trade policy
• The influence of game theory on understanding labor negotiations
• The role of game theory in understanding financial markets
• The role of game theory in strategic business decisions
• Game theory and its impact on pricing strategies
• The use of game theory in understanding competitive strategies
• Game theory and its role in merger and acquisition decisions
• The influence of game theory on supply chain management
• The role of game theory in understanding corporate governance
• The impact of game theory on marketing strategies
• Game theory and its role in understanding business negotiations
• The influence of game theory on organizational behavior
• The role of game theory in understanding innovation and R&D strategies
• The role of game theory in understanding voting behavior
• Game theory and its impact on political negotiations
• The use of game theory in understanding international relations
• Game theory and its role in understanding political coalitions
• The influence of game theory on policy making
• The role of game theory in understanding electoral competition
• The impact of game theory on understanding conflict and war
• Game theory and its role in understanding public policy decisions
• The influence of game theory on understanding political power dynamics
• The role of game theory in understanding political cooperation and conflict
• The role of game theory in algorithm design
• Game theory and its impact on network design and performance
• The use of game theory in understanding cybersecurity
• Game theory and its role in artificial intelligence
• The influence of game theory on distributed computing
• The role of game theory in understanding internet economics
• The impact of game theory on understanding data privacy
• Game theory and its role in understanding machine learning
• The influence of game theory on understanding software engineering
• The role of game theory in understanding social networks
• The role of game theory in understanding evolutionary biology
• Game theory and its impact on understanding animal behavior
• The use of game theory in understanding population dynamics
• Game theory and its role in understanding cooperation and conflict in nature
• The influence of game theory on understanding ecological interactions
• The role of game theory in understanding disease spread and control
• The impact of game theory on understanding conservation strategies
• Game theory and its role in understanding genetic algorithms
• The influence of game theory on understanding ecosystem management
• The role of game theory in understanding biodiversity
• The role of game theory in understanding social behavior
• Game theory and its impact on understanding social norms
• The use of game theory in understanding social networks
• Game theory and its role in understanding social conflict and cooperation
• The influence of game theory on understanding social influence and persuasion
• The role of game theory in understanding social decision making
• The impact of game theory on understanding social dilemmas
• Game theory and its role in understanding social justice and fairness
• The influence of game theory on understanding social change and stability
• The role of game theory in understanding social identity and group behavior
• The role of game theory in understanding mathematical optimization
• Game theory and its impact on understanding mathematical modeling
• The use of game theory in understanding mathematical logic
• Game theory and its role in understanding mathematical decision theory
• The influence of game theory on understanding mathematical probability
• The role of game theory in understanding mathematical statistics
• The impact of game theory on understanding mathematical operations research
• Game theory and its role in understanding mathematical graph theory
• The influence of game theory on understanding mathematical combinatorics
• The role of game theory in understanding mathematical dynamical systems
• The role of game theory in understanding behavioral economics
• Game theory and its impact on understanding quantum computing
• The use of game theory in understanding complex systems
• Game theory and its role in understanding network science
• The influence of game theory on understanding artificial intelligence 6. The role of game theory in understanding climate change strategies
• The impact of game theory on understanding sustainable development
• Game theory and its role in understanding social media dynamics
• The influence of game theory on understanding future economic models
• The role of game theory in understanding future political strategies

This comprehensive list of game theory research paper topics provides a wide range of options for your research. Each category offers unique insights into the different aspects of game theory, from fundamental concepts to future directions. Remember, the best research paper topic is one that not only interests you but also has sufficient resources for you to explore. We hope this list inspires you and aids you in your journey to write a compelling research paper in game theory.

Introduction to Game Theory

Game theory, a fascinating and influential field of study, is a theoretical framework for understanding social situations among competing players. 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 setting.

The key pioneers of game theory were mathematicians John von Neumann and John Nash, as well as economist Oskar Morgenstern. Game theory was originally developed to understand economic behavior and is still widely used in economics today. However, its applications have expanded to various other fields, including computer science, political science, and biology.

In essence, game theory models the rational behavior of individuals who are aware that their actions affect each other. It involves designing mathematical models to study interactions in structured scenarios (games) and predict the outcome of these interactions. Games in this context are situations where outcomes depend on the actions of multiple players. Each player has a set of possible actions and makes a decision based on their preferences and the expected actions of other players.

Game theory has two main branches: cooperative and non-cooperative game theory. In cooperative games, binding agreements among players are possible, while in non-cooperative games, binding agreements are not. Non-cooperative game theory, which focuses on predicting individual behavior, is more widely used.

Game theory has a wide range of applications. In economics, it is used to model competition and cooperation between firms, to analyze bargaining situations, and to understand and design auctions. In political science, it is used to model strategic voting, while in computer science, it is used in the design of algorithms.

Research papers in game theory allow students to delve deeper into specific areas, contributing to their personal knowledge and the broader academic community. These papers can explore a wide range of game theory research paper topics, from understanding the role of game theory in economic decisions to examining its applications in computer science or political science.

The importance of game theory extends beyond academia. It has real-world implications in various sectors, including economics, politics, and computer science. By understanding the strategic interactions modeled by game theory, we can design better policies, make better business decisions, and develop more efficient algorithms.

How to Choose a Game Theory Topic

Choosing a research topic is a critical step in the research process. The topic you select will guide your study, influence the complexity and relevance of your work, and determine how engaged you are throughout the process. There are numerous intriguing game theory research paper topics that can be explored. Here are some expert tips to assist you in this process:

• Understanding Your Interests: The first step in choosing a research topic is to understand your interests. What areas of game theory fascinate you the most? Are you interested in how game theory influences economic behavior, or are you more intrigued by its role in computer science or political science? Reflecting on these questions can help you narrow down your options and choose a topic that truly engages you. Remember, research is a time-consuming process, and your interest in the topic will keep you motivated.
• Evaluating the Scope of the Topic: Once you have identified your areas of interest, the next step is to evaluate the scope of potential game theory research paper topics. A good research topic should be neither too broad nor too narrow. If it’s too broad, you may struggle to cover all aspects of the topic effectively. If it’s too narrow, you may have difficulty finding enough information to support your research. Try to choose a topic that is specific enough to be manageable but broad enough to have sufficient resources.
• Assessing Available Resources and Data: Before finalizing a topic, it’s important to assess the available resources and data. Are there enough academic sources, such as books, journal articles, and reports, that you can use for your research? Is there accessible data that you can analyze if your research requires it? A preliminary review of literature and data can save you from choosing a topic with limited resources.
• Considering the Relevance and Applicability of the Topic: Another important factor to consider is the relevance and applicability of the topic. Is the topic relevant to current issues in game theory? Can the findings of your research be applied in real-world settings? Choosing a relevant and applicable topic can increase the impact of your research and make it more interesting for your audience.
• Seeking Advice: Don’t hesitate to seek advice from your professors, peers, or other experts in the field. They can provide valuable insights, suggest resources, and help you refine your topic. Discussing your ideas with others can also help you see different perspectives and identify potential issues that you may not have considered.
• Flexibility: Finally, be flexible. Research is a dynamic process, and it’s okay to modify your topic as you delve deeper into your study. You may discover new aspects of the topic that are more interesting or find that some aspects are too challenging to explore due to constraints. Being flexible allows you to adapt your research to these changes and ensure that your study is both feasible and engaging.

Remember, choosing a research topic is not a decision to be taken lightly. It requires careful consideration and planning. However, with these expert tips, you can navigate this process more effectively and choose a game theory research paper topic that not only meets your academic requirements but also fuels your passion for learning.

How to Write a Game Theory Research Paper

Writing a research paper in game theory, like any other academic paper, requires careful planning, thorough research, and meticulous writing. Here are some expert tips to guide you through this process:

• Understanding the Structure of a Research Paper: A typical research paper includes an introduction, literature review, methodology, results, discussion, and conclusion. The introduction presents your research question and its significance. The literature review provides an overview of existing research related to your topic. The methodology explains how you conducted your research. The results section presents your findings, and the discussion interprets these findings in the context of your research question. Finally, the conclusion summarizes your research and suggests areas for future research.
• Developing a Strong Thesis Statement: Your thesis statement is the central argument of your research paper. It should be clear, concise, and debatable. A strong thesis statement guides your research and helps your readers understand the purpose of your paper.
• Conducting Thorough Research: Before you start writing, conduct a thorough review of the literature related to your topic. This will help you understand the current state of research in your area, identify gaps in the literature, and position your research within this context. Use academic databases to find relevant books, journal articles, and other resources. Remember to evaluate the credibility of your sources and take detailed notes to help you when writing.
• Writing and Revising Drafts: Start writing your research paper by creating an outline based on the structure of a research paper. This will help you organize your thoughts and ensure that you cover all necessary sections. Write a first draft without worrying too much about perfection. Focus on getting your ideas down first. Then, revise your draft to improve clarity, coherence, and argumentation. Make sure each paragraph has a clear topic sentence and supports your thesis statement.
• Proper Citation and Avoiding Plagiarism: Always cite your sources properly to give credit to the authors whose work you are building upon and to avoid plagiarism. Familiarize yourself with the citation style required by your institution or discipline, such as APA, MLA, Chicago/Turabian, or Harvard. There are many citation tools available online that can help you with this.
• Seeking Feedback: Don’t hesitate to seek feedback on your drafts from your professors, peers, or writing centers at your institution. They can provide valuable insights and help you improve your paper.
• Proofreading: Finally, proofread your paper to check for any grammatical errors, typos, or inconsistencies in formatting. A well-written, error-free paper makes a good impression on your readers and enhances the credibility of your research.
• Incorporating Game Theory Concepts: When writing a game theory research paper, it’s crucial to accurately incorporate game theory concepts. Make sure you understand these concepts thoroughly and can explain them clearly in your paper. Use diagrams and examples where appropriate to illustrate these concepts.
• Analyzing and Interpreting Game Theory Models: Game theory research often involves analyzing and interpreting game theory models. Be sure to explain your analysis process and interpret the results in a way that is understandable to your readers. Discuss the implications of your findings for the broader field of game theory.
• Discussing Real-World Applications: Game theory is a practical field with many real-world applications. Discuss how your research relates to these applications. This can make your research more interesting and relevant to your readers.

Remember, writing a research paper is a process that requires time, effort, and patience. Don’t rush through it. Take your time to understand your topic, conduct thorough research, and write carefully. With these expert tips, you can write a compelling game theory research paper that contributes to your academic success and the broader field of game theory.

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• Introduction

Classification of games

One-person games.

• Games of perfect information
• Games of imperfect information
• Mixed strategies and the minimax theorem
• Utility theory
• Cooperative versus noncooperative games
• The Nash solution
• Theory of moves
• Biological applications
• Sequential and simultaneous truels
• Power in voting: the paradox of the chair’s position
• The von Neumann–Morgenstern theory
• The Banzhaf value in voting games

game theory

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• Game theory - Student Encyclopedia (Ages 11 and up)
• Table Of Contents

game theory , branch of applied mathematics that provides tools for analyzing situations in which parties, called players, make decisions that are interdependent. This interdependence causes each player to consider the other player’s possible decisions, or strategies, in formulating strategy . A solution to a game describes the optimal decisions of the players, who may have similar, opposed, or mixed interests, and the outcomes that may result from these decisions.

Although game theory can be and has been used to analyze parlour games, its applications are much broader. In fact, game theory was originally developed by the Hungarian-born American mathematician John von Neumann and his Princeton University colleague Oskar Morgenstern , a German-born American economist, to solve problems in economics . In their book The Theory of Games and Economic Behavior (1944), von Neumann and Morgenstern asserted that the mathematics developed for the physical sciences, which describes the workings of a disinterested nature, was a poor model for economics. They observed that economics is much like a game, wherein players anticipate each other’s moves, and therefore requires a new kind of mathematics, which they called game theory. Game theory was further developed in the 1950s by American mathematician John Nash , who established the mathematical principles of game theory, a branch of mathematics that examines the rivalries between competitors with mixed interests. (The name for this branch of studies may be somewhat of a misnomer—game theory generally does not share the fun or frivolity associated with games.)

(Read Steven Pinker’s Britannica entry on rationality.)

Game theory has been applied to a wide variety of situations in which the choices of players interact to affect the outcome. In stressing the strategic aspects of decision making , or aspects controlled by the players rather than by pure chance, the theory both supplements and goes beyond the classical theory of probability . It has been used, for example, to determine what political coalitions or business conglomerates are likely to form, the optimal price at which to sell products or services in the face of competition, the power of a voter or a bloc of voters, whom to select for a jury, the best site for a manufacturing plant, and the behaviour of certain animals and plants in their struggle for survival. It has even been used to challenge the legality of certain voting systems.

It would be surprising if any one theory could address such an enormous range of “games,” and in fact there is no single game theory. A number of theories have been proposed, each applicable to different situations and each with its own concepts of what constitutes a solution. This article describes some simple games, discusses different theories, and outlines principles underlying game theory. Additional concepts and methods that can be used to analyze and solve decision problems are treated in the article optimization .

Games can be classified according to certain significant features, the most obvious of which is the number of players. Thus, a game can be designated as being a one-person, two-person, or n -person (with n greater than two) game, with games in each category having their own distinctive features. In addition, a player need not be an individual; it may be a nation, a corporation, or a team comprising many people with shared interests.

In games of perfect information, such as chess , each player knows everything about the game at all times. Poker , on the other hand, is an example of a game of imperfect information because players do not know all of their opponents’ cards.

The extent to which the goals of the players coincide or conflict is another basis for classifying games. Constant-sum games are games of total conflict, which are also called games of pure competition. Poker, for example, is a constant-sum game because the combined wealth of the players remains constant, though its distribution shifts in the course of play.

Players in constant-sum games have completely opposed interests, whereas in variable-sum games they may all be winners or losers. In a labour-management dispute , for example, the two parties certainly have some conflicting interests, but both will benefit if a strike is averted.

Variable-sum games can be further distinguished as being either cooperative or noncooperative. In cooperative games players can communicate and, most important, make binding agreements; in noncooperative games players may communicate, but they cannot make binding agreements, such as an enforceable contract. An automobile salesperson and a potential customer will be engaged in a cooperative game if they agree on a price and sign a contract. However, the dickering that they do to reach this point will be noncooperative. Similarly, when people bid independently at an auction they are playing a noncooperative game, even though the high bidder agrees to complete the purchase.

Finally, a game is said to be finite when each player has a finite number of options, the number of players is finite, and the game cannot go on indefinitely. Chess, checkers , poker , and most parlour games are finite. Infinite games are more subtle and will only be touched upon in this article.

A game can be described in one of three ways: in extensive, normal, or characteristic-function form. (Sometimes these forms are combined, as described in the section Theory of moves .) Most parlour games, which progress step by step, one move at a time, can be modeled as games in extensive form. Extensive-form games can be described by a “game tree,” in which each turn is a vertex of the tree, with each branch indicating the players’ successive choices.

The normal (strategic) form is primarily used to describe two-person games. In this form a game is represented by a payoff matrix, wherein each row describes the strategy of one player and each column describes the strategy of the other player. The matrix entry at the intersection of each row and column gives the outcome of each player choosing the corresponding strategy. The payoffs to each player associated with this outcome are the basis for determining whether the strategies are “in equilibrium,” or stable.

The characteristic-function form is generally used to analyze games with more than two players. It indicates the minimum value that each coalition of players—including single-player coalitions—can guarantee for itself when playing against a coalition made up of all the other players.

One-person games are also known as games against nature. With no opponents, the player only needs to list available options and then choose the optimal outcome. When chance is involved the game might seem to be more complicated, but in principle the decision is still relatively simple. For example, a person deciding whether to carry an umbrella weighs the costs and benefits of carrying or not carrying it. While this person may make the wrong decision, there does not exist a conscious opponent. That is, nature is presumed to be completely indifferent to the player’s decision, and the person can base his decision on simple probabilities. One-person games hold little interest for game theorists.

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Game Theory

The study of mathematical models of conflict and cooperation between intelligent, rational decisionmakers, game theory is also known more descriptively as interactive decision theory. For more than seven decades, RAND researchers have used game theory to explore economics, political science, psychology, and conflict.

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A Primer on the Theory of Games of Strategy

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How Game Theory Could Solve the COVID-19 Vaccine Rollout Puzzle

Mar 11, 2021

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Journal Article

Aug 7, 2024

Debt Crises Between a Country and an International Lender as a Two-Period Game

This publication follows work done during the Tech and Narrative Lab on gaming topics related to systemic risk. It publishes a game theoretic model of debt crises.

Dec 19, 2023

Cybersecurity and Supply Chain Risk Management Are Not Simply Additive: Implications for Directions in Risk Assessment, Risk Mitigation, and Research to Secure the Supply of Defense Industrial Products

This report presents an examination of how cyber-related risks compare with other risks to defense-industrial supply chains and the implications of the differences in risks for directions in risk assessment and mitigation and for research.

Oct 5, 2023

Building U.S. Responses to Russia's Threats to Use Nonstrategic Nuclear Weapons: A Game Theoretic Analysis of Brinkmanship

Using a game theory approach, the authors examine U.S. tools and levers to respond to Russia’s potential employment of nonstrategic nuclear weapons in its conflict with Ukraine.

Jun 26, 2023

Understanding America's Technological Tit for Tat with China

China and the United States appear to be barreling towards a path that risks further ratcheting up the ongoing economic war. More-evolved strategies are needed beyond simple retaliatory spirals, to find peaceful equilibria and ensure technoeconomic competition does not spill over into military conflict.

May 18, 2023

Thinking Without Knowing: Psychological and Behavioral Consequences of Unjustified Confidence Regarding Blackjack Strategy

In two studies, we explored potential psychological and behavioral consequences of unjustified confidence, including outcome expectations, anxiety, risk taking, and information search and consideration.

Jan 25, 2023

First Mover Typology for the Space Domain: Building a Foundation for Future Analysis

The authors offer a categorization and nuanced views of first moves in military strategy as a basis for understanding and further analysis of first mover advantage in the space domain.

Jul 25, 2022

Cyber Deterrence with Imperfect Attribution and Unverifiable Signaling

Examines a game of deterrence in which the defender can signal its retaliatory capability but can only imperfectly attribute an attack. We show that there are equilibria in which the defender sends noisy signals to increase its expected payoff.

Mar 8, 2022

Is Putin Irrational? What Nuclear Strategic Theory Says About Deterrence of Potentially Irrational Opponents

Increasingly isolated and desperate, Putin might try to suddenly escalate the Ukraine conflict rather than back down in the face of international opposition. The United States and its allies must account for the possibility that even in the face of credible deterrent threats Putin might double down and lash out.

Feb 18, 2022

Developing a Winning Safety Strategy for Automated Vehicles

When policy problems involve many different groups with diverging interests along with significant uncertainty about the future, games can be a valuable way to explore the potential consequences of important policy decisions. What could gaming bring to the area of AV safety?

Aug 12, 2021

Engaging with North Korea: Lessons from Game Theory

In this report, the authors apply a game theoretic lens to the current confrontation between the United States and North Korea to provide insights and recommendations.

Jun 14, 2021

Game Theory: A Tool for the Vaccine Campaign

RAND operations researcher Luke Muggy discusses ways in which game theory could support the COVID-19 vaccination campaign, including through coordination of supply purchases and the development of tools that make the availability of vaccines transparent to the public.

May 1, 2021

On Balanced Games Without Side Payments: A Correction

The purpose of this paper is to repair Lemma 6.3 appearing in the author's previous paper of the same title (P-4910, September 1972).

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Game Theory: A General Introduction and a Historical Overview

• Reference work entry
• First Online: 01 January 2021
• Cite this reference work entry

• Tamer Başar 3  

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This entry provides an overview of the aspects of game theory that are covered in this Encyclopedia , which includes a broad spectrum of topics on static and dynamic game theory. The entry starts with a brief overview of game theory, identifying its basic ingredients, and continues with a brief historical account of the development and evolution of the field. It concludes by providing pointers to other entries in the Encyclopedia on game theory and a list of references.

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Bibliography

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Başar, T. (2021). Game Theory: A General Introduction and a Historical Overview. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_26

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We are excited to announce a Research Topic on “Game Theory and Complex Systems,” which explores the fascinating intersection of these two fields. This issue aims to bring together scholars from various disciplines, including physicists, computer scientists, behavioral economists, and social scientists, who employ game-theoretical techniques in their research. Game theory is a versatile tool, with applications in a multitude of disciplines, including statistical physics, computer science, biology, economics, finance, climate change negotiations, and sociology. The interdisciplinary nature of complex systems and game theory presents a unique opportunity for researchers to contribute diverse perspectives and methodologies. The primary goal of this Research Topic is to deepen our understanding of human behavior through the lens of game theory and complex systems. We encourage contributors to investigate the applications of these frameworks to human behavior, particularly focusing on empirical evidence and behavioral experiments. By examining decision-making dynamics, cooperation, and strategic interactions, we aim to enhance our ability to model and predict human behavior and provide valuable insights into real-world phenomena. Contributions should address how game theory can shed light on intricate social, economic, and biological dynamics, thereby advancing theoretical and applied knowledge in these fields. We invite researchers, practitioners, and scholars to submit original research articles, reviews, or theoretical papers for this Research Topic. Areas of interest include but are not limited to: evolutionary game theory in complex systems, agent-based modelling and simulations of strategic interactions, network effects on game-theoretical dynamics, applications in social networks, and behavioral experiments in game theory. Additionally, we welcome studies on game theory’s role in economic systems, decision-making in biological environments, multi-agent systems, and its application to climate change negotiations. All submissions should align with the interdisciplinary focus of the issue, contributing to the overarching understanding of game theory and complex systems.

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June 2, 2003

What is game theory and what are some of its applications?

Saul I. Gass, professor emeritus at the University of Maryland's Robert H. Smith School of Business, explains.

Game: A competitive activity involving skill, chance, or endurance on the part of two or more persons who play according to a set of rules, usually for their own amusement or for that of spectators ( The Random House Dictionary of the English Language, 1967).

Consider the following real-world competitive situations: missile defense, sales price wars for new cars, energy regulation, auditing tax payers, the TV show "Survivor," terrorism, NASCAR racing, labor- management negotiations, military conflicts, bidding at auction, arbitration, advertising, elections and voting, agricultural crop selection, conflict resolution, stock market, insurance, and telecommunications. What do they have in common?

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A basic example helps to illustrate the point. After learning how to play the game tick-tack-toe, you probably discovered a strategy of play that enables you to achieve at least a draw and even win if your opponent makes a mistake and you notice it. Sticking to that strategy ensures that you will not lose.

This simple game illustrates the essential aspects of what is now called game theory. In it, a game is the set of rules that describe it. An instance of the game from beginning to end is known as a play of the game. And a pure strategy--such as the one you found for tick-tack-toe--is an overall plan specifying moves to be taken in all eventualities that can arise in a play of the game. A game is said to have perfect information if, throughout its play, all the rules, possible choices, and past history of play by any player are known to all participants. Games like tick-tack-toe, backgammon and chess are games with perfect information and such games are solved by pure strategies. But whereas you may be able to describe all such pure strategies for tick-tack-toe, it is not possible to do so for chess, hence the latter's age-old intrigue.

Games without perfect information, such as matching pennies, stone-paper-scissors or poker offer the players a challenge because there is no pure strategy that ensures a win. For matching pennies you have two pure strategies: play heads or tails. For stone-paper-scissors you have three pure strategies: play stone or paper or scissors. In both instances you cannot just continually play a pure strategy like heads or stone because your opponent will soon catch on and play the associated winning strategy. What to do? We soon learn to try to confound our opponent by randomizing our choice of strategy for each play (for heads-tails, just toss the coin in the air and see what happens for a 50-50 split). There are also other ways to control how we randomize. For example, for stone-paper-scissors we can toss a six-sided die and decide to select stone half the time (the numbers 1, 2 or 3 are tossed), select paper one third of the time (the numbers 4 or 5 are tossed) or select scissors one sixth of the time (the number 6 is tossed). Doing so would tend to hide your choice from your opponent. But, by mixing strategies in this manner, should you expect to win or lose in the long run? What is the optimal mix of strategies you should play? How much would you expect to win? This is where the modern mathematical theory of games comes into play.

Games such as heads-tails and stone-paper-scissors are called two-person zero-sum games. Zero-sum means that any money Player 1 wins (or loses) is exactly the same amount of money that Player 2 loses (or wins). That is, no money is created or lost by playing the game. Most parlor games are many-person zero-sum games (but if you are playing poker in a gambling hall, with the hall taking a certain percentage of the pot to cover its overhead, the game is not zero-sum). For two-person zero-sum games, the 20th century¿s most famous mathematician, John von Neumann, proved that all such games have optimal strategies for both players, with an associated expected value of the game. Here the optimal strategy, given that the game is being played many times, is a specialized random mix of the individual pure strategies. The value of the game, denoted by v, is the value that a player, say Player 1, is guaranteed to at least win if he sticks to the designated optimal mix of strategies no matter what mix of strategies Player 2 uses. Similarly, Player 2 is guaranteed not to lose more than v if he sticks to the designated optimal mix of strategies no matter what mix of strategies Player 1 uses. If v is a positive amount, then Player 1 can expect to win that amount, averaged out over many plays, and Player 2 can expect to lose that amount. The opposite is the case if v is a negative amount. Such a game is said to be fair if v = 0. That is, both players can expect to win 0 over a long run of plays. The mathematical description of a zero-sum two-person game is not difficult to construct, and determining the optimal strategies and the value of the game is computationally straightforward. We can show that heads-tails is a fair game and that both players have the same optimal mix of strategies that randomizes the selection of heads or tails 50 percent of the time for each. Stone-paper-scissors is also a fair game and both players have optimal strategies that employ each choice one third of the time. Not all zero-sum games are fair, although most two-person zero-sum parlor games are fair games. So why do we then play them? They are fun, we like the competition, and, since we usually play for a short period of time, the average winnings could be different than 0. Try your hand at the following game that has a v = 1/5.

The Skin Game: Two players are each provided with an ace of diamonds and an ace of clubs. Player 1 is also given the two of diamonds and Player 2 the two of clubs. In a play of the game, Player 1 shows one card, and Player 2, ignorant of Player 1¿s choice, shows one card. Player 1 wins if the suits match, and Player 2 wins if they do not. The amount (payoff) that is won is the numerical value of the card of the winner. But, if the two deuces are shown, the payoff is zero. [Here, if the payoffs are in dollars, Player 1 can expect to win $0.20. This game is a carnival hustler¿s (Player 1) favorite; his optimal mixed strategy is to never play the ace of diamonds, play the ace of clubs 60 percent of the time, and the two of diamonds 40 percent of the time.]

The power of game theory goes way beyond the analysis of such relatively simple games, but complications do arise. We can have many-person competitive situations in which the players can form coalitions and cooperate against the other players; many-person games that are nonzero-sum; games with an infinite number of strategies; and two-person nonzero sum games, to name a few. Mathematical analysis of such games has led to a generalization of von Neumann¿s optimal solution result for two-person zero-sum games called an equilibrium solution. An equilibrium solution is a set of mixed strategies, one for each player, such that each player has no reason to deviate from that strategy, assuming all the other players stick to their equilibrium strategy. We then have the important generalization of a solution for game theory: Any many-person non-cooperative finite strategy game has at least one equilibrium solution. This result was proven by John Nash and was pictured in the movie, A Beautiful Mind. The book ( A Beautiful Mind, by Sylvia Nasar; Simon & Schuster, 1998) provides a more realistic and better-told story.

By now you have concluded that the answer to the opening question on competitive situations is "game theory." Aspects of all the cited areas have been subjected to analysis using the techniques of game theory. The web site www.gametheory.net lists about 200 fairly recent references organized into 20 categories. It is important to note, however, that for many competitive situations game theory does not really solve the problem at hand. Instead, it helps to illuminate the problem and offers us a different way of interpreting the competitive interactions and possible results. Game theory is a standard tool of analysis for professionals working in the fields of operations research, economics, finance, regulation, military, insurance, retail marketing, politics, conflict analysis, and energy, to name a few. For further information about game theory see the aforementioned web site and http://william-king.www.drexel.edu/top/eco/game/game.html.

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How game theory explains ‘irrational’ behavior

Moshe Hoffman

Apr 5, 2022

Game theory is often used to explain how rational people navigate tense negotiations and high-stakes decisions. But what does it have to do with unconscious human behavior, like what wines people enjoy or why they donate to certain charities?

In their new book “ Hidden Games: The Surprising Power of Game Theory to Explain Irrational Behavior ,” MIT Sloan research associate Erez Yoeli and research fellow Moshe Hoffman explore the less obvious ways game theory explains human behavior, from the ways athletes and scientists develop and pursue passions to why people enjoy certain pieces of art, eat certain foods, or donate to GoFundMe campaigns instead of high-impact charities.

Yoeli is a lecturer at Harvard University and the director of the Applied Cooperation Team at MIT, where he studies altruism and how to encourage people to adopt better behavior.  Hoffman is a research fellow at Max Planck Institute for Evolutionary Biology and a lecturer at Harvard University. He studies the motives that shape social behavior, preferences, and ideologies. 

Yoeli and Hoffman argue that people are bad at optimizing when they rely on their conscious minds to do so. But when people unconsciously rely on learned tastes and beliefs, they behave more optimally. The authors apply their argument, with mathematical models, to explain everything from why people like expensive watches to sex ratios in animals.

In the following excerpt, Yoeli and Hoffman explain how they use game theory to answer puzzling quirks of human and animal behavior.

What tricks do cable news networks use to misinform? Why does motivated reasoning work the way it does? Internalized racism? Why is modesty a virtue? Where does our sense of right come from? Why couldn’t the Hatfields and McCoys bury their hatchets?

In short: Why are human preferences and ideologies the way they are? Why do they work the way they do?

People tend to respond to questions like these with proximate answers, for example: Tannic wines are exceptional because they are more interesting. People develop a passion for crafts because they find it satisfying to work on discrete projects with a finite timeline, where they can quickly see the end results, or they develop a passion for research because they like the freedom to engage in long, detailed explorations of a particular topic and really become experts in it. We give out of empathy for the recipient and do so ineffectively because empathy itself is a blunt tool that’s not so sensitive to efficacy.

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While such responses are often interesting, helpful, and valid, they aren’t really answers, at least not in the sense we will be looking for in this book. Sure, tannic wines are more interesting, but what counts as interesting? And why do we even care if they’re interesting? Sure, some people develop a passion only when they quickly see the results of their handiwork while others only get excited by longer, in-depth projects, but we’re still left wondering why some are drawn in one direction while others are drawn in the opposite one, as well as why anyone develops any passion at all. Sure, empathy is a blunt tool, but why? Each of these answers raises at least as many questions as we started with!

We will, instead, attempt to give answers that are, in some sense, more ultimate. In doing so, the key tool we will be using is, of course, game theory.

Game theory is a mathematical tool kit designed to help us figure out how people, firms, countries, and so on will behave in interactive settings — when it matters not only what they do but also what others do. The tool kit has been successfully deployed to help firms design and bid in auctions (where how each bidder should bid depends on others’ bids). It is also a cornerstone of federal antitrust regulation.

At the Federal Trade Commission and U.S. Department of Justice, armies of economists spend their days evaluating proposed mergers and acquisitions with the help of a game theory model called Cournot competition (which helps them predict how prices will change, taking into account that all firms in the market will react to what the merged firm does and vice versa). A few blocks away, at the U.S. Department of State, game theory has influenced the thinking of generations of diplomats. For instance, the United States’ cold war strategy of mutual destruction and nuclear brinksmanship was reinforced by the game-theoretic analyses of Thomas Schelling (which took into account that the number of nukes the U.S. should make depended on the number that the USSR had and vice versa).

People aren’t trying to optimize when they become passionate about playing chess, develop new art movements, or give to charity. They do these things based on intuition or feel or . . . it just kinda happens without them even realizing it at all. That sounds nothing like the cold-hearted calculus involved in boardroom and situation-room decision-making.

Moreover, you might also be thinking that game theory traditionally rests on a key assumption that’s, well, let’s say questionable: the assumption that people behave optimally. That we are rational. That we have all the relevant information and use it as a computer might to maximize its benefits — doing complex calculations in the process. Maybe this assumption is decent for the crew in the boardroom, strategizing over their radio spectrum bid, but for the rest of us going about our day-to-day lives? There have been not one but two Nobel Prizes in economics for emphatically knocking that assumption down ( Daniel Kahneman’s in 2002 and Richard Thaler’s in 2017).

Even some of our motivating puzzles — willingly dying for a cause, giving to ineffective charities when effective ones stand at the ready — seem to be strong evidence in Danny and Dick’s favor.

We are going to use these two arguments to cancel each other out. Yes, people are quite often quite bad at optimizing when they are relying on their conscious minds to do the optimization. But when they are not consciously optimizing, and it is learning and evolution doing the optimization — as we will argue is often the case for tastes and beliefs — things start to look a lot more promising.

When it comes to evolution, the logic is likely already familiar. People’s tastes evolved to motivate us to act in ways that benefit us. We evolved a taste for fatty, salty, and sweet foods because that motivated us to seek out foods high in fat, salt, and calories in an environment where these were rare. We evolved an attraction to symmetrical faces, chiseled jaws, and broad hips because this motivated us to seek partners who were more healthy, successful, and fertile.

But it’s not like rap fans evolved from caveman ancestors who sat around the fire trading rhymes while modern art fans’ ancestors devoted their leisure time to abstract cave painting (“Ceci n’est pas une mammoth laineux”). Most of the tastes and beliefs we’re interested in aren’t biologically ingrained in us. They’re learned.

Excerpted from "Hidden Games: The Surprising Power of Game Theory to Explain Irrational Human Behavior" by Moshe Hoffman and Erez Yoeli. Copyright © 2022. Available from Basic Books, an imprint of Hachette Book Group, Inc.

Read next: 3 Ways to Nudge People Toward Better Behavior

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6.853: Topics in Algorithmic Game Theory

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Course Information

• Instructor: Constantinos Daskalakis Office Hours: send me an email.
• TA: Matt Weinberg Office Hours: Mondays and Wednesdays, 12pm-2pm, 32-G604.
• Lecture: Tuesdays and Thursdays 2:30-4:00, 1-134 (both are subject to change).
• Section: Mondays 5:00-6:00 in Soda 310.
• Textbook: Algorithmic Game Theory , by Noam Nisan, Tim Roughgarden, Eva Tardos, Vijay V. Vazirani (eds.), Cambridge University Press, September 2007.
• Lecture Notes: Lecture notes and/or presentations will be provided.
• Prerequisites: A course in algorithms (6.046 or equivalent), probability (6.041 or equivalent), and discrete mathematics (6.042 or equivalent).
• 35% from weekly homework problems ; these are assigned in class and posted here, and are due the next Tuesday from when they are given. Every week's problems are worth 10 points.
• 40% from the final project : this could either be a survey, or original research; students will be encouraged to relate the project to their own research interests.

Assignments

• Assignment 1, due Feb. 21. Files: Page1 , Page2 Chapter 1 Exercise 2 , Chapter 3 Exercise 6 , Chapter 4 Exercise 11 , Chapter 5 Exercise 4 partA , Chapter 5 Exercise 4 part B
• Solutions for assignment 1. Files: Solutions1

Course Outline

• Games, solution concepts, auctions.
• Min-max theorem & Linear Programming Duality;
• Game Dynamics: fictitious play;
• No-regret Learning: multiplicative weights update method;
• Multi-player Zero-sum games.
• Existence of Nash equilibria: proof via Sperner's lemma; emphasis on the combinatorial proofs of existence;
• Algorithms for computing Nash equilibria: the Lemke Howson algorithm, support enumeration algorithms, sampling methods, simplicial approximation algorithms;
• Complexity theory of total search problems and fixed points: definition of the complexity classes PLS, PPAD, PPP and relation to P, NP;
• The complexity of computing a Nash equilibrium: PPAD-completeness results;
• The complexity of pure Nash equilibria in congestion games: PLS-completeness results;
• Description method vs computational complexity in games; alternative game representations: graphical games, action graph games; emphasis on modeling the structure of the player interactions;
• Symmetries in games: algorithms for symmetric games; algorithms for anonymous games; relation to Central Limit Theorems in probability theory.
• Algorithms: Ellipsoid against hope;
• No internal-regret algorithms.
• the Arrow-Debreu existence theorem;
• Algorithms for markets with linear utility functions;
• Tatonnement;
• PPAD-hardness of markets with Leontief utility functions.
• Computational Hardness of Constant Elasticity of Substitution (CES) utility functions.
• Mechanisms with Money: second-price auction, digital goods, Vickrey-Clarke-Groves mechanism;
• Combinatorial Auctions: path auctions, frugality, inapproximability results;
• Bayesian Mechanism Design: Myerson's Theorem, prior-independent mechanisms;
• Multi-dimensional Mechanism Design.

Lectures ( scribe sheet )

• Lecture 1 (Sept 8th): Introduction to Algorithmic Game Theory: Incentives in Large Systems; Games; Nash Equilibria and their computation; the Price of Anarchy; Mechanism Design. Slides .
• Lecture 2 (Sept 13th): Two-player Zero-sum Games and Linear Programming. Notes .
• Lecture 3 (Sept 15th): Multiplayer Zero-Sum Games. Notes .
• Lecture 4 (Sept 20th): Distributed Dynamics for Zero-sum Games: Fictitious Play, Multiplicative-Weights-Updates. Notes .
• Lecture 5 (Sept 22th): Multiplicative-Weights-Updates Performance; Application of Online-Learning to Zero-Sum Games; Nash's Theorem. Notes .
• Lecture 6 (Sept 27th): Brouwer's Theorem; Visualization of Nash's Construction; Combinatorial proof of Brouwer's Theorem via Sperner's Lemma: the 2-dimensional case. ppt .
• Lecture 7 (Sept 29th): Sperner's Lemma in general dimensions: Simplicization of the hypercube; Sperner Colorings; Direction in high-dimensional Euclidean space. ppt .
• Lecture 8 (Oct 4th): Total Search Problems; FNP; Computational Problems SPERNER, BROUWER, NASH; Complexity Theory of Total Search Problems; PPAD. ppt .
• Lecture 9 (Oct 6th): Complexity Theory of Total Search Problems: PPAD, PPA, PPP, PLS; PPAD-completeness of SPERNER. ppt .
• Lecture 10 (Oct 13th): PPAD-Completeness of BROUWER; PPAD-Completeness of Nash Equilibrium in Graphical Games. ppt .
• Lecture 11 (Oct 18th): PPAD-completeness of 2-Player Games; Algorithms for Nash equilibrium: Simplicial Approximation, Support Enumeration, Lipton-Markakis-Mehta. ppt .
• Lecture 12 (Oct 20th): Symmetric Games; Lemke-Howson; Complexity of Approximating a Nash equilibrium. ppt .
• Lecture 13 (Oct 25th): Algorithms for Special Classes of 2-player and graphical games; Multi-player zero-sum games; Anonymous games. The Total Variation Distance bound. Proper Central Limit Theorems and their application to anonymous games. ppt .
• Lecture 14 (Oct 27th): Adam Smith-Augustin Cournot-Leon Walras. The Exchange Market Model. Walrasian Equilibria. The Arrow-Debreu Theorem. CES utilities. Fisher's Model. ppt .
• Lecture 15 (Nov 1st): The Eisenberg-Gale Program. Complexity of the Exchange Model. Gross-Substitutability. Weak-Axiom of Revealed Preferences (WARP). ppt .
• Lecture 16 (Nov 3rd): Exchange Economies with Gross-Substitutability: Centralized Computation (WARP as a Separation Oracle) and Distributed Computation (via Tatonnement). Convex Programs for CES Exchange Economies. ppt ; notes .
• Lecture 17 (Nov 8th): Introduction to Mechanism Design. Vickrey Auction. Mechanisms without Payment. Incentive Compatibility. Gibbard-Satterthwaite Theorem. notes .
• Lecture 18 (Nov 10th): Arrow's Impossibility Theorem. see here notes .-->
• Lecture 19 (Nov 15th): Proof of the Gibbard-Satterthwaite Theorem. see here notes .-->
• Lecture 20 (Nov 17th): Vickrey-Clarke-Groves Mechanisms. see here notes .-->
• Lecture 21 (Nov 17th): VCG Examples. The Revelation Principle. ppt .
• Lecture 22 (Nov 19th): Characterization of Incentive Compatible Mechanisms: Direct Characterization, Weak Monotonicity. Characterization of Implementable Social Choice Functions: Roberts Theorem. Bayesian Mechanisms; Bayes-Nash Implementation. First Price Auction. Revenue Equivalence Theorem. ppt .
• Lecture 23 (Dec 1st): Myerson's Revenue Optimal Auction. my notes . Also: Hartline's Notes .
• Lecture 24 (Dec 6th): Examples of Myerson's Auction. Bulow-Klemperer. Prior-Free Revenue Maximization. Competitive Analysis. Matt's Slides .
• Lecture 25 (Dec 8th): Price of Anarchy. Roughgarden-Tardos Paper .
• Lecture 26 (Dec 13th): Project Presentations.

Online Resources

• Topics in Algorithmic Game Theory
• Algorithmic Game Theory by Eva Tardos
• Topics in Algorithmic Game Theory by Tim Roughgarden and Jason Hartline
• Algorithmic Mechanism Design by Jason Hartline

Topics in Game Theory

• January 2011
• Publisher: Il Gabbiano
• ISBN: 978-88-96293-16-4

• University of California, Riverside

• Kore University of Enna

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