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What is Game Theory: Strategic Decision Making Guide

Discover what is Game Theory and its real-world applications in economics, business, and politics. Learn how strategic thinking shapes decision-making processes

What is Game Theory

Game theory is a powerful tool for understanding strategic decision-making. It looks at how individuals, firms, and other entities make decisions when their actions affect each other’s outcomes. It considers their own interests and what others might do next1.

Game theory is used in many fields, including economics, business, psychology, politics, and biology1.

The origins of game theory go back to 1944. Austrian economist Oskar Morgenstern and mathematician John von Neumann published “Theory of Games and Economic Behavior”. Since then, 12 leading economists and scientists have won the Nobel Prize in Economic Sciences for their work in game theory23.

At the heart of game theory is the Nash equilibrium, named after Nobel laureate John Nash2. It’s an outcome where no player can get a better payoff by changing their strategy, assuming others’ strategies stay the same12. This concept is key for understanding competitive behaviors and predicting outcomes in many fields13.

Game theory looks at different types of games. These include cooperative and non-cooperative games, zero-sum and non-zero-sum games, and situations where everyone moves at the same time1. These game types help model various strategic interactions. From price competition between firms to social dilemmas like the prisoner’s dilemma, game theory helps us understand and predict these scenarios13.

By understanding these game structures and applying game-theoretic principles, decision-makers can improve their strategies. They can make better choices in complex, competitive environments.

Key Takeaways

  • Game theory studies strategic decision-making and competitive interactions between players
  • It has applications in economics, business, psychology, politics, and biology
  • Nash equilibrium is a core concept where no player can improve their payoff by changing strategies unilaterally
  • Game theory encompasses cooperative and non-cooperative games, zero-sum and non-zero-sum games, and simultaneous move situations
  • It helps analyze competitive behaviors, predict outcomes, and optimize strategies in various scenarios

Introduction to Game Theory

Game theory is a branch of math that explores strategic decision-making. It looks at how players interact and influence each other’s results4. By understanding these interactions, game theory helps us make better choices.

The history of game theory goes back to the 16th and 17th centuries. Mathematicians like Cardano, Pascal, and Huygens studied games of chance4. But it wasn’t until the 20th century that John von Neumann, Oskar Morgenstern, and John Nash made it a distinct field45. Their work introduced key ideas like the Nash equilibrium, used in many fields5.

Definition of Game Theory

Game theory studies how choices lead to outcomes based on preferences4. It covers games where one wins and the other loses, and games where both can win or lose4. It uses the axiomatic theory of expected utility to analyze decisions under uncertainty4.

Importance of Game Theory in Decision Making

Game theory is crucial for making rational decisions. It helps us understand strategic interactions, allowing us to make better choices4. It’s used in many areas, like business and diplomacy, to solve complex problems5.

It teaches us about dominant strategies and Nash equilibrium. These ideas are applied in many industries, from sports to international trade5. By using game theory, we can make more informed decisions, leading to better outcomes.

History and Development of Game Theory

Game theory, the study of strategic decision-making, has a rich history. It started in the 1940s with mathematician John von Neumann and economist Oskar Morgenstern6. Their book, “Theory of Games and Economic Behavior,” introduced rational players and conflicting interests6.

Von Neumann founded game theory, starting at a young age. By 26, he had published 32 papers7. John Forbes Nash Jr. then made big contributions in the 1950s, proving equilibrium in every game7. His work expanded on non-cooperative game theory7.

Key Contributors to Game Theory

Many have shaped game theory over time. Besides von Neumann, Morgenstern, and Nash, others include:

  • Reinhard Selten
  • John Harsanyi
  • Lloyd Shapley
  • Robert Aumann

John Nash, Reinhard Selten, and John Harsanyi won the Nobel Prize in 1994 for their work on non-cooperative games7.

Evolution of Game Theory over Time

Game theory has grown through stages, each with its own focus. The early version, by von Neumann and Morgenstern, used utility functions6. But, studies like the Allais paradox showed problems with these functions6.

Now, game theory focuses on the Nash player, who aims for a Nash equilibrium6. The latest stage, new game theory, considers players with limited knowledge6.

Stage Key Assumptions Key Contributors
Classical Game Theory Rational players, von Neumann-Morgenstern utility functions von Neumann, Morgenstern
Modern Game Theory Nash player, coordination to achieve Nash equilibrium John Nash
New Game Theory Harsanyi player, limited knowledge about other players John Harsanyi

Game theory keeps growing, adding insights from psychology and biology. This leads to evolutionary game theory. It looks at how strategies change over time in groups, offering a new view on decision-making.

Basic Concepts and Terminology

To understand game theory, you need to know about players, strategies, and payoffs. Players make choices in a game. The game’s outcome depends on these choices, and each player gets a payoff8.

Games fall into two types: zero-sum and non-zero-sum. Zero-sum games mean one player wins, and another loses. The total payoff is always zero. Non-zero-sum games allow for both wins and losses, where players’ interests can align9.

Cooperative and Non-Cooperative Games

Game theory also talks about cooperative and non-cooperative games. Cooperative games involve players working together to reach a goal. Non-cooperative games are about players making their own decisions without agreements9.

Non-cooperative games are shown in strategic form or normal form. This form is a matrix of payoffs for each strategy combination. It helps find Nash equilibria, where no player can get a better payoff alone8.

Knowing these basics is key to using game theory in fields like economics and business. It helps us understand decision-making and find the best outcomes.

Nash Equilibrium and its Significance

In game theory, Nash equilibrium is key for making smart decisions and finding the best results10. John Nash, an American mathematician, introduced it. He won the Nobel Prize in Economics in 1994 for his work. Nash equilibrium finds the best solutions in games where players don’t work together11.

The Nash existence theorem says every game has at least one Nash equilibrium12.

Nash equilibrium means each player knows what others will do and picks the best strategy12. It shows that changing actions won’t help if others don’t change10. This idea is vital for understanding how people make decisions in strategic situations11.

The prisoner’s dilemma shows Nash equilibrium in action12. It’s a classic example of how Nash equilibrium works10. It helps find the best strategies in situations like companies deciding on ads11.

But, Nash equilibrium might not always lead to the best outcome10. Games can have more than one Nash equilibrium, especially when players make decisions quickly11. Also, knowing the opponent’s strategies is needed, which can be hard in real life12.

Nash equilibrium is important not just in game theory but in many fields like social sciences and economics10. AI uses game theory, including Nash equilibrium, to improve how different programs interact12. By understanding Nash equilibrium, people can make better decisions in complex situations.

Dominant Strategies and Equilibrium

In game theory, dominant strategies and equilibrium are key. A dominant strategy is the best move for a player, no matter what others do13. When everyone has a dominant strategy, we reach a unique Nash equilibrium, called the dominant strategy equilibrium.

Nash equilibrium, introduced by John Forbes Nash, Jr. in 1950 and 1951, is a game theory cornerstone14. His work, made famous by “A Beautiful Mind” in 2001, shows the need to think about all players’ strategies14.

Game theory has four outcomes: strictly dominant, weakly dominant, equivalent, and intransitive13. A strictly dominant outcome gives one player a clear win. A weakly dominant outcome means one player wins but not as strongly against some strategies13. An equivalent outcome, like the prisoner’s dilemma, happens when both players get the same result, which is fair for both13.

Prisoner’s Dilemma and its Implications

The prisoner’s dilemma is a classic example of how dominant strategies can lead to a bad outcome. Two suspects are interrogated separately and can choose to confess or stay silent. The best strategy for both is to confess, which reduces their jail time1413. Yet, this outcome is worse than if they had both stayed silent.

Suspect 2 Confesses Suspect 2 Remains Silent
Suspect 1 Confesses 5 years each 0 years, 10 years
Suspect 1 Remains Silent 10 years, 0 years 1 year each

The prisoner’s dilemma shows the conflict between individual gain and the best outcome for all. This is known as pareto optimality. It shows how seeking the best strategy can lead to a bad outcome for everyone.

The Nash equilibrium is an optimal stable state where no player has an incentive to change their strategy, taking all factors into account.

Game theory is used in many areas, like economics, business, and psychology. It helps players in markets, military strategists, managers, and even game players make better decisions13. Knowing about dominant strategies and equilibrium helps us make smart choices and guess what others will do.

Mixed Strategies and Randomization

In game theory, players use mixed strategies. This means they choose actions based on a probability, unlike pure strategies that pick one action15. This random choice makes it hard for opponents to guess their next move, similar to how soccer goalkeepers dodge in penalty kicks16.

mixed strategy equilibrium

Concept of Mixed Strategies

A mixed strategy gives a chance to each pure strategy. It lets players randomly pick a strategy and figure out the expected payoff15. This idea is key in real life, like in military battles where armies surprise each other with random attacks16. For example, in rock, paper, scissors, playing each action equally is a mixed strategy equilibrium17.

Calculating Mixed Strategy Equilibria

John Forbes Nash showed that every finite game has an equilibrium. This includes mixed strategy Nash equilibria, where at least one player uses a mixed strategy15. To find these equilibria, players need to figure out the probability that makes their opponent unsure of their choice. For example, in the battle of the sexes game, the Man will randomize his choice if the Woman goes to the Ballet ¾ of the time and to the Baseball game ¼ of the time17.

Many real-world examples use mixed strategies. Businesses randomize prices or products to keep their market share16. Prey species use random escape patterns to avoid predators16. Even in science, randomized trials use mixed strategies to ensure fair treatment and valid results16. By understanding mixed strategies, game theory helps in making strategic decisions in many areas.

What is Game Theory: An In-Depth Look

Game theory is a way to study how people make strategic decisions. It’s part of Rational Choice Theory18. Since the 1940s, it has grown a lot, thanks to people like John von Neumann19.

Mathematical Foundations of Game Theory

Game theory uses math from probability, optimization, and combinatorics. A game has players, strategies, and payoffs18. It looks at how rational decisions are made based on what we want and what might happen18.

Games between two people can be shown with matrices. Each spot in the matrix shows what each player gets from their choices18. Players rank outcomes based on how good they think they are18.

Assumptions and Limitations of Game Theory

Game theory assumes players are rational and know the game well. But, real people might not always act this way. They might not have all the information or make choices based on more than just self-interest.

“Not all zero-sum games are fair, but most two-person zero-sum parlor games are fair games.”20

There are two main parts of game theory. Non-cooperative games are about strategies without enforcement. Cooperative games allow for agreements that can be legally enforced18. John Nash showed how to find stable strategies for everyone, making sure no one changes if others stick to their plan20.

Even with its flaws, game theory is used in many areas. It helps in fields like operations research, economics, and even politics20. It’s a key tool for analyzing competitive situations20.

Game Theory in Economics and Business

Game theory is key for studying strategic moves in economics and business. It helps us see how people and companies make choices that impact each other21. It’s so important that 11 game theorists have won the Nobel Memorial Prize in Economic Sciences22.

Oligopoly Markets and Strategic Interactions

Oligopoly markets have a few big players, leading to complex strategies. Companies think about what their rivals might do when making decisions22. For instance, drug companies use game theory to figure out when to introduce new products22.

Pricing Strategies and Competition

Game theory is vital for setting prices and competing in markets. Companies use it to guess what their competitors will do and set their prices accordingly. The Nash equilibrium, named after John Nash, helps find the best choices for everyone involved2223.

But game theory also shows that what’s best for one might not be best for all, like in the prisoners’ dilemma23. This shows how cooperation and betrayal can happen in strategic situations21.

Auction Theory and Mechanism Design

Auction theory is a part of game theory that deals with designing auctions. It looks at how different auction rules affect bidders and the outcomes. Game theory helps create auctions that make more money, are efficient, and prevent cheating.

Game theory also talks about using mixed strategies, threats, promises, bargaining, and hiding or revealing information23. Companies can use these to outdo their competitors, like Polaroid did against Kodak23.

Even though game theory is very useful, it has its limits. It assumes people act rationally, which isn’t always true21. Still, it’s a crucial tool for economists and business leaders to understand game theory in business and navigate complex markets.

Applications of Game Theory in Political Science

Game theory is key in political science, helping us understand voting behavior, forming coalitions, and international relations. It models how political parties, candidates, and countries interact. This helps predict outcomes and guide decisions in complex political situations24.

The Prisoner’s Dilemma is a classic example of game theory in politics. It shows how collective decisions are made24. The model assumes rational actors, no communication, and the goal of getting the most utility24. It shows that confessing is the best strategy for both, leading to a stable outcome where no one changes their mind24.

Game theory helps us understand cooperation on big issues like arms control and environmental pollution24. But, there are concerns about its assumptions, like rationality and meaningful payoffs24.

In international relations, misunderstandings and distrust can lead to violence and war, as Alexander Wolitzky’s research shows25. Wolitzky, an economist at MIT, has worked on applying game theory to war, labor, networks, and technology25.

“Game theory provides a powerful framework for understanding strategic interactions in political science, from voting behavior to international negotiations.”

Despite its flaws, game theory is still useful for political scientists. It offers a structured way to study complex political negotiations and decision-making. As research grows, game theory will keep helping us understand politics and make better policies.

If you want to learn more about game theory in political science, there are many resources available. Articles and websites offer deeper insights into this interesting field24.

Game Theory in Psychology and Behavioral Economics

Game theory has made its mark in psychology and behavioral economics. It sheds light on how people make decisions. Behavioral game theory looks at emotions, biases, and heuristics in decision-making. It knows that choices don’t always follow what’s best for us26.

The roots of behavioral game theory go back to Allais in 1953 and Ellsberg in 1961. They introduced paradoxes that questioned traditional game theory26. In the 1970s, Tversky and Kahneman added regret theory and prospect theory. These models included psychological factors in decision-making26. Over the last three decades, it has become a key area in developmental research. It uses machine learning to better understand behavior in games26.

Bounded Rationality and Cognitive Limitations

Bounded rationality is a key concept in behavioral game theory. It recognizes that people have limits in their thinking. Unlike traditional game theory, which assumes rationality, behavioral game theory sees that people don’t always make the best choices26. The Prisoner’s Dilemma is a famous example of this. It shows how decisions in a game are connected2728.

Social Preferences and Fairness Considerations

Behavioral game theory also looks at social preferences like fairness and equity. Ultimatum games, for example, study how emotions affect decisions and the importance of trust26. Common resource games look at cooperation and what people find desirable26. Games in behavioral game theory help us understand social preferences. For instance, ultimatum games show negative reciprocity26.

Game theory is used in many fields, including psychology, evolution, war, politics, and business27. It helps people make the best decisions in a competitive world28. Staying informed about current events helps us understand decision-making in real life.

Game Description
Ultimatum Game Two players in a take-it-or-leave-it bargaining game27
Volunteer’s Dilemma Situations where someone must undertake a task for the benefit of all27
Centipede Game Extensive-form game where players take turns deciding how to split a pot of money27

Behavioral game theory adds psychological factors and social preferences to our understanding of decision-making. It challenges the idea of perfect rationality and self-interest. It gives us valuable insights into human behavior and how we interact with each other.

Evolutionary Game Theory and Biology

Evolutionary game theory is where biology meets math. It looks at how living things adapt and change in groups. It started with R. A. Fisher’s work on mammals’ sex ratios29. John Maynard Smith and George R. Price made it a key part of biology in 197330.

This theory is different from regular game theory. It focuses on how strategies change in a group, not just individual choices30.

Maynard Smith introduced the idea of evolutionarily stable strategies (ESS) in 197229. An ESS is a strategy that stays in a group if most members have it31. It’s stable because invaders with other strategies will lose over time31.

Evolutionary game theory helps explain many biological behaviors. For example, it shows why animals often fight in a ritual way instead of a real fight30. This leads to a mix of aggressive and passive behaviors in a group30.

Other examples include the war of attrition and the prisoner’s dilemma. Each scenario has its own strategies and math30.

Fitness is key in evolutionary game theory. It decides if a strategy will stick around in a group31. The fitter the genes, the more offspring they’ll have31. In these games, winning means being able to reproduce more30.

Game Scenario Competing Strategies Outcome
Hawk-Dove Aggressive (Hawk) vs. Passive (Dove) Stable mix of strategies
War of Attrition Persist vs. Concede Evolutionary stable strategy
Prisoner’s Dilemma Cooperate vs. Defect Defection dominates

Evolutionary game theory helps us understand many biological phenomena. It’s also caught the attention of economists and sociologists2930. As research grows, it will give us more insights into how living things adapt and change.

Limitations and Criticisms of Game Theory

Game theory is useful for making strategic decisions, but it has its flaws. It assumes players are rational and have all the information, which isn’t always true. Studies show that kids start to think more selfishly as they get older, showing how hard it is to apply game theory in real life32.

Game theory can be hard to use because it’s mathematically complex. It focuses on finding a stable point, but real-world situations are often changing and unpredictable. Achieving a stable point in real life is hard because of communication issues and changing strategies33.

Assumptions of Rationality and Perfect Information

One big problem with game theory is its assumption that people always make rational choices. But, people are often driven by emotions and biases, not just logic. In experiments, people are sometimes tricked into making certain choices, which makes game theory’s predictions less reliable32.

Challenges in Real-World Applications

Using game theory in real life is tough because of the complexity of human interactions. The theory might not work well when people act independently or have loose connections. It also needs a lot of data, which can be hard to get, making it hard to apply accurately33.

game theory limitations

The prisoner’s dilemma shows how game theory assumes players always choose the best strategy. But, experiments show that sometimes cooperating, even if it means losing, can be better in the long run32. This raises questions about the wisdom of always choosing the best strategy, especially if it might lead to negative consequences32.

Alternative Approaches and Extensions

To fix game theory’s problems, new ideas have been developed. Bounded rationality considers how people’s brains limit their choices. Evolutionary game theory looks at how strategies change over time. Behavioral game theory uses psychology and economics to understand human behavior better.

Approach Key Features
Bounded Rationality Accounts for cognitive limitations and satisficing behavior
Evolutionary Game Theory Incorporates dynamic and adaptive aspects of strategic interactions
Behavioral Game Theory Integrates insights from psychology and behavioral economics

Despite its flaws, game theory is still useful for studying strategic decisions. By understanding its criticisms and limitations, we can use it better and find new ways to tackle real-world challenges.

Game Theory in Practice: Real-World Examples

Game theory is a way to make smart choices in many areas. It’s used in business, international relations, and managing resources. It shows how useful this tool can be in real life.

In business, game theory helps make big decisions. Companies use it to figure out prices, when to enter markets, and even if to merge. By knowing what others might do, businesses can make the best choices for themselves34.

Strategic Decisions in Business and Management

Game theory helps with economic models and pricing strategies34. For example, in markets with a few big players, it predicts how they’ll react to each other. This helps businesses plan their moves carefully.

International Relations and Conflict Resolution

In international relations, game theory is a big help. It analyzes conflicts and negotiations between countries. It gives insights into how different countries might act, helping find ways to solve problems.

The US uses game theory in airport security and port patrols34. Singapore applies it to its coastguard and Civil Defense Force34. These examples show how game theory improves national security and uses resources wisely.

Environmental and Resource Management

Game theory also helps with environmental issues. National parks and wildlife reserves use it to fight poaching34. The World Wide Fund for Nature (WWF) uses it to protect animals and manage resources34.

It also tackles the “tragedy of the commons” problem. Game theory designs ways to keep resources safe by encouraging cooperation. This way, resources can be used without being overused.

Game theory gets even better with technology like machine learning and AI. These tools use data to predict what others might do. This helps make better decisions in many fields, from security to managing resources34.

Future Directions and Research in Game Theory

Game theory research is growing and reaching into new fields like economics, computer science, and biology. Algorithmic game theory is a new area that combines game theory and computer science. It focuses on creating efficient algorithms for solving complex problems35. For example, it has helped in making ride-sharing platforms more efficient35.

Behavioral game theory adds psychology to game models. It tries to understand how humans make decisions, like in the Ultimatum Game35. Evolutionary game theory links biology and economics, studying how strategies evolve in populations, like in birds35.

Network games study strategic decisions in connected networks. They look at how network structure affects things like technology adoption35. Dynamic games, which involve changing strategies over time, are also important, especially in climate change negotiations35.

Multi-agent reinforcement learning is another exciting area. It helps agents learn from rewards and punishments, like in optimizing traffic flow in self-driving cars35. Fair division problems, like sharing COVID-19 vaccines, are also being studied35.

Since the 1950s, game theory has seen a lot of books and articles. It has many specializations, like cooperative and noncooperative theories36. Researchers have explored topics like voting theory and mechanism design36.

Some areas of game theory rely more on data, like in oligopoly theory and evolutionary game theory36. The Prisoners’ Dilemma has inspired thousands of studies, showing the wide scope of game theory36.

Thanks to algorithms, we can now solve complex games like two-player zero-sum games with 10⁸ states37. But games like two-player no-limit Texas hold’em, with 10¹⁶⁵ states, are still hard to solve37. Over the last decade, new techniques have helped agents play these games better37.

Computing Nash equilibria in games with more than two players is very hard37. Other concepts, like subgame perfect equilibrium, are even harder to compute37.

Despite the challenges, Nash equilibrium-based agents have done well in games like 3-player Kuhn poker37. Algorithms can find close approximations of Nash equilibrium strategies in three-player Texas hold’em tournaments, but convergence is not guaranteed37.

Game theory is growing and finding new uses in many fields. Empirical studies and experimental game theory are key in testing theories and studying real-world decisions. The future of game theory research will focus on more complex models that include behavioral factors and dynamic interactions. This will lead to new insights and innovations in strategic decision-making.

Conclusion

Game theory is a key tool for understanding strategic decision-making and how rational agents interact. It has shown its worth in many fields. With 70% of articles on its use and an average of 23 citations per piece38, its value is clear. Its math roots have been explored in many studies, especially in 201138.

Game theory is used in economics, business, political science, psychology, and biology. It helps us understand social dilemmas, like the prisoner’s dilemma. Here, acting rationally can lead to bad results for everyone39.

By knowing this, we can make better choices when working with others39. The field has two main parts: cooperative and noncooperative game theory40. Each part gives a different view on how we interact strategically.

Even with its flaws, game theory is crucial for those who analyze and make decisions in complex situations. As it grows, with contributions from experts like Zhukovskiy, V.I., Podinovskii, V.V., and Kudryavtsev, K.N38, it will help us understand more complex issues. This will make it even more important for making strategic decisions.

FAQ

What is game theory and why is it important for decision-making?

Game theory is a branch of math that studies how people make decisions in competitive situations. It helps us understand what others might do and plan our moves accordingly. This is key in many fields like economics, business, and politics.

What are the key concepts and terminology in game theory?

In game theory, we talk about players, strategies, and payoffs. Games can be zero-sum, where one wins and the other loses, or non-zero-sum, where both can gain or lose. It also looks at cooperative and non-cooperative games.

What is Nash equilibrium and why is it significant in game theory?

Nash equilibrium is a key idea in game theory. It’s when no player can get a better payoff by changing their strategy alone. It helps predict likely outcomes, but might not always be the best outcome.

How does game theory apply to economics and business?

Game theory helps businesses make smart decisions in competitive markets. It models oligopoly markets and guides pricing and market entry strategies. It’s also used in auction theory and designing mechanisms.

What is behavioral game theory and how does it differ from traditional game theory?

Behavioral game theory looks at how psychology and economics affect decision-making. It recognizes that people are not always perfectly rational. It aims to create more realistic models of human behavior in strategic situations.

What are the limitations and criticisms of game theory?

Critics say game theory assumes players are perfectly rational and have all the information. It’s also complex and might overlook real-world dynamics. New approaches like bounded rationality and evolutionary game theory try to address these issues.

What are some real-world examples of game theory applications?

Game theory is used in business, international relations, and environmental management. In business, it helps with pricing and market strategies. In international relations, it analyzes conflicts and cooperation. It’s also used in managing environmental resources.

What are the future directions and research areas in game theory?

Game theory is evolving, with a focus on more realistic models. Research includes behavioral factors, incomplete information, and dynamic interactions. Areas like algorithmic game theory and empirical studies are also growing.

Source Links

More Articles

  1. Game Theory: A Comprehensive Guide – https://www.investopedia.com/terms/g/gametheory.asp
  2. Master Strategic Decision-Making with Game Theory: A Beginner’s Guide – https://www.learnsignal.com/blog/game-theory-strategic-decision-making-business/
  3. How Game Theory Strategy Improves Decision-Making – https://www.investopedia.com/articles/investing/111113/advanced-game-theory-strategies-decisionmaking.asp
  4. Game theory – https://en.wikipedia.org/wiki/Game_theory
  5. Game Theory Explained | American Experience | PBS – https://www.pbs.org/wgbh/americanexperience/features/nash-game/
  6. Gameth1.PDF – https://law.yale.edu/sites/default/files/documents/pdf/holler.pdf
  7. History of Game Theory – https://christosaioannou.com/History of Game Theory.pdf
  8. PDF – https://faculty.sites.iastate.edu/tesfatsi/files/inline-files/GameDef.pdf
  9. Game Theory: the Basic Concepts – https://gsme.sharif.edu/~g.k.haddad/uploads/pdfs/game-theory-the-basic-concepts-5e984646e4218319461927.pdf
  10. Nash Equilibrium: How It Works in Game Theory, Examples, Plus Prisoner’s Dilemma – https://www.investopedia.com/terms/n/nash-equilibrium.asp
  11. Nash Equilibrium – https://corporatefinanceinstitute.com/resources/economics/nash-equilibrium-game-theory/
  12. Nash Equilibrium: An Introduction | Built In – https://builtin.com/data-science/nash-equilibrium
  13. Dominant Strategy – https://corporatefinanceinstitute.com/resources/career-map/sell-side/capital-markets/dominant-strategy/
  14. Comparing Dominant Strategy Solution vs. Nash Equilibrium Solution – https://www.investopedia.com/ask/answers/071515/what-difference-between-dominant-strategy-solution-and-nash-equilibrium-solution.asp
  15. Strategy (game theory) – https://en.wikipedia.org/wiki/Strategy_(game_theory)
  16. Mixed Strategies and Randomization | Game Theory Class Notes – https://library.fiveable.me/game-theory/unit-5
  17. Mixed Strategies – https://saylordotorg.github.io/text_introduction-to-economic-analysis/s17-03-mixed-strategies.html
  18. Game Theory | Internet Encyclopedia of Philosophy – https://iep.utm.edu/game-th/
  19. Game Theory: Your Complete Guide | The Motley Fool – https://www.fool.com/terms/g/game-theory/
  20. What is game theory and what are some of its applications? – https://www.scientificamerican.com/article/what-is-game-theory-and-w/
  21. What is game theory in economics | Universidad Europea Blog – https://universidadeuropea.com/en/blog/game-theory-economics/
  22. How Is Game Theory Useful in Business? – https://www.investopedia.com/ask/answers/09/game-theory-business.asp
  23. Game Theory – Econlib – https://www.econlib.org/library/Enc/GameTheory.html
  24. Game Theory / Formal Models – https://politicalscienceguide.com/research/methods-and-analysis/game-theory-and-modelling/
  25. What game theory tells us about politics and society – https://news.mit.edu/2018/game-theory-politics-alexander-wolitzky-1204
  26. Behavioral game theory – https://en.wikipedia.org/wiki/Behavioral_game_theory
  27. Game Theory in Psychology: Examples and Strategies – https://www.simplypsychology.org/game-theory.html
  28. What Is Game Theory In Behavioral Economics? – https://www.superprof.com/blog/behavioral-economics-decisions/
  29. Evolutionary Game Theory – https://plato.stanford.edu/entries/game-evolutionary/
  30. Evolutionary game theory – https://en.wikipedia.org/wiki/Evolutionary_game_theory
  31. net – https://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch07.pdf
  32. How Game Theory Works – https://science.howstuffworks.com/game-theory7.htm
  33. What are the limitations of game theory in real-world economic analysis? – https://www.linkedin.com/advice/1/what-limitations-game-theory-real-world-economic-lr9ic
  34. Real-World Decision-Making Using Game Theory – https://cityperspectives.smu.edu.sg/article/real-world-decision-making-using-game-theory-0
  35. Future Directions In Game Theory Research – FasterCapital – https://fastercapital.com/topics/future-directions-in-game-theory-research.html
  36. The Present and Future of Game Theory – https://elischolar.library.yale.edu/cgi/viewcontent.cgi?article=3152&context=cowles-discussion-paper-series
  37. Most important open problems in computational game theory – https://medium.com/ganzfried-gleans/most-important-open-problems-in-computational-game-theory-c08ddfa92fab
  38. Conclusion – https://link.springer.com/chapter/10.1007/978-3-030-25546-6_6
  39. Game Theory: Understanding Strategic Interaction in Everyday Life – https://www.linkedin.com/pulse/game-theory-understanding-strategic-interaction-life-mansoor-ph-d-
  40. What is Game Theory? – http://www.dklevine.com/general/whatis.htm
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