File | Description | Size | Format | Access Settings | Version | |
---|---|---|---|---|---|---|
PeiT.pdf | 1.42 MB | Adobe PDF | OPEN | None |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Q&A for work
Connect and share knowledge within a single location that is structured and easy to search.
i am an ib student and need to write an extended essay on math. Basically extended essay is a 4000 word limited article which focuses on a problem, however I need some ideas to write about in my extended essay. I have a interest in game theory and real analysis, and want to write about that topic but I need a specific problem just like a prisoners dilemma. I am open to any ideas, if you have an idea that is not related to game theory, please mention and i can take into consideration but remember that i am only a high school student.
An interesting question in game theory would be the ever-elusive definition of what it means for an agent/person/player to be 'rational.'
To motivate, imagine a world with one person in it, trying to do his or her best in the face of outside forces. Within such a context, it is not unreasonable to suppose that the person either knows the true probabilities with which events may happen, or at the least has some subjective beliefs about this. In such a world then, given these beliefs about what events they are facing, it makes sense to deem a person rational if they act in such a way as to maximize their expected utility (where the expectation is taken with regard to their beliefs/the true probabilities over events).
Consider now game theory, where multiple (even just two) equally clever people are matched up against each other. Even in the simplest possible context when the payoffs/structure of the game and the rationality of both players is common knowledge (either formally or informally construed), what it means to be rational is much more difficult and elusive thing, and indeed arguments over its definition have at least implicitly been the driving force behind the small cottage industry of refinements to the basic Nash equilibrium.
If you already have a background in basic game theory, depending upon your mathematical level you might find it interesting to discuss the various motivations for Nash equilibrium versus sub-game perfect Nash equilibrium, and perhaps, depending upon your mathematical background, things such as trembling-hand perfect equilibrium or sequential equilibrium.
Not the answer you're looking for browse other questions tagged real-analysis probability game-theory ..
About this sample
Words: 1385 |
Published: Aug 1, 2022
Words: 1385 | Pages: 3 | 7 min read
Prisoner’s dilemma, philosophy and ethics.
To export a reference to this article please select a referencing style below:
Let us write you an essay from scratch
Get high-quality help
Verified writer
+ 120 experts online
By clicking “Check Writers’ Offers”, you agree to our terms of service and privacy policy . We’ll occasionally send you promo and account related email
No need to pay just yet!
1 pages / 469 words
2 pages / 820 words
2 pages / 763 words
1 pages / 485 words
Remember! This is just a sample.
You can get your custom paper by one of our expert writers.
121 writers online
Browse our vast selection of original essay samples, each expertly formatted and styled
Evolutionary game theory (EGT) is a branch of game theory that studies the dynamics of strategic interactions among individuals in a population where the strategies evolve over time. The significance of EGT lies in its ability [...]
Game theory, a mathematical tool for understanding the dynamics of strategic interactions among decision-makers, forms the foundation of our analysis. While its theoretical underpinnings rest on the assumption of rationality and [...]
I first learned about Game Theory during my Economics class, as an introduction to oligopolies and cartels. Ever since, I’ve been fascinated by the prisoner’s dilemma – how sometimes the most logical decision isn’t the option [...]
Game Theory is a groundbreaking theory which has explained various analyses in different domains of Science and Commerce. In here, strategies of Evolutionary Biology are explained in the light of Game Theory. Mathematics and [...]
Take advantage of holidays and good weather to play outdoors with children, be in contact with nature and especially share unforgettable moments together. Here you have some games to have fun in the garden, in the park or in the [...]
Algebra bears major importance throughout youth and adulthood by providing mental assistance in solving daily tasks quicker, a backbone to other school related subjects, aid in understanding the mathematical work done by others, [...]
By clicking “Send”, you agree to our Terms of service and Privacy statement . We will occasionally send you account related emails.
Where do you want us to send this sample?
By clicking “Continue”, you agree to our terms of service and privacy policy.
Be careful. This essay is not unique
This essay was donated by a student and is likely to have been used and submitted before
Download this Sample
Free samples may contain mistakes and not unique parts
Sorry, we could not paraphrase this essay. Our professional writers can rewrite it and get you a unique paper.
Please check your inbox.
We can write you a custom essay that will follow your exact instructions and meet the deadlines. Let's fix your grades together!
We use cookies to personalyze your web-site experience. By continuing we’ll assume you board with our cookie policy .
Reference Library
Collections
Study notes, videos, interactive activities and more!
Economics news, insights and enrichment
Currated collections of free resources
Browse resources by topic
Resource Selections
Currated lists of resources
Study Notes
Last updated 4 Jul 2018
When can game theory be used to good effect in A level economics essays?
You would normally use game theory at A2 level when discussing the market structure of oligopoly . But in fact there are many other instances where you might be able to apply game theory to topics contained within the A2 syllabus – this revision note tries to provide you with a few ideas!
Revision video : Game Theory (A Level Economics Revision Update 2018)
2nd October 2012
26th June 2015
12th February 2016
14th September 2016
Oligopoly - why is insulin so expensive.
14th February 2019
24th March 2020
Our subjects.
Boston House, 214 High Street, Boston Spa, West Yorkshire, LS23 6AD Tel: 01937 848885
© 2002-2024 Tutor2u Limited. Company Reg no: 04489574. VAT reg no 816865400.
One-person games.
Our editors will review what you’ve submitted and determine whether to revise the article.
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.
Papers published on a yearly basis, theory of games and economic behavior.
19,337 citations
8,276 citations
7,845 citations
7,018 citations
5,049 citations
Network information, performance.
Year | Papers |
---|---|
2025 | 1 |
2024 | 354 |
2023 | 751 |
2022 | 1,149 |
2021 | 989 |
2020 | 1,159 |
Imagine you and a friend are playing a game where your goal is to communicate secret messages to each other using only cryptic sentences. Your friend's job is to guess the secret message behind your sentences. Sometimes, you give clues directly, and other times, your friend has to guess the message by asking yes-or-no questions about the clues you've given. The challenge is that both of you want to make sure you're understanding each other correctly and agreeing on the secret message.
MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) researchers have created a similar "game" to help improve how AI understands and generates text. It is known as a “consensus game” and it involves two parts of an AI system — one part tries to generate sentences (like giving clues), and the other part tries to understand and evaluate those sentences (like guessing the secret message).
The researchers discovered that by treating this interaction as a game, where both parts of the AI work together under specific rules to agree on the right message, they could significantly improve the AI's ability to give correct and coherent answers to questions. They tested this new game-like approach on a variety of tasks, such as reading comprehension, solving math problems, and carrying on conversations, and found that it helped the AI perform better across the board.
Traditionally, large language models answer one of two ways: generating answers directly from the model (generative querying) or using the model to score a set of predefined answers (discriminative querying), which can lead to differing and sometimes incompatible results. With the generative approach, "Who is the president of the United States?" might yield a straightforward answer like "Joe Biden." However, a discriminative query could incorrectly dispute this fact when evaluating the same answer, such as "Barack Obama."
So, how do we reconcile mutually incompatible scoring procedures to achieve coherent, efficient predictions?
"Imagine a new way to help language models understand and generate text, like a game. We've developed a training-free, game-theoretic method that treats the whole process as a complex game of clues and signals, where a generator tries to send the right message to a discriminator using natural language. Instead of chess pieces, they're using words and sentences," says Athul Jacob, an MIT PhD student in electrical engineering and computer science and CSAIL affiliate. "Our way to navigate this game is finding the 'approximate equilibria,' leading to a new decoding algorithm called 'equilibrium ranking.' It's a pretty exciting demonstration of how bringing game-theoretic strategies into the mix can tackle some big challenges in making language models more reliable and consistent."
When tested across many tasks, like reading comprehension, commonsense reasoning, math problem-solving, and dialogue, the team's algorithm consistently improved how well these models performed. Using the ER algorithm with the LLaMA-7B model even outshone the results from much larger models. "Given that they are already competitive, that people have been working on it for a while, but the level of improvements we saw being able to outperform a model that's 10 times the size was a pleasant surprise," says Jacob.
"Diplomacy," a strategic board game set in pre-World War I Europe, where players negotiate alliances, betray friends, and conquer territories without the use of dice — relying purely on skill, strategy, and interpersonal manipulation — recently had a second coming. In November 2022, computer scientists, including Jacob, developed “Cicero,” an AI agent that achieves human-level capabilities in the mixed-motive seven-player game, which requires the same aforementioned skills, but with natural language. The math behind this partially inspired the Consensus Game.
While the history of AI agents long predates when OpenAI's software entered the chat in November 2022, it's well documented that they can still cosplay as your well-meaning, yet pathological friend.
The consensus game system reaches equilibrium as an agreement, ensuring accuracy and fidelity to the model's original insights. To achieve this, the method iteratively adjusts the interactions between the generative and discriminative components until they reach a consensus on an answer that accurately reflects reality and aligns with their initial beliefs. This approach effectively bridges the gap between the two querying methods.
In practice, implementing the consensus game approach to language model querying, especially for question-answering tasks, does involve significant computational challenges. For example, when using datasets like MMLU, which have thousands of questions and multiple-choice answers, the model must apply the mechanism to each query. Then, it must reach a consensus between the generative and discriminative components for every question and its possible answers.
The system did struggle with a grade school right of passage: math word problems. It couldn't generate wrong answers, which is a critical component of understanding the process of coming up with the right one.
“The last few years have seen really impressive progress in both strategic decision-making and language generation from AI systems, but we’re just starting to figure out how to put the two together. Equilibrium ranking is a first step in this direction, but I think there’s a lot we’ll be able to do to scale this up to more complex problems,” says Jacob.
An avenue of future work involves enhancing the base model by integrating the outputs of the current method. This is particularly promising since it can yield more factual and consistent answers across various tasks, including factuality and open-ended generation. The potential for such a method to significantly improve the base model's performance is high, which could result in more reliable and factual outputs from ChatGPT and similar language models that people use daily.
"Even though modern language models, such as ChatGPT and Gemini, have led to solving various tasks through chat interfaces, the statistical decoding process that generates a response from such models has remained unchanged for decades," says Google Research Scientist Ahmad Beirami, who was not involved in the work. "The proposal by the MIT researchers is an innovative game-theoretic framework for decoding from language models through solving the equilibrium of a consensus game. The significant performance gains reported in the research paper are promising, opening the door to a potential paradigm shift in language model decoding that may fuel a flurry of new applications."
Jacob wrote the paper with MIT-IBM Watson Lab researcher Yikang Shen and MIT Department of Electrical Engineering and Computer Science assistant professors Gabriele Farina and Jacob Andreas, who is also a CSAIL member. They presented their work at the International Conference on Learning Representations (ICLR) earlier this month, where it was highlighted as a "spotlight paper." The research also received a “best paper award” at the NeurIPS R0-FoMo Workshop in December 2023.
Research areas, press contact, rachel gordon, related news.
IMAGES
VIDEO
COMMENTS
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 ...
Game Theory (Revised: July 2018) These lecture notes extend some of the basic ideas in game theory that were covered in 15.010. We will begin by explaining what we mean by rational — or rationalizable — strategies. We will apply this concept to a discussion of the War of Attrition, which can turn out to be a rather complicated game.
Game Theory Behind Shop Competition. This paper covers game theory at a basic level and looks at an elementary application of game theory, the prisoner's dilemma. The paper goes on to use the example of competitive pizza shops and how game theory can help to make the best business decisions...
Relation to Psychology. Game theory is a theoretical framework that is used for the optimal decision-making of players in a strategic setting. A key characteristic of game theory is that a player's payoff is dependent on the strategy of other players. Game theory is thought to apply to any situation with two or more players where there are ...
This essay explores the various domains where applied game theory has made a substantial contribution. 1. Economics. One of the primary fields where applied game theory has been instrumental is economics, where it helps to model the actions and reactions of consumers, firms, and governments (Dixit & Nalebuff, 1991).
The paper topics in this lesson are designed to encourage students to demonstrate their knowledge of the concepts, applications, and history of game theory. The topics can be used in either essay ...
Game Theory - Free Essay Examples and Topic Ideas. Game theory is a mathematical approach to studying strategic decision-making. It involves analyzing the interactions of different players in a given situation and predicting their behavior based on their rationality and self-interest. The theory helps to explain how decisions are made in ...
Game theory is one to more complexed topics but reveals a clear understanding from different scholars. Don Ross explained that game theory is the study that interacts with the different choices of economics agents which bring forth many different outcomes with the point to the preferences of those agents, where the outcomes in question might have been intended by none of the agents (Ross, 2016).
2 pages / 725 words. Game theory is defined as the science of strategy. In decision making situations, individuals are faced with conflicting and cooperative methods of strategy against rational opponents in which different combinations of strategies result in different payouts (Dixit, Nalebluff). Payouts differ depending on the type of...
We will discuss research ideas and explore topics in game theory and more broadly in economic theory. ... We also present others' papers in the topics of interest. Every year, depending on the people around, certain topics are explored in greater detail than others. These topics were evolutionary game theory in 2000-2001, when Weibull visited ...
Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an ...
Free essay examples for your ideas about Game Theory; Essay topics examples and ideas on Game Theory; ESSAY EXAMPLES; ESSAY TOPIC; Julia Robinson Mathematician to be researched. Author Tutor Course Date Julia Robinson Julia Bowman Robinson was born in December 1919 to her parents Helen Hall Bowman and Ralph Bowers Bowman in St. Louis, Missouri ...
Mathematical Games and Strategies: An Analysis of Chess, Othello, and Poker. Abstract This research paper analyses three strategy games—Chess, Othello, and Poker—from the perspective of game theory. Mathematical modeling techniques are used to develop optimal strategies for each game to provide insights into their underlying principles and ...
PEI TING (2021-08-16). ESSAYS ON GAME THEORY. ScholarBank@NUS Repository. Abstract: This thesis consists of two parts that are commonly studied in game theory: the first part analyzes basic solution concepts, rationalizability and Nash equilibrium, in game theory by studying their distributions in random games; the second part studies a model ...
Basically extended essay is a 4000 word limited article which focuses on a problem, however I need some ideas to write about in my extended essay. I have a interest in game theory and real analysis, and want to write about that topic but I need a specific problem just like a prisoners dilemma.
This thesis contains three essays in evolutionary game theory. In the first chapter, we study the impact of switching costs on the long run outcome in 2X2 coordination games played in the circular city model of local interactions. We find that for low levels of switching costs, the risk dominant convention is the unique long run equilibrium.
Game Theory examines our interactions and decisions in social contexts through the lens of 'games'. It explores the outcomes of the different strategies available to their participants (known as either 'players' or 'agents') and looks to find the most 'rational' option, which means maximizing the payoff in terms of their own self-interest).
You would normally use game theory at A2 level when discussing the market structure of oligopoly. But in fact there are many other instances where you might be able to apply game theory to topics contained within the A2 syllabus - this revision note tries to provide you with a few ideas! Applying Game Theory in A Level Economics - revision video.
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 ...
Game theory is a research topic. Over the lifetime, 28468 publications have been published within this topic receiving 780917 citations. Popular works include Theory of Games and Economic Behavior, The Theory of Industrial Organization and more. ... Papers Topics Journals Authors Conferences Institutions Questions Citation Styles.
In November 2022, computer scientists, including Jacob, developed "Cicero," an AI agent that achieves human-level capabilities in the mixed-motive seven-player game, which requires the same aforementioned skills, but with natural language. The math behind this partially inspired the Consensus Game. While the history of AI agents long ...
A game theoretical question is how to construct a system such that the optimal strategy for the individual aligns with the optimal strategy for the collective. That would allow you to exercise some of the ideas in game theory as well as connect your study to some highly relevant global medicine. A popular write-up on the issue in general can be ...