Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/02%3A_Two-Person_Zero-Sum_Games/2.05%3A_Equilibrium_PointsIn this section, we will try to gain a greater understanding of equilibrium strategies in a game. In general, we call the pair of equilibrium strategies an equilibrium pair, while we call the specific...In this section, we will try to gain a greater understanding of equilibrium strategies in a game. In general, we call the pair of equilibrium strategies an equilibrium pair, while we call the specific payoff vector associated with an equilibrium pair an equilibrium point.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/02%3A_Two-Person_Zero-Sum_GamesIn this chapter, we will look at a specific type of two-player game. These are often the first games studied in game theory as they can be straightforward to analyze. All of our games in this chapter ...In this chapter, we will look at a specific type of two-player game. These are often the first games studied in game theory as they can be straightforward to analyze. All of our games in this chapter will have only two players. We will also focus on games in which one player's win is the other player's loss.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/04%3A_Non-Zero-Sum_Games/4.02%3A_Prisoner's_Dilemma_and_ChickenBoth Prisoner's Dilemma and Chicken are models of games where we describe the choice of strategy as “Cooperate” and “Defect”. In Prisoner's Dilemma, we think of “cooperating” as cooperating with the o...Both Prisoner's Dilemma and Chicken are models of games where we describe the choice of strategy as “Cooperate” and “Defect”. In Prisoner's Dilemma, we think of “cooperating” as cooperating with the other player, and “defecting” as turning against the other player. In Chicken, players cooperate by swerving and defect by driving straight. Using these examples, think about how these games can model other everyday interactions where you could describe your choices as cooperating and defecting.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/00%3A_Front_Matter/02%3A_InfoPageThe LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californ...The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/03%3A_Repeated_Two-Person_Zero-sum_Games/3.04%3A_Mixed_Strategies%3A_Expected_Value_SolutionIn this section, we will use the idea of expected value to find the equilibrium mixed strategies for repeated two-person zero-sum games.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/01%3A_What_is_Game_TheoryAlthough we will play many games throughout this book, our goal is to understand how rational, distrustful players would play the game. These games are meant to serve as models for situations of confl...Although we will play many games throughout this book, our goal is to understand how rational, distrustful players would play the game. These games are meant to serve as models for situations of conflict. We will explore how to “solve” games under certain assumptions about our players. As with any mathematical model, we will need to make assumptions about how our players will behave, what information they have, and the constraints of the game.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/00%3A_Front_Matter
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/zz%3A_Back_Matter/30%3A_References[2] Douglas Hofstadter, Metamagical Themas: Questing for the Essence of Mind and Pattern, Basic Books, 1985. [3] Jennifer Nordstrom, “Battles of Wits and Matters of Trust: Game Theory in Popular Cultu...[2] Douglas Hofstadter, Metamagical Themas: Questing for the Essence of Mind and Pattern, Basic Books, 1985. [3] Jennifer Nordstrom, “Battles of Wits and Matters of Trust: Game Theory in Popular Culture”, Mathematics and Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media, eds. [4] William Poundstone, Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb, Anchor Books, 1993.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)Many colleges offer courses in quantitative reasoning for all students. One model for a quantitative reasoning course is to provide students with a single cohesive topic. Ideally, such a topic can piq...Many colleges offer courses in quantitative reasoning for all students. One model for a quantitative reasoning course is to provide students with a single cohesive topic. Ideally, such a topic can pique the curiosity of students with wide ranging academic interests and limited mathematical background. This text is intended for use in such a course. This text may also be appropriate for a high school enrichment course.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/04%3A_Non-Zero-Sum_Games/4.08%3A_Popular_Culture%3A_Prisoner's_Dilemma_and_ChickenIn this section, we will look at applications of Prisoner's Dilemma and Chicken in popular culture.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/04%3A_Non-Zero-Sum_Games/4.03%3A_A_Class-Wide_ExperimentWe are going to look at a class-wide game. Each member of the class secretly chooses a single letter: “C” or “D,” standing for “cooperate” or “defect.” This will be used as your strategy choice in th...We are going to look at a class-wide game. Each member of the class secretly chooses a single letter: “C” or “D,” standing for “cooperate” or “defect.” This will be used as your strategy choice in the following game with each of the other players in the class. Here is how it works for each pair of players: if they both cooperate, they get each get 3 points. If they both defect, they each get 1 point. If one cooperates and one defects, the cooperator gets nothing, but the defector gets 5 points.
