What is Game theory: Definition and 83 Discussions

Game theory is the study of mathematical models of strategic interaction among rational decision-makers. It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. In the 21st century, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.
Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.
Game theory was developed extensively in the 1950s by many scholars. It was explicitly applied to evolution in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. As of 2014, with the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole, eleven game theorists have won the economics Nobel Prize. John Maynard Smith was awarded the Crafoord Prize for his application of evolutionary game theory.

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  1. Fra

    A Game theory, quantum physics and the Bell inequality (paper)

    The reason for highlighting this paper is to highlight (and exemplify by how different researcher think about this) a new "perspective" to understanding the different between "ignorance of the physicists" which is reallly what Bell assumptions imples. And "ignorance of they players", which is...
  2. M

    Game theory: competitive auction for the money in a chest

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  3. M

    Game theory: dice game to aim for sum no greater than 9

    Hi, I was attempting the following question and would appreciate any insight on how others would approach this game theory/probability-type question. Question: You have been chosen to play a game involving a 6-sided die. You get to roll the die once, see the result, and then may choose to...
  4. Leo Liu

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  5. Frabjous

    Prob/Stats Two-Person Game Theory by Rapoport

    From a retiree’s stack of left behind books, I picked up a copy of Two-Person Game Theory (1966) by Rapoport. Is this an acceptable first (and possibly only) reading on the topic?
  6. S

    I Who would win a perfect game of chess?

    While chess hasn't been solved yet, other games have. For example, I know that in in some games, like connect four, if both players play perfectly, the player who goes first will always win. On the other hand, some games, like tic tac toe, a perfect game will result in a draw; in fact, I...
  7. Posty McPostface

    Can external factors enforce ethical outcomes in the prisoner's dilemma?

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  8. Posty McPostface

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  9. E

    About the strategy of reducing the total suffering in a queue

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  10. P

    Can human traits be formalized?

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  11. N

    I Stochastic Minimax partition problem card game

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  12. V

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  13. S

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  14. 1

    Where do physics and game theory meet?

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  15. W

    I Game Theory: Strategy for game with non-square payoff matrix

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  16. B

    Is Game Theory a Self-Contained Subject?

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  17. C

    Mathematical Game Theory (Von Neumann Morganstern Utility)

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  18. nomadreid

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  19. D

    Game Theory Q: Proving Player Win w/Axiom of Choice

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  20. M

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  21. C

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  22. C

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  23. R

    Help with shared constraints (game theory)

    I've been struggling with shared constraints problems for a while now. I have a game between two players with a shared constraint. For example, player 1 is trying to maximize f(x,y) by choosing x, and player 2 is trying to maximize g(x,y) by choosing y. The players are competing in a...
  24. D

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  25. A

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  26. B

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  27. W

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  28. I

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  29. A

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  30. Einj

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  31. M

    Game theory: Optimal Strategy. Need help with a system of equations.

    This problem is not schoolwork, it is from "The Mathematics of Poker". I have three equations based off a 3x3 Rock, Paper, Scissors payout table where winning with scissors is given a +2 payout instead of +1. Homework Statement Find the solution to the system of equations Homework...
  32. K

    Two-person sequential game, game theory

    Hello! Here is my solution. Is it right? Thank you! Homework Statement An investor, whom we will refer to as player I, is considering bidding for a company called Fortune F. Currently, the shares of F are valued at $100. If I can take over the company it is known that F would be worth $110...
  33. W

    What Are the Prerequisites for Understanding Game Theory?

    any prerequisites to cover the following Course content: The courses examines the theory of games and its applications in economics: Game trees with perfect information, NIM, combinatorial games. Backward induction. Extensive and strategic (normal) form of a game. Nash equilibrium...
  34. R

    Game Theory ( 2 player zero-sum game)

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  35. M

    Game Theory 2x2 Matrix: Finding Optimal Strategy for (-3,-4), (-7,2)

    Homework Statement {(-3,-4),(-7,2)} Find the value of the game (basically saying find x*) Homework Equations E((x,1-x), 1)=E((x,1-x),2)) The Attempt at a Solution Basically I used dot product of (x,1-x) and column 1 (-3,-7). I got 4x-7 for that, which is my E((x,1-x). Then I found the dot...
  36. P

    How to Solve Bayesian Game Equations?

    Homework Statement My Textbook gives the following example problem: Cournot Duopoly with incomplete information. The profit functions are given by: u_i = q_i(θ_¡ - q_i - q_j) Firm 1 has one type θ_1 = 1, but firm 2 has private information about its type θ_2. Firm 1 believes that...
  37. C

    Simple summation, difficult inference. (game theory)

    hi guys, new user, long time lurker. the following simple proof is proposed with the highlighted summations. you do not need to know what the proof is of to answer my question (it is that the payoff for a skew symmetric game, rock paper scissors, is zero). i need help understanding how you...
  38. R

    Game Theory Help: Solving Task Before WWII Invasion

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  39. C

    Please help me question on the game theory, thanks

    A person has a utility function defined over her wealth given by u(w)=ln(w). Her initial wealth is $2 and she faces a risky prospect in which she will lose $1 with probability 0.4 and gain $1 with probability 0.6. (i) Show that this person is risk averse by demonstrating that her utility...
  40. M

    Game Theory: Winning Moves for (20, 21, 28)

    (1 pt) We shall denote a position in three-pile Nim by (a,b,c), so that there are a chips in the first pile, b in the second, and c in the third. Given the following position in Nim, list all winning moves. As an example, if the piles are (2,2,2) then we can list all winning moves as...
  41. R

    Game Theory a problem which is a bit similar to the Impossible Puzzle

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  42. C

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  43. A

    A few basic questions about combinatorial game theory

    I am trying to teach myself the basic theory behind combinatorial game theory regarding impartial games, the solution to Nim, and the Sprague-Grundy theorem. I understand most of it, but I have a few questions about parts that are still unclear to me. 1. Why are Nim-sums computed using binary...
  44. R

    Solving Chop Games with Nim Heap Equivalent: Problem 1

    1) Problem 1 For every i; j with 1<=i; j<=8 fi nd a nim heap which is equivalent to the i x j game of Chop. CHOP Game Start with an i x j array of boxes viewed as a plank which is secured only at the lower left hand corner. Each player is a pirate, and they alternate turns. On each turn a...
  45. B

    Game theory teaches robots how to deceive

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  46. R

    Winning Strategy in a Diamond Game: Proving Player 1's Advantage

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  47. D

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  48. H

    Game Theory - A graphical solution to all 2-person n x n strategy games?

    I was not sure where to post this. It didn't seem to fit in the homework/self-study category, and I believe it is thought-provoking enough to warrant posting in the general forums. I am sorry if I am wrong. In game theory, 2-person non-zero-sum games with 2n strategies can be graphically...
  49. S

    How to introduce Game Theory to HS students without boring them

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  50. thrill3rnit3

    Is Game Theory the Perfect Summer Learning Opportunity for High Schoolers?

    Hello, I will be a rising high school senior next year, and I'm looking for something worthwhile to learn over this summer. I'm really interested in learning mathematical game theory. I was wondering on the prerequisites before learning game theory (I've done maths up to linear algebra and real...
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