Zero Sum Game

(noun)

The idea that if group A acquires any given resource, group B will be unable to acquire it.

Related Terms

Examples of Zero Sum Game in the following topics:

  • Conflict

    • Conflict theory relies upon the notion of a zero sum game, meaning that if group A acquires any given resource, group B will be unable to acquire it.

  • A single-variable model for the Mario Kart data

    • Interpret the coefficient for the game's condition in the model.
    • Note that cond new is a two-level categorical variable that takes value 1 when the game is new and value 0 when the game is used.
    • Examining the regression output in Table 8.3, we can see that the p-value for cond new is very close to zero, indicating there is strong evidence that the coefficient is different from zero when using this simple one-variable model.
    • Summary of a linear model for predicting auction price based on game condition.
    • Scatterplot of the total auction price against the game's condition.

  • Including and assessing many variables in a model

    • In this equation, y represents the total price, x1 indicates whether the game is new, x2 indicates whether a stock photo was used, x3 is the duration of the auction, and x4 is the number of Wii wheels included with the game.
    • We estimate the parameters β0 , β1 , ..., β4 in the same way as we did in the case of a single predictor.We select b0 , b1 , ..., b4 that minimize the sum of the squared residuals:
    • We typically use a computer to minimize the sum in Equation (8.4) and compute point estimates, as shown in the sample output in Table 8.5.
    • The estimated value of the intercept is 36.21, and one might be tempted to make some interpretation of this coefficient, such as, it is the model's predicted price when each of the variables take value zero: the game is used, the primary image is not a stock photo, the auction duration is zero days, and there are no wheels included.
    • That means the total auction price would always be zero for such an auction; the interpretation of the intercept in this setting is not insightful.

  • Probability solutions

    • Sum is greater than 1.
    • Probabilities are between 0 and 1, and they sum to 1.
    • Sum is less than 1.
    • Probabilities are between 0 and 1, and they sum to 1.
    • 2.41 A fair game has an expected value of zero: $5 × 0.46 + x × 0.54 = 0.

  • Two-Component Forces

    • An object with constant velocity has zero acceleration.
    • A motionless object still has constant (zero) velocity, so motionless objects also have zero acceleration.
    • so objects with constant velocity also have zero net external force.
    • In static systems, in which motion does not occur, the sum of the forces in all directions always equals zero.
    • A moving car for which the net x and y force components are zero

  • The Loop Rule

    • Applied to circuitry, it is implicit that the directed sum of the electrical potential differences (voltages) around any closed network is equal to zero.
    • Mathematically, Kirchhoff's loop rule can be represented as the sum of voltages in a circuit, which is equated with zero:
    • In this example, the sum of v1, v2, v3, and v4 (and v5 if it is included), is zero.
    • Kirchhoff's loop rule states that the sum of all the voltages around the loop is equal to zero: v1 + v2 + v3 - v4 = 0.
    • An example of Kirchhoff's second rule where the sum of the changes in potential around a closed loop must be zero.

  • Summing an Infinite Series

    • A series is the sum of the terms of a sequence.
    • The sequence of partial sums ${S_k}$ associated to a series $\sum_{n=0}^\infty a_n$ is defined for each k as the sum of the sequence ${a_n}$ from $a_0$ to $a_k$:
    • By definition the series $\sum_{n=0}^\infty a_n$ converges to a limit $L$ if and only if the associated sequence of partial sums  converges to $L$.
    • An easy way that an infinite series can converge is if all the $a_{n}$ are zero for sufficiently large $n$s.
    • Working out the properties of the series that converge even if infinitely many terms are non-zero is, therefore, the essence of the study of series.

  • First Condition

    • The first condition of equilibrium is that the net force in all directions must be zero.
    • This means that both the net force and the net torque on the object must be zero.
    • Here we will discuss the first condition, that of zero net force.
    • In order to achieve this conditon, the forces acting along each axis of motion must sum to zero.
    • The forces acting on him add up to zero.

  • Random variables exercises

    • (c) If the game costs $5 to play, should you play this game?
    • Here is the game he is considering playing: The game costs $2 to play.He draws a card from a deck.
    • What does this say about the riskiness of the two games?
    • (c) Expected values are the same, but the SDs differ.The SD from the game with tripled winnings/losses is larger, since the three independent games might go in different directions (e.g. could win one game and lose two games).
    • 2.41 A fair game has an expected value of zero: $5 × 0.46 + x × 0.54 = 0.Solving for x: -$4.26.

  • Partitioning the Sums of Squares

    • Partition sum of squares Y into sum of squares predicted and sum of squares error
    • Define r2 in terms of sum of squares explained and sum of squares Y
    • The sum of squares error is the sum of the squared errors of prediction.
    • First, notice that the sum of y and the sum of y' are both zero.
    • This indicates that although some Y values are higher than their respective predicted Y values and some are lower, the average difference is zero.