Consider a Simultaneous Game for Two Players

question 17

Multiple Choice

Consider a simultaneous game for two players. Each player has a choice between two strategies, Friend and Foe. If both players play Friend, each wins $1,000. If both play Foe, they win nothing. If one plays Foe and the other plays Friend, the Foe wins $2,000 and the Friend wins nothing. Which of the following statements is (are) TRUE?
I. This game has a mixed-strategy equilibrium.
II. This game has a pure-strategy equilibrium.
III. The Nash equilibrium is for both players to play Friend.

• A) I and II
• B) I, II, and III
• C) II and III
• D) II

---

Definitions:

Real Solutions

The set of all real numbers that satisfy an equation.

Quadratic Equation

An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.

Square Root Property

A principle that relates the square of a number to its square root, often used to solve equations.

Square Root Property

A principle that states if \(x^2 = n\), then \(x\) is equal to the positive or negative square root of \(n\).