More Retail Discount Wars Your Abercrom B men's fashion...

More Retail Discount Wars Your Abercrom B men's fashion outlet has a $30 \%$ chance of launching an expensive new line of used auto-mechanic dungarees (complete with grease stains) and a $70 \%$ chance of staying instead with its traditional torn military-style dungarees. Your rival across from you in the mall, Abercrom A, appears to be deciding between a line of torn gym shirts and a more daring line of "empty shirts" (that is, empty shirt boxes). Your corporate spies reveal that there is a $20 \%$ chance that Abercrom A will opt for the empty shirt option. The following payoff matrix gives the number of customers your outlet can expect to gain from Abercrom A in each situation: Abercrom $\mathbf{A}$ $\begin{array}{ll}\text { Torn Shirts } & \text { Empty Shirts }\end{array}$ Mechanics $\left[\begin{array}{rr}10 & -40 \\ -30 & 50\end{array}\right]$ Abercrom B $\quad$ Military What is the expected resulting effect on your customer base?

More Retail Discount Wars Your Abercrom B men's fashion outlet has a $30 \%$ chance of launching an expensive new line of used auto-mechanic dungarees (complete with grease stains) and a $70 \%$ chance of staying instead with its traditional torn military-style dungarees. Your rival across from you in the mall, Abercrom A, appears to be deciding between a line of torn gym shirts and a more daring line of "empty shirts" (that is, empty shirt boxes). Your corporate spies reveal that there is a $20 \%$ chance that Abercrom A will opt for the empty shirt option. The following payoff matrix gives the number of customers your outlet can expect to gain from Abercrom A in each situation:
Abercrom $\mathbf{A}$ $\begin{array}{ll}\text { Torn Shirts } & \text { Empty Shirts }\end{array}$ Mechanics $\left[\begin{array}{rr}10 & -40 \\ -30 & 50\end{array}\right]$
Abercrom B $\quad$ Military
What is the expected resulting effect on your customer base?

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Key Concepts

Expected Value

This is a statistical concept that calculates the weighted average of all possible outcomes, where each outcome is multiplied by its probability of occurrence. It provides a single summary value that represents the average result of a process if it were repeated many times.

Probability

This concept represents the likelihood of various events occurring and is typically expressed as a number between 0 and 1 (or as a percentage). It is essential for quantifying uncertainty in decision making and is used when calculating expected values.

Payoff Matrix

A payoff matrix is a tabular representation used to display the outcomes of different strategies chosen by competing decision makers. Each cell of the matrix represents the result (or payoff) when a specific pair of strategies is employed, making it a useful tool in strategic and game-theoretic analysis.

Decision Analysis

This is the systematic evaluation of decisions under uncertainty. It involves identifying possible outcomes, their associated probabilities, and the resulting benefits or losses, with the aim of optimizing decision making by comparing expected outcomes.

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