In the original matrix, AA has the highest joint total, six, while BB is the mutual-best-response outcome with total two. Each player prefers higher own points in this model. The HTML evaluates an explicit pair of actions and displays both payoffs; neither role is silently filled.
Work through the example
Enter A for Row and B for Column, then Evaluate. Row receives zero and Column four, total four. For BB, switching alone to A lowers either player from one to zero. At AA, either player can switch alone to B and rise from three to four. Discuss each unilateral comparison separately.
Give players separately labeled action slips, then reveal both together. Ask which player’s payoff is being compared and which opposing action remains fixed. A joint total answers a different question from an individual best response. Keep the written inequalities with the explanation, and record real choices only after players make them; a teacher demonstration is not a class result.
EconPort's Georgia State teaching module explains games through players, available actions, and conditional payoffs, then examines dominant strategies and equilibrium. This packet uses those concepts with an independent point matrix, rather than the source's prison story or experimental results. EconPort game-theory module
Put the payoff order above the matrix
Every cell is ordered (Row points, Column points). Row chooses the row; Column chooses the column.
| Row action | Column A | Column B |
|---|---|---|
| A | (3, 3) | (0, 4) |
| B | (4, 0) | (1, 1) |
For AB, Row chose A and Column chose B. Row receives zero and Column receives four, for a total of four. Reversing the roles produces BA: Row receives four and Column receives zero. The combined total is unchanged, but the individual payoffs are exchanged.
Keep a role label on each action slip. An unlabeled “B” cannot tell you whether it identifies a row or a column. Give each pair the matrix and a blank record for both choices, the resulting cell, individual points, and the combined total. None of those actual-play fields should contain an example choice before learners act.
Ask four conditional questions
Hold the other player's action fixed and compare only the deciding player's payoff:
| Player deciding | Other player's fixed action | Own payoff from A | Own payoff from B | Better response in this model |
|---|---|---|---|---|
| Row | Column A | 3 | 4 | B |
| Row | Column B | 0 | 1 | B |
| Column | Row A | 3 | 4 | B |
| Column | Row B | 0 | 1 | B |
This is the teacher's illustrative analysis, not an observed class result. Each comparison favors B strictly. Thus B strictly dominates A for each player under the stated preference for their own points.
The comparisons also catch a common reading error: Column's payoff is the second number, including when Column compares choices across a fixed row. If a learner reads the first number for both roles, ask them to label whose points each entry represents before repeating the comparison.
Separate the joint total from mutual best responses
AA has a combined total of six. AB and BA each total four, while BB totals two. AA therefore gives the highest joint total among these four cells.
But AA is not a pair of mutual best responses. With Column fixed at A, Row can switch to B and increase its own points from three to four. With Row fixed at A, Column can do the same. The two unilateral changes are separate comparisons; do not describe them as one simultaneous move from AA to BB.
Recreate this example
Build one self-contained responsive HTML example titled “Game theory classroom: whose payoff improves?” for readers completing the stated task. Return the complete HTML with embedded CSS and JavaScript. Use no remote fonts, libraries, images, requests, account connections, or saved-state claims.
Original one-shot matrix payoffs ordered Row,Column: AA=(3,3), AB=(0,4), BA=(4,0), BB=(1,1). Declare preference for higher own points. Display matrix, initially blank labeled Row and Column action inputs accepting A/B, Evaluate and Reset. Require two explicit valid choices. Show cell ID, individual payoffs, total and whether mutual best responses. Explain all four individual comparisons favor B, 4>3 or 1>0. Keep AA joint total six distinct from BB total two. Input changes clear stale results.
Use a two-player matrix board with separate role inputs and conditional comparisons design with a compact header. Keep the actual sample data, controls, and useful default result visible early on a 360px-wide screen. Use readable text at least 16px, generous paragraph spacing, strong contrast, semantic labels, visible keyboard focus, and wrapping source blocks. Stack records on narrow screens rather than forcing a wide table.
Wire each action to an explicit type=button click handler using element selectors; the host permits scripts but blocks form submission. Update the visible result when the described action occurs. Show specific error feedback for invalid or missing input and clear stale feedback after dependent inputs change. Use plain text when displaying user values.
Visible fixed teaching choices are not confidential storage or observed learner outcomes. Keep the source fixture and worked teacher or developer example distinct from actual user records. Include the domain-specific explanation and next check beside the result. Provide no fake download, send, deployment, approval, or persistence button. Everything operates locally for the current page session.
Review the prepared copy in NOS
After pairs explain why AA and BB answer different questions, compare their inequalities with the matrix. An HTML teacher key can be rendered in NOS; eligible static discussion prompts can be changed visually without regenerating the page. Preserve actual choices and explanations on the activity record.