The question#

What changes when Moss chooses a reply instead of holding the stop lap SlopU hoped it would keep?

This week’s boundary:

• a deterministic synthetic four-car field with one responding rival
• one fixed objective and three permitted stops per car
• SlopU announces; Moss observes and replies
• no hazards, sampling or probability

Week 5’s position-aware candidate traces are supplied. We replace one fixed trace with a response.

Two tactics, neither a promise#

An undercut stops earlier than the comparison car to use the new-tyre phase before that car stops.

An overcut stays out longer and tries to gain enough before stopping.

The names describe move order. They do not guarantee a pass, a time gain or a finishing position.

Conditional language#

• best response — the action that scores best given the other action
• response function — a mapping from every observed SlopU action to the Moss reply that makes SlopU’s result worst
• falsifier — evidence fixed in advance that would retain, reject or qualify the call

“Best response to Moss stop 13” is complete. “The optimum” hides the action the answer depends on.

Keep Week 5’s objective#

result = (SlopU finishing position, adjusted_finish)

• lower finishing position is better for SlopU
• adjusted time breaks only a same-position tie
• SlopU chooses the smaller lexicographic result
• Moss chooses the reply that makes it larger

Every cell that follows is a fictional full-field SlopU result.

Two actions: the whole fixture#

Read a column to hold Moss fixed. Read a row to let Moss reply to the SlopU action named at left.

Hold Moss fixed#

SlopU compares positions first in each fixed-Moss column:

Moss stops now: P1 beats P3 → wait
Moss waits:     P2 beats P4 → stop now

Each best response is conditional on its named Moss action. Neither says what Moss chooses after seeing SlopU’s reply.

Now let Moss reply#

SlopU announced wait, so Moss reads the wait row:

Moss stops now → P1, 600.900 s
Moss waits     → P4, 603.000 s

Moss chooses the worse SlopU result. Its reply is wait, returning P4.

The apparent P1 was never a guarantee. It belonged to one fixed Moss action.

Compare returned results#

For each SlopU announcement, Moss returns the worse position:

SlopU stop now → worse(P3, P2) = P3
SlopU wait     → worse(P1, P4) = P4

SlopU then selects the better returned position:

better(P3, P4) = P3

So SlopU announces stop now. Best remains position-first under the response model; it is not a promise to win.

The research move#

Aguad and Thraves (2024) model two drivers’ interacting pit decisions as a feedback Stackelberg game solved by dynamic programming. Their deterministic formulation comes before a stochastic extension.

That supports the move from independent pit choices to a rival who responds. It does not supply this week’s positions, times, response table or selected stop. Our three-by-three fixture is a bounded teaching model, not their algorithm.

Fix Moss at stop 13#

Start with Week 5’s fixed-field result: Moss stops on 13 while Oriole and Tern retain their supplied traces.

Position first, adjusted time second: stop 13 remains Week 5’s P2 answer.

Now Moss gets to answer that stop.

Commit before the reveal#

For the fixed-rival stop-13 recommendation:

• retain unchanged if every supplied Moss reply leaves SlopU P2 or better
• replace if any reply leaves SlopU P4
• otherwise qualify it as vulnerable but retain it for this bounded task

This falsifier is written while the response columns are locked. Thresholds written after seeing them are hindsight, not a test.

The full response table#

Every cell is SlopU’s synthetic full-field result: position first, adjusted finish second.

The stop-13 row reaches P4 under Moss stop 12, so the precommitted replacement condition is crossed.

Moss’s response function#

Read each SlopU row and select its worst position/time result:

This table is the response function: one Moss reply for every observed SlopU action.

SlopU chooses among replies#

SlopU compares the returned row results:

all P4 → min(2806.500, 2806.200, 2805.900) = 2805.900

SlopU selects stop 14. Moss replies with stop 14. The model returns P4 at 2805.900 s.

All returned positions are P4, so the adjusted-time tie-break selects the best returned result. It is not a claim that SlopU wins.

The answer keeps moving#

1. Hold Moss at stop 13: Week 5’s stop 13 remains P2.
2. Moss answers that stop by stopping earlier on 12; the Week 5 recommendation falls to P4.
3. Hold Moss at stop 12: SlopU stop 14 is the P2 overcut.
4. Hold Moss at stop 14: SlopU stop 12 is the P2 undercut.
5. Map every Moss reply: each row returns P4, and the time tie-break selects SlopU stop 14 at 2805.900 s.

Undercut and overcut are best responses to named Moss actions. Neither is the answer without one.