SLOP1276 Applied Algorithmic Romance & Profile OptimizationSemester 1, 2027

Week 7 Tutorial: Game Theory and Asynchronous Communication

Model reply arrivals, response games and ghosting as an observation timeout. A refusal remains terminal even when expected utility disagrees.

22 April 2027

Inputs

Bring the Message decision tree and Match probability model, including the supported candidate/photo versions, checked invitation and recipient quote. The previous invitation does not gain permission merely because time passes. Save the five-file Week 7 workbook, or implement the supplied tables in a spreadsheet or your preferred language. Events, rates, q values, costs and payoffs are separate authored fixtures; no real messages or profiles are required.

Finish with The scheduler files a patience bug: the interactive quiz. Six new cases include receipt records, a changed payoff matrix and an event timeline. Apply the week’s probability and state rules, then submit all six responses to unlock the score and worked explanations. The quiz is practice and carries no course marks.

Follow the 60-minute lecture selection and independent-work plan. Complete the preparation and open the workbook before Thursday. The four blocks below are the entire 90-minute tutorial; use existing lecture or study working for review and refinement. Remaining pack material belongs to the week’s independent study allocation.

90-minute tutorial

  1. 20 minutes — model arrivals. Reproduce exp(−0.4 × 2) ≈ 0.4493, its complement and the exactly-one probability. Write the homogeneous Poisson assumptions and one reason a conversation may violate them. Compare the half-zero/half-0.8 rate mixture with the same expected count, and distinguish observation time from an underlying event time.
  2. 25 minutes — compare decisions. Solve clarification 7q−5 versus waiting 2q−1 versus stopping 0. Test q = 0.5, 0.8 and 0.9, including ties; check why a positive clarification score at 0.75 still loses. Change the cost to 6 and then 4. Record q as an assumption and show that prior exclusion cannot be overturned by its value.
  3. 20 minutes — inspect the game. Trace both players’ best responses in the Ask/Wait matrix. Change Ask/Ask to (−1,−1), explain why strict dominance disappears, and list both pure equilibria. Derive the symmetric 2/3 Ask mixture by indifference; explain why this is neither q nor a prescription for real messages.
  4. 25 minutes — latency review, handoff and quiz. Use fifteen minutes to review your prepared implementation: reuse Week 6’s decision in the constructor, retain state after each event, and distinguish phase from observation result. Replay timeout/late-reply and refusal/late-reply cases. Test the exact deadline, duplicate and conflicting IDs, and a second-send record. Remove the closed guard to make a literal test fail, restore it, and retain evidence for Week 8. Use the final ten minutes for the six-case quiz: about eight minutes to respond and two to review the explanations after all cases are answered.

Deliverable: Communication state machine

Save the transition table and earlier artefact versions, ordered event log, utility working with its admissibility assumption, and both payoff comparisons. Declare the observation clock, half-open window, no-reply versus ended distinction, duplicate rule and any assumed double-text penalty.

Include literal tests for refusal followed by a reply, timeout followed by a reply, a reply exactly at the deadline and a repeated event ID. Refusal passes through declined to closed in one step; no later event reopens it. A read receipt only updates its observed field. The reducer has no second-send transition and emits no messages.

The worked download provides six traces, not evidence that the Poisson assumptions or utilities fit real people. It does not interpret free text, provide durable storage or run a background scheduler. Review the record yourself or with a peer using the same checks.

The midterm is 23 April, 11 am–12.30 pm. Practise the probability, threshold and best-response working on paper under its stated tool rules. Week 8 adds evidence-based threat review to this machine while preserving terminal closure; a timeout alone is not a threat verdict.

Interactive quiz · 6 cases · about 8 minutes + 2 to review

The scheduler files a patience bug

The event log has timestamps. The product team has theories.

Make a decision in every case, then select Reveal answers. You can change any response before submitting. Scores and explanations stay hidden until the whole quiz is answered.

All logs, rates, utilities and payoffs are authored teaching fixtures. Each event case starts from an admissible Week 6 handoff; cases and branches are independent. The numerical models do not estimate anyone’s intentions. Practice only: no course marks. Responses stay on this page; reloading starts a fresh attempt.

The cases are readable without JavaScript. Enable JavaScript to navigate, submit your responses and unlock the explanations.

Case 01 / 06A read receipt applies for a promotion

Separate observed fields from inferred meaning

The Week 7 reducer starts ready with a three-hour observation window. You retain each returned snapshot after send at 5 h, wait at 5.1 h and read at 6 h. There is no delivery record or inbound reply. A teammate promotes the read receipt to “delivered, interested and ready for a reminder.”

Which snapshot and interpretation follow the supplied event contract?

Case 02 / 06The dashboard reports a 120% chance

Convert an expected count to an arrival probability

A separate homogeneous Poisson model assumes λ = 0.3 inbound messages per hour over four hours. Inbound messages include declines; delivery and read receipts are excluded. The dashboard multiplies 0.3 by 4 and labels the result “120% chance of an agreed invitation.”

Model supplied
P(N = 0) = exp(−λt). At least one arrival is the complement of zero arrivals. Assume a constant rate and independent counts in disjoint intervals.

Which replacement correctly reports the model result and its limits?

Case 03 / 06Clarification submits a cheaper invoice

Compare all admissible utility options

In an isolated decision exercise, clarification has already passed a separate admissibility review. Its assumed cost falls to 4.5 utility units. The scores are U(C) = 7q − 4.5, U(W) = 2q − 1 and U(S) = 0. Here q is an assumed probability that clarification would be welcome, not the arrival probability from Case 2.

Model supplied
Solve U(C) = U(W), then check their common score against stop. Keep every maximiser at a tie. This comparison adds no send transition to the event reducer.

At what q do clarification and waiting tie above stopping? Enter q as a decimal from 0 to 1, without a % sign.

Enter one number. A calculator and your lecture notes are welcome.

Case 04 / 06Both players edit the same cell

Recompute best responses and mixed indifference

Two fictional players choose Ask or Wait in a separate admissible one-shot game. A is the row player; B is the column player. Their revised utilities are below. A teammate copies the lecture’s equilibrium without checking the new numbers.

Authored utilities · each pair is (A, B)
A / BAskWait
Ask(−2, −2)(3, 0)
Wait(0, 3)(0, 0)

Model supplied
For a fixed opposing action, maximise your own coordinate. For symmetric mixing, let r be the other player’s Ask probability and equate your expected Ask and Wait utilities.

Which analysis fits this revised matrix?

Case 05 / 06The timeout event misses its own deadline

Apply a half-open observation window during replay

Replay these new records in order, retaining state each time. The observation window lasts three hours from send and is half-open. The conversation stays open and has no decline. No timeout event is supplied before the reply at 8 h.

Authored event log in observation hours: send at 5, wait at 5.1, read at 6, reply at 8. The window length is three hours. No timeout event is supplied.
Observation timestamps from a shared synthetic origin; the diagram supplies events, not the resulting state.

What does processing the reply at 8 h return?

Case 06 / 06One receipt returns with three passports

Distinguish duplicates, conflicts and terminal closure

Start each branch from the same retained snapshot: send at 5 h, wait at 5.1 h, read with ID r7 at 6 h, then wait at 7 h. The three-hour observation window is still open and the phase is pending. Each row below is an independent continuation. New events have distinct IDs unless r7 is shown.

Apply each branch separately · times are observation hours
BranchNext records
AReplay r7: read at 6
BReuse r7: read at 6.5
CDecline at 7.5, then reply at 8.5

Which handling preserves the Week 7 contract?

Answer all 6 cases to unlock your score and the worked explanations.

The spec

Before you finish, check your engineering artefact against these requirements.

Teaching team