24 Game theory: Hawks and doves

24.1 Introduction

This is a whole-class, card-based game-theory activity. Students play the Hawk–Dove game — first with a single repeated partner (Game One), then with a new partner every round (Game Two) — and enter results into one shared, live spreadsheet so the class can watch the round-by-round patterns emerge on screen. With benefit $B > $ cost \(C\), Hawk is the dominant strategy in a one-off encounter, but mutual Hawk–Hawk is worse for both players than mutual Dove–Dove: the game has the structure of the Prisoner’s Dilemma, and repeated interaction with the same partner changes the incentives.

The pedagogical core is that students write down a prediction before playing and then test it against real, live class data.

24.2 Key Concepts

  • Payoff table (payoff to Player 1): Hawk vs Hawk \(= (B-C)/2\); Hawk vs Dove \(= B\); Dove vs Hawk \(= 0\); Dove vs Dove \(= B/2\). With \(B=4, C=3\): 0.5, 4, 0, 2.
  • Dominant strategy: with \(B>C\), Hawk beats Dove regardless of the opponent — theory predicts all-Hawk in one-off play.
  • Repeated interaction: with the same partner, retaliation makes persistent Hawk–Hawk costly, favouring cooperation (Dove).

24.3 Learning Outcomes

By the end of this exercise, students will be able to: - Explain the basic concepts of game theory and strategic interaction. - Apply the Hawk–Dove model to biological and social examples. - Appreciate how a simple model illuminates complex decision-making. - Generate a testable prediction before collecting data and check it against live class results.

24.4 Activity Overview

Suggested Timings: - 5 minutes: Introduce game theory and the payoff table. - 5 minutes: Students work through “what does theory predict?” and record predictions for both games. - 15 minutes: Game One (repeated partner, 15 rounds). - 15 minutes: Game Two (rotating partners, 15 rounds). - 10 minutes: Compare live charts with predictions; discuss.

24.5 Instructor setup (before class)

  1. Duplicate the “Hawk-Dove Live Results” spreadsheet (one copy per year). It needs three tabs:
    • Game1_Data — one row per pair (Pair ID pre-filled), two H/D entry columns per round, plus formula-computed benefit and total columns. Keep B and C in named cells the formulas refer to.
    • Game2_Data — one row per student (Player ID pre-filled), same per-round and total columns.
    • Live_Dashboard — a “% Hawk by round” line chart and a “mean hawkishness vs total benefit” scatter, wired to the data tabs.
  2. Share for editing (“anyone with the link can edit”) and project the Live_Dashboard throughout.
  3. Assign Pair IDs / Player IDs in advance (by seat or attendance) — do not let students invent labels; the IDs are what let the data line up automatically.
  4. Keep the spreadsheet after class as the year’s archived dataset for the “Results of the hawk-dove games” chapter.

24.6 Instructions for Facilitating

  1. Hand out Hawk/Dove card pairs; make sure each pair/player knows their ID.
  2. Game One: partners conceal cards, reveal on your signal, agree on what was played, and enter both letters in their row. Repeat 15 rounds.
  3. Game Two: use a rotating inner/outer circle so partners change each round with no time lost finding a partner; call “rotate” between rounds.
  4. Pause after each game to read the two live charts together.
  5. Have a paper fallback ready (“no wifi”: jot results, enter at the end).

24.7 Questions & Model Answers

  1. With \(B>C\), what is the best strategy in a single anonymous encounter?
    • Hawk. Against a Dove you get \(B\) (4) vs 2 for playing Dove; against a Hawk you get \((B-C)/2\) (0.5) vs 0. Hawk dominates, so theory predicts everyone plays Hawk.
  2. Why might Game One (same partner) differ from Game Two (new partners)?
    • Against a fixed partner, playing Hawk invites retaliation; getting stuck in Hawk–Hawk (0.5 each) is worse than settling into Dove–Dove (2 each). So cooperation can pay when interactions repeat, whereas changing partners each round rewards Hawk.
  3. What is the experimental hypothesis?
    • Hawkish play becomes less frequent and less profitable between repeated partners (Game One), and more frequent and more profitable with changing partners (Game Two). The null hypothesis is no systematic difference between the two settings.
  4. What happens if you raise \(C\) relative to \(B\) (e.g. \(C>B\))?
    • Hawk is no longer strictly dominant; when the cost of a Hawk–Hawk fight exceeds the benefit, a mix of strategies (or more Dove play) can be favoured. A good discussion prompt about evolutionarily stable strategies.

24.8 Teaching Tips

  • Prediction first: insist students record predictions before Game One — the payoff of the exercise is comparing prediction with live data.
  • IDs, not names: pre-assigned Pair/Player IDs prevent the name-matching mess that free-text labels caused in past years.
  • Use the live charts: pausing to read the projected charts after each game keeps the theory–data link immediate.
  • The full analysis of the class data is worked through in the “Results of the hawk-dove games” chapter.

24.9 Common Pitfalls

  • Skipping the prediction step, which removes the point of the activity.
  • Students choosing their own labels, breaking automatic data aggregation.
  • Confusing the two games’ setups — repeated vs rotating partner — when entering data.
  • Reading “Hawk wins” too broadly: it dominates only in one-off encounters and only while \(B>C\); repetition and payoff changes flip the conclusion.

24.10 Acknowledgement

This exercise is adapted from https://www.jove.com/science-education/10611/group-behaviour.