22 Game theory: Hawks and doves
22.1 Background
Game theory is a mathematical discipline that examines decision-making in competitive environments. It provides a framework to analyze strategic interactions between rational actors and understand their choices. One particularly fascinating concept in game theory is the Hawk and Dove idea. Representing two distinct strategies, the Hawk embodies aggression and assertiveness, always seeking to escalate conflicts and dominate opponents. On the other hand, the Dove adopts a more peaceful and conciliatory approach, aiming to avoid confrontations and achieve cooperative outcomes.
By studying the Hawk and Dove strategies we can gain insights into understanding the delicate balance between competition and cooperation, shedding light on the dynamics of conflicts and the evolution of cooperative behavior in both the natural world and human societies.
The simple model unravels the intricacies of strategic decision-making, with profound implications across various fields, from biology and social sciences to economics and politics.
In this activity, you will play the hawk and dove game with a single partner and then with multiple partners to observe the hypothetical costs and benefits of the antagonist or cooperative behavior, respectively.
Learning outcomes:
- Understanding of the fundamental concepts of game theory and its application in analyzing strategic interactions in competitive environments.
- Ability to apply game theory concepts to real-world contexts in biology, or politics.
- Appreciation of how simple models can be used to address complex biological or political decision making.
22.2 Your task
Before the activity starts, review the cost-benefit payoff table below to understand how to score the game.
22.3 The payoff table
The general payoff table looks like this:
| Player 2 | |||
|---|---|---|---|
| Hawk | Dove | ||
| Player1 | Hawk | (B-C)/2 | B |
| Dove | 0 | B/2 |
You can determine the benefit by looking at the left column and choosing the row corresponding to the card you played. The box that corresponds to your partner’s choice is in the top row. For this game, B equals four (4), and C equals three (3). So depending on the cards played, player one (i.e., you) would gain a score of two (2), four (4), zero (0), or one-half (0.5). Like this:
| Player 2 | |||
|---|---|---|---|
| Hawk | Dove | ||
| Player1 | Hawk | 0.5 | 4 |
| Dove | 0 | 2 |
22.3.1 Hypotheses
The experimental hypothesis for this exercise could be that the dove strategy will become more frequent between repeated partners, and the hawk strategy will become more frequent when interacting with a variety of partners. Conversely, the null hypothesis could be that there will be no change in strategy over time with repeat or different partner combinations.
22.3.2 GAME ONE
- On a piece of paper, or in Excel (you could use this file here), use a form to collect your results. It should have enough rows for 15 rounds of the game and look like this (where I include an example in the first row):
| Round | player 1 card | player 2 card | P1 benefit | P2 benefit |
|---|---|---|---|---|
| 1 | hawk | hawk | 0.5 | 0.5 |
| 2 | … | … | … | … |
| … | … | … | … | … |
| 15 | … | … | … | … |
Collect a set of two game cards.
Take out the cards labeled hawk and dove and place them face down on the table or conceal them in your hands.
When the instructor gives the signal, show either of the two cards to the student sitting across from you. Try to strategise how to receive the highest benefit from every interaction, but do not communicate with your partner.
In each round, note the cards played and the benefit recieved by each player. Also do it here on this Google Form.
Repeat the interaction by showing cards to the same partner and determining the benefit, on your instructor’s signal, for a total of 15 rounds.
At the end of those 15 rounds, the student with the highest total benefit value is determined to be the “winner”, or the most fit.
As a class, I will determine the percentages of hawks and doves played as well as the average benefit received for each round, using this formula: Class average benefit = (sum total benefit)/(number of players)
22.3.3 GAME TWO
For the second game, you should find a new partner for EACH of the 15 rounds (if possible).
Continue playing for 15 rounds or until students end up back in their starting positions, recording the data as before in Excel) or on paper. Also record the results on a Google Form here.
For each round, I will determine the percentages of hawks and doves played that round and the average benefit received, again using the formula: Class average benefit = (sum total benefit)/(number of players)
22.4 SUMMARISE RESULTS
For both the single partner hawk-dove game and the multiple partners hawk-dove game, I will use the whole class data to plot the percentages as two separate lines - one for the percentage of hawks, and one for the percentage of doves, for each of the 15 rounds.
We will take note of whether the cards played changed as more rounds were played.
We will consider which type of strategy would most likely evolve in a setting where partners interact repeatedly.
Think about which tactic might be beneficial for a species that relies on cooperation.
Discuss as a class what would likely happen if you increased or decreased the relative value of the benefits you receive.
22.5 Acknowldgement
This exercises is taken from https://www.jove.com/science-education/10611/group-behavior