# Experiment 6 The conflict game

## 6.5 Student instructions

### Introduction

In this game, you will play five rounds. In each round, you will be randomly matched with another student and you both will have to decide simultaneously how to behave in negotiating a deal worth 2000: cooperatively (as a Dove) or aggressively (as a Hawk). At the end of the round, you will receive a payoff according to the information in the payoff matrix (see Figure A for an example).

Figure A Students’ screen for a realization of $X=315$ and $Y=957$.

Observe that in each round, you might play with a different student who will be randomly selected from all participants; and that sometimes you will be the Blue player and at other times the Green player. Finally, recall that you will both decide simultaneously and you will play five rounds.

### Profits

Profits are calculated using the two variables, $X$ and $Y$. The value of $X$ will always be a random number between 0 and 500, and that of $Y$ will be a random number between 500 and 1500. They will take a different value at the beginning of each round and participants will know the round’s value before they decide.

Note that there are three possible payoff combinations. At the end of the experiment, you will earn the sum of the profits of all the rounds.

1. If both students in the pair behave as a Dove, they will not fight and will therefore split the 2000 prize equally.
2. If both behave as a Hawk, they will fight fiercely, hurting each other and getting only 250 each.
3. If one behaves as a Hawk and the other as a Dove, then the Hawk gets a prize of $Y$, while the Dove gets $X$.

Figure B shows this explanation and other details that will be shown in your instructor’s screen.

Figure B Instructor screen.

## 6.8 Homework questions

### The conflict game

There are two players: Blue and Green. Blue will choose between Dove and Hawk and Green between Dove and Hawk. Both will make their decision simultaneously. The payoffs are represented in Figure C. In addition, there are two variables, $X$ and $Y$. The value of $X$ will always be a number between 0 and 500, and the value of $Y$ will always be a number between 500 and 1500.

Dove Hawk
Dove 1000 , 1000 X , Y
Hawk Y , X 250 , 250

Figure C Payoff matrix.

1. Represent the following four games in normal form and then find the Nash equilibria:
1. $Y$ < 1000 and $X$ > 250
2. $Y$ < 1000 and $X$ < 250
3. $Y$ > 1000 and $X$ > 250
4. $Y$ > 1000 and $X$ < 250.
2. Represent the above four games in their extensive (sequential) form with perfect information and find the perfect Nash equilibrium in subgames.
3. Clearly define a way to measure conflict in this game by a quantitative variable. Explain your answer.