Students / Subjects

# Game Theory - Normal Form Games with Dominant Pure Strategies

Summary: Students play one or more two-player, two-strategy normal form games in which players have dominant pure strategies. Most of this module revolves around the Prisoner's Dilemma. The experiments can be conducted outside the lecture period on EconPort or during the lecture period with paper and pencil.

Motivation: Simple 2 x 2 normal form games with dominant pure strategies introduce students to the rudiments of game theory and strategic thinking, as well as providing some simple models that offer insights into numerous real-world phenomena. Playing the games, rather than simply reading about them helps make the strategic nature of the games clearer and makes lecture more entertaining.

Concepts Covered:

1. Basic elements of a game;
2. Dominant Strategy;
3. Prisoner's Dilemma and the institutional innovations (commitment devices) that societies have developed to mitigate this dilemma.

## Experiments

Considerations:

1. Although hypothetical payoffs can be used, better results are usually achieved using salient material payoffs. These payoffs can be in cash or in extra credit points (the latter tends to be cheaper for the professor and more desirable to students).
2. In each experiment, the teacher has the option of creating their own payoffs or choosing the default payoffs, which are consistent with the instructions below. If the teacher uses his or her own payoff formulations, the instructions will need to be modified accordingly.

Pre-configured Computerized Experiments

1. Prisoner's Dilemma (in gains)
student instructions

2. Prisoner's Dilemma (in losses)

3. Law Clerk Matching
student instructions

4. Hockey Helmet Rules
student instructions

5. Research and Development Expenditures
student instructions

6. King Solomon's Problem
student instructions

## Lecture

The lecture material is developed based on the assumption that this lecture will be the first lecture in game theory for the course. However, it is structured to make cutting and pasting easy.

Thus far, we have viewed economic decision makers as acting in an environment in which marginal benefits and marginal costs are independent of the decisions made by others in the economy. For example, when I go to the store to buy a pound of cheese, the price is given and I need only decide if my marginal benefits are greater than or equal to the price.

However, there exist many cases in which relevant costs and benefits depend not only on the behavior of the decision makers themselves but also on the behavior of others. Interdependence is key word here.

1. Should the prisoners confess? (based on Experiment 1)

2. Commitment problems and devices (This section of the lecture can be done immediately after the introduction of the Prisoner's Dilemma, mid-way, at the end, or after extensive form games are introduced.)

3. Why do judges hire their law clerks well before law school students have completed their studies and have demonstrated their skills in the field of law? (based on Experiment 3)

4. Why do hockey players support helmet rules, even though they choose not to wear helmets when there is no rule? (based on Experiment 4)

5. Why do duelists walk 20 paces before firing at their opponents? (similar structure to Experiment 4 and similar focus on how rules are used to avoid Prisoner Dilemma situations)

6. Should Cisco spend more on research and development? (based on Experiment 5)

7. Why is King Solomon considered to have possessed divine wisdom (1 Kgs. 3:28)? (based on Experiment 6)