Playing Games with Experimental Economics

In this blog I am reprising an article produced by our good friend Mark Johnston from New Zealand in an early edition of the now discontinued Latte Magazine(2007). I am doing so because I know that many colleagues are interested in trying some experimental games with their students for example when teaching game theory, behavioural economics and the provision of public goods.

Globalisation, conflicts and cooperation

Experimental economics is a rapidly expanding field. Whilst the majority of theory deals with large-scale phenomena such as volatile share prices or the values of a nation’s gross national product, economists are increasingly fascinated by down-to-earth interactions between people, for example the sharing and helping that goes on within office workers, households, families and groups of children.

Game theory is based on the idea that everybody tries to maximise but that people sometimes make mistakes! It tries to model our behaviour and explain how incentives can affect the decisions we make. Experimental economics is a research method whereas behavioural economics studies economic models that include psychological factors such as:

o Social preferences
o Problems of self-control
o Limits on our rationality

The Silent Co-ordination Game

In this game you make a choice of number from 1 to 7. The pay-off is your reward from that choice but, the reward depends on the smallest value of X selected by another player in the game. Say that you choose 7 and the smallest number selected by the rest of the players is 2 then you receive £0.30. If you chose 4 and the smallest number of the group is 3 you receive £0.80.

So the most efficient choice is for everyone to choose 7 as all will receive £1.30 and the most secure or prudent option is 1 as this payoff (£0.70) is guaranteed!

To play the game in the classroom start by asking everyone to write down their choice on a piece of paper without anyone else seeing! Choices are then collected by the teacher and the minimum choice reported on the board.

Everyone can then keep their own account of how much they earned, based on their choice and the minimum that anyone chose. This game can be played over as many rounds as you like but the interesting aspect of it is how many rounds happen before the group starts coordinating their efforts where everyone is going to benefit the most – i.e. everyone choosing 7.

In some instances some groups might have a lack of trust so select the most prudent option 1.

The Ultimatum Game

In this game start by imagining that somebody offers you £100. All you have to do is agree with some other anonymous person on how to share the sum!

The rules in this game are strict!

1. The two players cannot exchange information.
2. A coin toss decides which student will propose how to share the money.
3. Suppose that you are the proposer. You can make a single offer of how to split the sum, and the other person—the responder— can say yes or no.
4. The responder also knows the rules and the total amount of money at stake.
5. If their answer is yes, the deal goes ahead.
6. If their answer is no neither of you gets anything
   

In both cases, the game is over and will not be repeated. What will you do? You may not be surprised to learn that two thirds of offers are between 40 and 50 percent.

From research carried out only four in 100 people offer less than 20 per cent! Proposing such a small amount is risky, because it might be rejected. More than half of all responders reject offers that are less than 20 percent.

But here is the puzzle:

Why should anyone reject an offer as “too small”? The responder has just two choices: take what is offered or receive nothing. The only rational option for a selfish individual is to accept any offer. Even £1 is better than nothing. A selfish proposer who is sure that the responder is also selfish will therefore make the smallest possible offer and keep the rest. This game-theory analysis, which assumes that people are selfish and rational, tells you that the proposer should offer the smallest possible share and the responder should accept it. But this is not how most people play the game.

The Beauty Contest
Below are the rules for this simple contest:

1. Players select a number from 0 to 100 (all numbers are allowed, including decimals).
2. The teacher collects all of the chosen numbers.
3. The teacher then averages the numbers. Call the average X.
4. The teacher calculates two thirds of the value of X. Let Y = (2/3)X.
5. The player whose number is closest to Y wins £20.
6. If there is a tie, tied players split the prize.

How should you play this game?

A rational player should try to maximize their winnings (i.e., their “payoff”).
To be on the safe side, we say that a rational player should maximize their average (or “expected”) payoff, since there is sometimes a degree of uncertainty. So what is the rational equilibrium?

o What if everyone guessed 0?
o The average guess would be 0.
o Given what everybody else is doing (picking 0), the best thing for me to do is also to pick 0, since my guess is 2/3 of the average guess.
o So if everyone picks 0, everyone is maximizing their expected payoff given what everyone else is doing.
o Everyone picking 0 is a rational equilibrium.

For some groups the most popular reasoning is:

Equal probability distribution: E[average] = 50, so two thirds of 50 = 33.

Here are some teaching and learning lessons from the Beauty Contest game:

o Game theory predicts that everyone is equally (and perfectly) rational
o But real players are not all perfectly rational
o Players have a different education
o They have different levels of experience
o Different types of thinking
o Different intensity of thinking

If people were all perfectly rational, it would be impossible to consistently be “one-step ahead of the competition,” since everyone anticipates everyone else’s' moves.

In the real world of business staying “one-step ahead of the competition” is a reasonable goal (which some highly experienced, well informed people will achieve). But it is also possible to be “one-step behind the competition” (which some less experienced, less informed people will achieve). It’s useful to try to figure out where you stand!

Why is it called the beauty contest?

In the General Theory, Keynes describes a newspaper beauty contest in which readers are challenged to guess which published photos other readers will pick as the most beautiful.

“It is not a case of choosing those which, to the best of one's judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree, where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees.”

The challenge in the game we have looked at was also to select a number that reflected your best guess of what other players would do (and vice versa).

The Public Good game

Four players in a group get £20 each. Each individual has to decide independently how much to invest into a common pool of cash! The teacher then doubles the common pool and distributes it equally amongst members of the group. This game can be played over a single round or a suggested ten rounds.

Key points when using this game in the classroom:

1. If everyone contributes the full £20 – all double their money!
2. A selfish player ought to contribute nothing as for every £1 he invests only £0.50 is returned. £1 x 2 ÷ 4 = £0.50
3. If everyone followed the selfish rational strategy – no money is distributed.
4. Experience suggests that between 40-60% of players contribute in 'one-shot games' and in the first round of repeated games
5. On the announcement of the final round less than 30% tend to contribute to the common pool
6. You may find when playing this with your students that, the bigger the group, the higher the likelihood that contribution rates will fall
7. With an increase in “learning” over many games contribution rates start to rise. Students are learning to appreciate the potential benefits from cooperative behaviour!
   

Final thoughts

For a long time, theoretical economists claimed that there was a being called Homo economicus—a rational individual relentlessly bent on maximizing a purely selfish reward. But the lesson from some of the experiments in this article is that real people are a crossbreed of homo-economicus and homo-emoticus, a hybrid species that can be ruled as much by emotion as by cold logic and selfishness! As economics edges ever closer to the disciplines of biology and psychology we can expect more insights to emerge from experimentation into people's behaviour.