# Economic Classroom Experiments/Team Draft

Team captains in a sports draft who naively pick their most preferred players end up with a weaker team than those who anticipate the choices of others.

## Overview
### Level

Any level

### Prerequisite knowledge

None

### Suitable modules

Any

### Intended learning outcomes

* Subgame perfection, backward induction.
* More advanced students can learn the strange result of Brams and Straffin where such a selection can make everyone worse off.

## Computerized Version

A computerized version of this experiment is available on the Exeter games site.
You can quickly log in as a subject to try out this group participation experiment, by playing alone against the computer, which always makes its preferred choice. You may also find the sample instructions helpful.

### Abstract

Students play together in pairs or threes and take turns choosing objects from a pool. Once each object has been chosen it is removed from the pool and cannot be chosen a second time by any player. The analogy is with a sports draft with the players as team selectors and the objects as footballers. The players have a valuation for each object with a strict preference ordering which is different for each player. These valuations are common knowledge.
There are versions of the game for 2 players choosing 2 objects each (total 4 objects), 2 players choosing 3 objects each (total 6 objects) and 3 players choosing 2 objects each (total 6 objects). There is also a 'solo player' option where students play individually against the computer, which takes the role of the other player(s) and uses the sincere strategy of always choosing the object with the highest valuation.

### Discussion of Likely Results

The default setup is for 2 players choosing 2 objects each and appears in the paper by Brams and Straffin.
| Player 1 | Player 2 |
| A:£4.00 | B:£4.00 |
| B:£3.00 | C:£3.00 |
| C:£2.00 | D:£2.00 |
| D:£1.00 | A:£1.00 |
Consider first what happens if player 1 plays sincerely and chooses object A first. Note that player 2 cannot now do any better than to choose object B first, after which player 1 will pick C, leaving player 2 with B and D for a payoff of £6 and player 1 with A and C for a payoff of £6. (If instead player 2 were to choose either C or D first, player 1 would pick B, leaving player 2 with C and D for a smaller payoff of £5.)
Now consider what happens if player 1 chooses object B first. Now player 2's most valuable object has gone and he cannot do any better than to end up with both C and D for a payoff of £5. So it does not profit player 2 to pick object A and he should therefore pick either C or D first. So now player 1 ends up with A and B for a payoff of £7 and player 2 ends up with C and D for a payoff of £5.

### Further Points

Such a selection has been used as a method for conflict resolution between political parties. Was used as a part of the Good Friday agreements.

### Further Reading

Brams and Straffin. Prisoners' Dilemma and Professional Sports Drafts.
Brams and Kaplan. 'Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System,' Journal of Theoretical Politics, 2004 16 (2):143-173.
Brams. 'Mathematics and Democracy' 2007, Princeton University Press.
O'Leary, Brendan, Bernard Grofman and Jorgen Elklit (2001). 'The Use of Divisor Mechanisms to Allocate and Sequence Ministerial Portfolio Allocations: Theory and Evidence from Northern Ireland.' Mimeo, Department of Political Science, University of Pennsylvania.