The Mathematics of Tit for Tat
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Golden Balls
TV show from Feb 2008 to Feb 2009 where a jackpot is to be shared between 2 contestants who secretly choose to "split" or "steal".
- If both players "split", the jackpot is split equally between them.
- If 1 player "splits" and the other "steals", the stealer gets the whole jackpot and the splitter leaves with nothing.
- If both players "steal", they both leave with nothing.
| Cooperate | Defect | |
| Cooperate | (3,3) | (0,5) |
| Defect | (5,0) | (1,1) |
Axelrod's computer tournament
3 teams
Cooperator
Always cooperate.
Defector
Always defect.
Alternator
Start by cooperating and then switch.
Random
Play randomly.
Tit For Tat
Start by cooperating and then do whatever your opponent does in the previous round.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| Alternator | C | D | C | D | C | D | C | D |
| Tit For Tat | C | C | D | C | D | C | D | C |
| C | D | |
| C | (3,3) | (0,5) |
| D | (5,0) | (1,1) |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| Alternator | 3 | 5 | 0 | 5 | 0 | 5 | 0 | 5 |
| Tit For Tat | 3 | 0 | 5 | 0 | 5 | 0 | 5 | 0 |
| Alternator | Cooperator | Defector | Random | Tit For Tat | |
| Alternator | 2.0 | 4.0 | 0.5 | 2.3 | 2.5 |
| Cooperator | 1.5 | 3.0 | 0.0 | 1.5 | 3.0 |
| Defector | 3.0 | 5.0 | 1.0 | 3.0 | 1.0 |
| Random | 2.2 | 4.0 | 0.5 | 2.3 | 2.7 |
| Tit For Tat | 2.5 | 3.0 | 1.0 | 2.3 | 3.0 |
| Year | Author | Size | Source Code |
| 1979 | Axelrod | 13 | Not immediately available |
| 1979 | Axelrod | 64 | Not immediately available |
| 1979 | Axelrod | 64 | Available |
| 1991 | Bendor | 13 | Not immediately available |
| 2002 | Stephens | 16 | Not applicable |
| 2005 | Kendall | 223 | Not available |
| 2012 | Stewart | 13 | Not fully available |
Demonstration
Applications of Game Theory
- Economics
- Biology
- Computer Science
(1928-2015)
Brouwer's fixed point theorem
