players choose independently from a menu of actions with consequences depending on all choices in a known way.This is a fascinating mathematical subject, and indeed the language of Prisoner's dilemma and Nash equilibrium has spread far beyond the mathematics world. There are many introductory textbooks and also many non-technical books such as Len Fisher's Rock, Paper, Scissors: Game Theory in Everyday Life. I don't have any general insights to add to such books. But notwithstanding the title above, there are in fact very few everyday life, or familiar game, settings which fit the specific setting of game theory. So instead of writing about game theory I will record a general principle which is relevant to the kind of games people actually play.
Play conservatively when ahead, play boldly when behind.Of course this is much too well known to count as an insight. But one can readily use it to make testable predictions. For instance
In American football, classify interceptions by quarter and whether the offense was ahead or behind; of these 8 possibilities, the most frequent will be "4th quarter, behind".And this is borne out by data.
number of points attempted | 1 | 2 | 3 | 4 | 5 |
probability of success | 0.5 | 0.22 | 0.13 | 0.08 | 0.05 |
Expectation of score | 0.5 | 0.44 | 0.39 | 0.32 | 0.25 |
Point difference | Turns remaining | ||||
---|---|---|---|---|---|
5 | 4 | 3 | 2 | 1 | |
+3 | 1 ; 0.88 | 1; 0.89 | 1; 0.91 | 1; 0.91 | 1; 1.0 |
+2 | 1 ; 0.81 | 2; 0.83 | 1; 0.86 | 1; 0.82 | 1; 1.0 |
+1 | 1 ; 0.71 | 1; 0.73 | 1; 0.76 | 1; 0.55 | 1; 1.0 |
0 | 1 ; 0.55 | 1; 0.55 | 1; 0.56 | 1; 0.30 | 1; 0.50 |
-1 | 1 ; 0.38 | 1; 0.37 | 1; 0.34 | 2; 0.19 | 2; 0.22 |
-2 | 2 ; 0.25 | 3; 0.24 | 3; 0.23 | 3; 0.12 | 3; 0.13 |
-3 | 3 ; 0.16 | 3; 0.15 | 4; 0.14 | 4; 0.06 | 4; 0.08 |
-4 | 4 ; 0.10 | 4; 0.08 | 5; 0.07 | 5; 0.02 | 5; 0.05 |