Iterated Games

Often players in a scenario that can be modeled as a strategic form game engage in repeated interactions with each other. In such instances, their selection of a strategy on a given "iteration" may depend on their history of previous interactions. By way of example, a player might start by playing strategy 1 and continue playing it unless the history of interactions were such that the opposing player had played 0 on his/her last two turns. This Demonstration permits a selection for each player from the 2,097,152 (2^21) strategies that depend on the prior two interactions of the players. It shows the resulting "directed graph" of histories the players could observe, the steady-state cycle of histories that will be observed, the payoffs from the selected strategic form game, and the mean payoffs received by the players in the steady state.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Histories that are part of the steady-state cycle are shown as framed.
There are 2^42 (≈ 4.4 trillion) possible strategy combinations that the players can employ in this game and that can be selected using the two top sliders.
A "tit-for-tat" strategy can be implemented by having player 1 use strategy 1398101 and by having player 2 use strategy 1973785.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+