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I'm currently working in different simulations focused on the study of artificial evolution of communications in robots, and I have stumbled against the problem of its mathematic formulation.

The problem is, given a set of independent scenarios, for every iteration, in a population of robots, each one of the robots may have a state and could perform an action. Such state and action may become directly or indirectly related to a reward that may or not be shared with other robots (ex. team players).

Some examples of scenarios may be:

  • An scenario in which to gather and energy source and survive, the robots need a partner for the extraction. They may have capabilities to broadcast messages.
  • The robots fight in a Battle Royale, and to kill somebody is more effective in numbers. As they get closest to be the sole survivors, they win more and more reward points.
  • The robots are given different sets of attributes, that could give or not more attractiveness to possible partners, they can only remember the last 10 robots that they have seen, but will always remember its spouse, and its 'best man' (the robot which first referred its spouse). When a robot gets a partner is free to do whatever it wish until he dies, which could be perfectly be of help to its best man and to find its partner ;).

As you can see, the list of scenarios is really open; it may have more or less hardcoded conditions to test evolution and use of communication, which is the main approach to test in this work, applying environmental pressure to promote it.

If you can help me in any way, I would be really grateful.

All the approach is open for suggestions/changes, although I would prefer not to work from a probabilistic approach because the scenarios may vary a lot, and if it could be expressed in relation to maximize reward could be ideal, but every thought is welcome.

Thanks.

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I doubt it has anything to do with model theory (so I removed the tag). –  tomasz Nov 28 '12 at 18:17
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