Chaotic behavior of learning automata in multi-level games under delayed information

Distributed decision makers are modeled as players in a game with two levels. High level decisions concern the game environment and determine the willingness of the players to form a coalition (or group). Low level decisions involve the actions to be implemented within the chosen environment. Decisions are made using probability distributions which are updated using a learning automaton scheme. A player has knowledge of another player´s likelihood of making a particular decision but this information is delayed, perhaps due to network broadcasts or other environmental influences. These delays create the potential for instabilities in the decision making process and particular parameter settings can lead to period-doubling and the onset of chaos