Game theory is a mathematical formulation of cooperative
or competitive interaction between multiple entities. The key concern in game
theory is to extract rational (optimal) behavior from a given interaction
between autonomous agents. We model the FFM world as a zero-sum game.
Our game theoretic model consists of a game matrix. The game consists of two
entities, and each one of them can choose from two strategies 1) attack or 2)
flee. The utility functions for each strategy is based on two parameters 1)
Difference in energy level and 2) Likelihood of attack or flee by the other
agent based on previous interactions.
We will denote 'Ua,b' the utility of taking action 'a' when the opponent
agent takes action 'b' (where the actions can be 'A' for attacking and 'F' for
fleeing. We note with δ the ratio of energy levels of the current and
opponent agent, and 'mu' the likelihood of attack by the opponent agent. Each
utility function is defined as follows:
where
Given the matrix, the optimal strategy is chosen by summing up the utility for
each strategy. The strategy that provides the maximum utility is then chosen as
the optimal strategy.
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Several heuristics were used to guide the agent to explore the map and eat
available food. The expert agent uses an internal data structure representing
the perceived game map as a base for the heuristics.
Heuristic 1: IF the agent is not able to eat since last 20 to 100
simulations and there is no food or other agent in sight THEN move to the
least explored direction on the map for 50 simulation steps.
Heuristic 2: IF the agent is not able to eat since last 100 to 200
simulations and there is no food or agent in sight THEN obtain two random
directions (which are non-opposite to each other), and move in those directions
for 200 simulation steps.
Heuristic 3: IF there is more than one agent in the sensor range
THEN flee in the direction which has the least number of agents.
Heuristic 4: IF the agent energy level reaches 35000*mateEnergyFactor
and there is no agent or food in sensor range THEN multiply and increase
mateEnergyFactor by 0.2.
Heuristic 5: IF food is visible in the sensor range and no agent is
visible THEN approach the food and eat it.
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