This chapter has touched on some of the issues that arise with multiple agents. The following are the main points to remember:

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  A multiagent system consists of multiple agents who act autonomously and have their own utility over outcomes. The outcomes depend on the actions of all the agents. Agents can compete, cooperate, coordinate, communicate, and negotiate.

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  The strategic form or normal form of a game specifies the expected outcome given controllers for each agent.

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  The extensive form of a game models agents’ actions and information through time in terms of game trees.

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  A multiagent decision network models probabilistic dependency and information availability.

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  Perfect-information games can be solved by backing up values in game trees or searching the game tree using minimax with $\alpha$–$\beta$ pruning.

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  In partially observable domains, sometimes it is optimal to act stochastically.

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  A Nash equilibrium is a strategy profile for each agent such that no agent can increase its utility by unilaterally deviating from the strategy profile.

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  By introducing payments, it is possible to design a mechanism that is dominant-strategy truthful and economically efficient.

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  Game-theoretic AI can be used to model and promote prosocial environmental behavior.