Decisions in Multi-Agent Environments
Economic reasoning changes when the environment contains other agents, falling under the umbrella of game theory (c.f., Fudenberg and Tirole, 1991). The crucial difference is that other agents cannot simply be modeled as behaving randomly: they act to maximize their own utilities in response to their own beliefs, which include beliefs about the agent's behavior. Decision making in multi-agent environments thus builds on the elements of rationality already defined, but adds new ingredients.
To capture these dynamics, we subdivide the analysis into different representations of strategic interaction as is common in many game theory textbooks. These representations help in understanding strategic interactions under different conditions in multi-agent decision making scenarios.
Modules
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3.1Normal Form Games
Traditionally in game theory textbooks, a game is described by a matrix which shows the agents, strategies, and payoffs.
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3.2Extensive Form Games
As mentioned, games permit multiple descriptions and extensive form games are represented as trees, showcasing the sequential aspect of decision making.
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3.3Imperfect Information in Extensive Form Games
In many situations agents must act with partial or no knowledge of the actions of others, or even limited memory of their own past actions.
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3.4Infinitely Repeated Games
We have seen in the previous modules that long-term interactions are fundamentally different from one-shot interactions especially in the presence of uncertainty.
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3.5Bayesian Games
So far, the number of agents, the actions available to each agent, and the payoffs have all been assumed to be common knowledge among the agents.