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I want to model an interaction between a government and its citizens using the game theory extensive form, but I want to express the posibility that the citizens don't act as a unique agent. For example, government imposes a new tax, some of the citizens pay it without problems, but others don't do it because socioeconomical problems.

Obviously, both situations can happen at the same time so in the extensive form there wouldn't be a unique selected leaf node. Does this mean that I can't use extensive form in this case?

I'm looking for an example in the game theory literature, but I can't find anything.

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One approach is taken by the Optimal Taxation literature, which considers the problem of a government taxing people when it does not know their ability, and can only observe their income. Mankiw is a place to start http://scholar.harvard.edu/files/mankiw/files/optimal_taxation_in_theory.pdf Piketty and Saez is more advanced https://eml.berkeley.edu/~saez/piketty-saezNBER12handbook.pdf That work is often less game-theoretic. A more game theoretic approach is the mechanism design literature, often called implementation theory. That is often concerned with problems such as providing public goods (such as a park) and getting people to pay for it. See chapter 10 of Osborne and Rubinstein, A Course in Game Theory. You might also want to look at work on Auction theory, where you can have a seller and many potential buyers, or the work on oligopolies and entry deterrence, where you have an incumbent firm and many possible rivals. Hope this helps.

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