Much of game theory for more than two agents concerns what happens when some subset of the agents can make binding side-agreements. Social choice theory is the branch of decision theory concerning agents who all agree to be bound by the outcome of a social choice procedure, such as a voting.
In this presentation, we consider the problem of aggregating different agents' preferences, discussing voting rules and the challenges faced in collective decision making. finally, we are going to define perfect voting systems and present Arrow's Theorem and also the Gibbard-Satterthwaite Theorem, which prove that there is no perfect voting system.