Manipulation in games with multiple levels of output
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In (j,k)-games each player chooses amongst j ordered options and there are k possible outcomes. In this paper, we consider the case where players are assumed to prefer some outcomes to others, and note that when k>2 the players have an incentive to vote strategically. In doing so, we combine the theory of cooperative game theory with social choice theory, especially the theory of single-peaked preferences. We define the concept of a (j,k)-game with preferences and what it means for it to be manipulable by a player. We also consider Nash equilibriums with pure strategies for these games and find conditions that guarantee their existence.
CitationFreixas, J., Parker, C. Manipulation in games with multiple levels of output. "Journal of mathematical economics", Dec 2015, vol. 61, p. 144-151.