Gibbard-Satterthwaite Games for k-Approval Voting Rules

The Gibbard-Satterthwaite theorem implies the existence of voters, called manipulators, who can change the election outcome in their favour by voting strategically. When a given preference profile admits several such manipulators, voting becomes a game played by these voters, who have to reason strategically about each others’ actions. To complicate the game even further, counter-manipulators may then try to counteract the actions of manipulators. Our voters are boundedly rational and do not think beyond manipulating or countermanipulating. We call these games Gibbard–Satterthwaite Games. In this paper we look for conditions that guarantee the existence of a Nash equilibria in pure strategies.