Acyclicity of improvements in finite game forms

Game forms are studied where the acyclicity, in a stronger or weaker sense, of (coalition or individual) improvements is ensured in all derivative games. In every game form generated by an ‘ordered voting’ procedure, individual improvements converge to Nash equilibria if the players restrict themselves to ‘minimal’ strategy changes. A complete description of game forms where all coalition improvement paths lead to strong equilibria is obtained: they are either dictatorial, or voting (or rather lobbing) about two outcomes. The restriction to minimal strategy changes ensures the convergence of coalition improvements to strong equilibria in every game form generated by a ‘voting by veto’ procedure.