An equilibrium in a sequence of decisions with veto of first degree

Abstract

In this paper we model a sequence of decisions via a simple majority voting game with some players possessing an unconditional or conditional veto. The players vote (yes, no or abstain) on each motion in an infinite sequence, where two rounds of voting take place on each motion. The form of an equilibrium with retaliation is introduced, together with necessary and sufficient conditions for an equilibrium in such a game. A theorem about the form of the equilibrium is proved: given that one veto player abstained in the first round, in the second round of voting on a motion: (1) a veto player should vote for the motion if the value of the j-th motion to the i-th player (measured relative to the status quo) is greater than t2, veto if it is less than t1and otherwise abstain; (2) a non-veto player should vote for the motion if the value of the j-th motion to the i-th player (measured relative to the status quo) is greater than t3and otherwise abstain; (3) the thresholds t1, t2and t3satisfy given conditions.