We consider an infinitely repeated legislative bargaining game with three players who split a fixed surplus in every period. The status quo allocation evolves endogenously over time, as agents can approve new proposals by simple majority rule. One player is permanently endowed with veto power, and must approve any amendment to the status quo. The veto player’s recognition probability is defined as the probability (p) that she is randomly selected as the agenda setter in a given period. First, we characterize symmetric Markov Perfect Equilibria for all possible primitives, and show that there exists a threshold value of p below which the veto player can asymptotically extract the full surplus, by offering a sequence of alternating bribes to each of her opponents whenever she is selected as the proposer (as in Nunnari (2019a)). Beyond this threshold, however, we show existence of other MPEs with only partial surplus extraction, in which non-veto players can sustain strictly positive surplus shares in the long run by forming a permanent blocking coalition against the veto player. Assuming no agent has commitment power, we show that the partial extraction MPE is unique after applying a coalition-proofness refinement. In comparative statics, we show that cooperation between non-veto players is more likely to be sustainable if agents are more patient and if the initial status quo division is more egalitarian. In ongoing work, we show that our MPE is robust to having an arbitrary odd number of players. Our findings imply that a sufficiently patient and powerful veto player (e.g. a monarch with a high recognition probability) may have an incentive to cede some of her agenda-setting power to her non-veto opponents (e.g. the bourgeoisie and nobility), through a “voluntary democratization” process which permanently lowers p.
Author(s): Ravideep Sethi, Ewout Verries