Twin relationships in Parsimonious Games: some results

In a vintage paper concerning Parsimonious games, a subset of constant sum homogeneous weighted majority games, Isbell introduced a twin relationship based on transposition properties of the incidence matrices upon minimal winning coalitions of such games. A careful investigation of such properties allowed the discovery of some results on twin games presented in this paper. In detail we show that a) twin games have the same minimal winning quota and b) each Parsimonious game admits a unique balanced lottery on minimal winning coalitions, whose probabilities are given by the individual weights of its twin game

Binomial menu auctions in government formation

In a menu auction, players submit bids for all choices the auctioneer A can make, and A then makes the choice that maximizes the sum of bids. In a binomial menu auction (BMA), players submit acceptance sets (indicating which choices they would support), and A chooses the option that maximizes his utility subject to acceptance of the respective players. Monetary transfers may be implicit, but players may also bid by offering "favors" and the like. BMAs provide a unified representation of both monetary and non-monetary bidding, which I apply to model government formation. First, I analyze general BMAs, characterize the solution under complete information and establish outcome uniqueness (for both, sealed bid and Dutch formats). Second, in case monetary transfers are possible, BMAs are shown to implement VCG mechanisms. Finally, in case transfers are impossible, BMAs extend the model of proto-coalition bargaining and are specifically applied to government formation.menu auction; demand commitment; proto-coalition bargaining; VCG mechanism

Demand bargaining and proportional payoffs in majority games

We study a majoritarian bargaining model in which players make payoff demands in decreasing order of voting weight. The unique subgame perfect equilibrium outcome is such that the minimal winning coalition of the players that move first forms with payoffs proportional to the voting weights. This result advances previous analysis in terms of one or more of the following: a) the simplicity of the extensive form (finite horizon with a predetermined order of moves); b) the range of the majority games covered; c) the equilibrium concept (subgame perfect equilibrium is sufficient for a unique prediction).Demand bargaining Coalition formation Weighted majority games Minimal winning coalitions