Maria Montero

Noncooperative foundations of the nucleolus in majority games

Abstract This paper studies coalition formation, payoff division and expected payoffs in a “divide the dollar by majority rule” game with random proposers. A power index is called self-confirming if it can be obtained as an equilibrium of the game using the index itself as probability vector. Unlike the Shapley value and other commonly used power indices, the nucleolus has this property. The proof uses a weak version of Kohlbergs [SIAM J. Appl. Math. 20 (1971) 62] balancedness result reinterpreting the balancing weights as probabilities in a mixed strategy equilibrium.

Enlargement and the balance of power: an experimental study

Many important decisions are taken according to weighted majority rule. Power indices predict that enlargement of the voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the existing voters may actually gain, a phenomenon known as the paradox of new members. We test for this effect using laboratory experiments. Participants propose and vote on how to divide a budget according to weighted majority voting rules, and we measure the voting power of a player by his average payoff in the experiment. By comparing voting power across voting bodies of varying size, we find empirical support for the paradox of new members. Our results also allow an assessment of the predictive performance of standard power indices.

Voting Power in the EU Council of Ministers and Fair Decision Making in Distributive Politics

We analyze and evaluate the different decision rules describing the Council of Ministers of the EU starting from 1958 up to now. Most of the existing studies use the Banzhaf index (for binary voting) or the Shapley–Shubik index (for distributive politics). We argue in favor of the nucleolus as a power measure in distributive situations and an alternative to the Shapley–Shubik index. We then calculate the nucleolus and compare the results of our calculations with the conventional measures. In the second part, we analyze the power of the European citizens as measured by the nucleolus under the egalitarian criterion proposed by Felsenthal and Machover (1998), and characterize the first best situation. Based on these results we propose a methodology for the design of the optimal (fair) decision rules. We perform the optimization exercise for the earlier stages of the EU within a restricted domain of voting rules, and conclude that Germany should receive more than the other three large countries under the optimalvoting rule.

Inequity Aversion May Increase Inequity

Inequity aversion models have been used to explain equitable payoff divisions in bargaining games. I show that inequity aversion can actually increase the asymmetry of payoff division if unanimity is not required. This is due to the analogy between inequity aversion and risk aversion. Inequity aversion may also affect comparative statics: the advantage of being proposer can decrease as players become more impatient.

Noncooperative Bargaining in Apex Games and the Kernel

This paper studies non-cooperative bargaining with random proposers in apex games. Two di¤erent protocols are considered: the egalitarian propocol, which selects each player to be the proposer with the same probability, and the proportional protocol, which selects each player with a probability proportional to his number of votes. Expected equilibrium payo¤s coincide with the kernel for the grand coalition regardless of the protocol. Expected payo¤s conditional on a coalition may depend on the protocol: given a coalition of the apex player with a minor player, an egalitarian protocol yields a nearly equal split whereas a proportional protocol leads to a proportional split. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

Gaining power through enlargement: Strategic foundations and experimental evidence☆

Power indices suggest that adding new members to a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the original members may actually gain even if voters are bargaining over a fixed budget. We show that this phenomenon can occur as an equilibrium of a non-cooperative bargaining game based on the Baron and Ferejohn (1989) model of legislative bargaining. We implement this game in the laboratory and find that power can be gained by adding new members as the theory predicts.

The demand bargaining set: general characterization and application to majority games

The invention relates to a package handling and sorting system which sorts small packages according to destination, segregating those with the same destinations for combined shipments. The system depends on a unique combination of conveying equipment automatically controlled by programmed data processing units which utilize data obtained by scanning electronically readable package labels, as well as other information and detection equipment, to examine packages introduced into the system, and to transfer those consigned to the same location to vehicles routed to such locations. The system also generates an electronic trail of package movements, thus providing the capability to trace packages lost in transit.

On the Nucleolus as a Power Index

This paper argues that the nucleolus can compete with the Shapley value as a measure of P-power. It currently has more solid noncooperative foundations for majority games. It also identifies a set of attractive coalitions that are expected to form (unlike the Shapley value, which is based on the values of all coalitions) and does better than the Shapley value at some postulates of voting power. On the negative side, it may give the same payoff to players of different types or/and give a payoff of zero to players that are not dummies, though this behavior is ruled out for constant-sum weighted majority games.

The Paradox of New Members: Strategic Foundations and Experimental Evidence

Power indices suggest that adding new members to a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the original members may actually gain, a phenomenon known as the paradox of new members. We show that the paradox can occur as an equilibrium of a noncooperative bargaining game based on the Baron-Ferejohn (1989) model of legislative bargaining. We implement this game in the laboratory and find empirical support for the paradox.

Demand Commitment in Legislative Bargaining

Morelli (1999) provides a model of government formation in which the parties make payoff demands and the order of moves is chosen by the leading party. Morellis main proposition states that the ex post distribution of payoffs inside the coalition that forms is proportional to the distribution of relative ex ante bargaining power. We provide a counterexample in which the leading party is able to obtain the entire payoff; furthermore, there are coalitions for which proportional payoff division does not occur for any order of moves.