Gradual Negotiations and Proportional Solutions

I characterize the proportional N-person bargaining solutions by individual rationality, translation invariance, feasible set continuity, and a new axiom - interim improvement. The latter says that if the disagreement point d is known, but the feasible set is not - it may be either S or T, where S is a subset of T - then there exists a point d' in S, d' > d, such that replacing d with d' as the disagreement point would not change the final bargaining outcome, no matter which feasible set will be realized, S or T. In words, if there is uncertainty regarding a possible expansion of the feasible set, the players can wait until it is resolved; in the meantime, they can find a Pareto improving interim outcome to commit to - a commitment that has no effect in case negotiations succeed, but promises higher disagreement payoffs to all in case negotiations fail prior to the resolution of uncertainty.Bargaining; Proportional solutions

Fairness, Efficiency, and the Nash Bargaining Solution

A bargaining solution balances fairness and efficiency if each player's payoff lies between the minimum and maximum of the payoffs assigned to him by the egalitarian and utilitarian solutions. In the 2-person bargaining problem, the Nash solution is the unique scale-invariant solution satisfying this property. Additionally, a similar result, relating the weighted egalitarian and utilitarian solutions to a weighted Nash solution, is obtained. These results are related to a theorem of Shapley, which I generalize. For n>=3, there does not exist any n-person scale-invariant bargaining solution that balances fairness and efficiency.Bargaining; fairness; efficiency; Nash solution

Endogenous Bid Rotation in Repeated Auctions

I study collusion between two bidders in a general symmetric IPV repeated auction, without communication, side transfers, or public randomization. I construct a collusive scheme, endogenous bid rotation, that generates a payoff larger than the bid rotation payoff.Auctions; Bid rotation; Collusion; Repeated games

Bribing in second-price auctions

An IPV 2-bidder second-price auction is preceded by two rounds of bribing: prior to the auction each bidder can try to bribe his rival to depart from the auction, so that he (the briber) will become the sole participant and obtain the good for the reserve price. Bribes are offered sequentially according to an exogenously given order - there is a first mover and a second mover. I characterize the unique efficient collusive equilibrium in monotonic strategies; in it, the second mover extracts the entire collusive gain. This equilibrium remains an equilibrium even when valuations are interdependent, and if they are separable then the full surplus extraction result continues to hold. Additionally, a family of pooling equilibria is studied, in which all the types of the first mover offer the same bribe.Second-price auctions, collusion, bribing, signaling, surplus extraction

Bribing in First-Price Auctions: Corrigendum

We clarify the sufficient condition for a trivial equilibrium to exist in the model of Rachmilevitch (2013). Rachmilevitch (2013), henceforth R13, studies the following game. Two ex ante identical players are about to participate in an independent-private-value first-price, sealed bid auction for one indivisible object. After the risk-neutral players learn their valuations but prior to the actual auction, player 1 can offer a take-it-or-leave-it (TIOLI) bribe to his opponent in exchange for the opponent dropping out of the contest. If the offer is accepted, player 1 is the only bidder and obtains the item for free; otherwise, both players compete non-cooperatively in the auction as usual. This is called the first-price TIOLI game.1 R13 shows that under the restriction to continuous and monotonic bribing strategies for player 1, any equilibrium of this game must be trivial—the equilibrium bribing function employed by player 1, if it is continuous and non-decreasing, must be identically zero. In this note, we clarify the sufficient conditions under which a trivial equilibrium exists. These are less stringent than originally proposed

The Midpoint-Constrained Egalitarian Bargaining Solution

A payoff allocation in a bargaining problem is midpoint dominant if each player obtains at least one n-th of her ideal payoff. The egalitarian solution of a bargaining problem may select a payoff configuration which is not midpoint dominant. We propose and characterize the solution which selects for each bargaining problem the feasible allocation that is closest to the egalitarian allocation, subject to being midpoint dominant. Our main axiom, midpoint monotonicity, is new to the literature; it imposes the standard monotonicity requirement whenever doing so does not result in selecting an allocation which is not midpoint dominant. In order to prove our main result we develop a general extension theorem for bargaining solutions that are order-preserving with respect to any order on the set of bargaining problems

Gross substitution and complementarity are not symmetric relations

I construct an example of well-behaved (convex, continuous, monotone) preferences over two goods, x and y, such that x is a gross substitute for y but y is a gross complement for x. A sufficient (but not necessary) condition for preventing this "pathology" is that the demand for either good be a strictly increasing function of income.Substitution; complementarity; consumer theory;

Disagreement point axioms and the egalitarian bargaining solution

Bargaining, Egalitarian solution, Disagreement point monotonicity,

A Behavioral Arrow Theorem

Abstract In light of research indicating that individual behavior may violate standard rationality assumptions, we introduce a model of preference aggregation in which neither individual nor collective preferences must satisfy transitivity or other coherence conditions. We introduce an ordinal rationality measure to compare preference relations in terms of their level of coherence. Using this measure, we introduce a new axiom, monotonicity, which requires the collective preference to become more rational when the individual preferences become more rational. We show that no collective choice rule satisfies monotonicity and the standard Arrovian assumptions: unrestricted domain, weak Pareto, independence of irrelevant alternatives, and nondictatorship

The midpoint-constrained egalitarian bargaining solution

Karos D, Rachmilevitch S. The midpoint-constrained egalitarian bargaining solution. Mathematical Social Sciences. 2019;101:107-112