Shiran Rachmilevitch

Bribing in first-price auctions

I study a symmetric 2-bidder IPV first-price auction prior to which one bidder can offer his rival a bribe in exchange for the latterʼs abstention. I focus on pure and undominated strategies, and on continuous monotonic equilibria—equilibria in which the bribing function is continuous and nondecreasing. When types are distributed continuously on the unit interval, such an equilibrium, if it at all exists, is necessarily trivial—its bribing function is identically zero. I provide a sufficient condition for its existence and sufficient conditions for its nonexistence. When the minimum type is strictly positive, a non-trivial equilibrium may exist, but it must be pooling. I provide a sufficient condition for the existence of such an equilibrium. When types are distributed continuously on the unit interval and dominated strategies are allowed, a non-trivial non-pooling equilibrium exists, at least under the uniform prior.

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.

First-best collusion without communication

I study a 2-bidder infinitely repeated IPV first-price auction without transfers, communication, or public randomization, where each bidderʼs valuation can assume, in each of the (statistically independent) stage games, one of three possible values. Under certain distributional assumptions, the following holds: for every ϵ>0 there is a nondegenerate interval Δ(ϵ)⊂(0,1), such that if the biddersʼ discount factor belongs to Δ(ϵ), then there exists a Perfect Public Equilibrium with payoffs ϵ-close to the first-best payoffs.

Efficiency-free characterizations of the Kalai–Smorodinsky bargaining solution

Abstract Roth (1977) axiomatized the Nash (1950) bargaining solution without Pareto optimality, replacing it by strong individual rationality in Nash’s axiom list. In a subsequent work (Roth, 1979) he showed that when strong individual rationality is replaced by weak individual rationality, the only solutions that become admissible are the Nash and the disagreement solutions. In this paper I derive analogous results for the Kalai–Smorodinsky (1975) bargaining solution.

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.

A characterization of the Kalai–Smorodinsky bargaining solution by disagreement point monotonicity

We provide a new axiomatization of the Kalai–Smorodinsky bargaining solution, which replaces the axiom of individual monotonicity by disagreement point monotonicity and a restricted version of Nash’s IIA.

Axiomatizations of the equal-loss and weighted equal-loss bargaining solutions

The 2-person equal-loss bargaining solution (Chun Econ Lett 26:103–106, 1988) is characterized on the basis of the following axioms: concavity, Pareto optimality, symmetry, and restricted monotonicity. Replacing symmetry by strong individual rationality and extending the bargaining domain so that it contains a degenerate problem that consists solely of the disagreement point results in a characterization of a weighted version of the equal-loss solution.

Duality, area-considerations, and the Kalai-Smorodinsky solution

We introduce a new solution concept for 2 -person bargaining problems, which can be considered as the dual of the Equal-Area solution (EA) (see Anbarciźand Bigelow (1994)). Hence, we call it the Dual Equal-Area solution (DEA). We show that the point selected by the Kalai-Smorodinsky solution (see Kalai and Smorodinsky (1975)) lies in between those that are selected by EA and DEA. We formulate an axiom-area-based fairness-and offer three characterizations of the Kalai-Smorodinsky solution in which this axiom plays a central role.

Symmetry and approximate equilibria in games with countably many players

I study games with countably many players, each of whom has finitely many pure strategies. The following are constructed: (i) a game that has a strong