Competitive Equilibria in Decentralized Matching with Incomplete Information

This paper shows that all perfect Bayesian equilibria of a decentralized dynamic matching market with two-sided incomplete information of independent private values variety converge to competitive equilibria. Each buyer wants to purchase a bundle of heterogeneous, indivisible goods and each seller owns one unit of a heterogeneous indivisible good (as in Kelso and Crawford (1982) or Gul and Stacchetti (1999)). Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through bilateral bargaining between buyers and sellers. The paper considers a market in steady state. It is shown that as frictions, i.e., discounting and fixed costs of search become small, all equilibria of the market game converge to perfectly competitive equilibria.Bargaining, Search, Matching

Competitive Equilibria in Decentralized Matching with Incomplete Information

This paper shows that all perfect Bayesian equilibria of a dynamic matching game with two-sided incomplete information of independent private values variety are asymptotically Walrasian. Buyers purchase a bundle of heterogeneous, indivisible goods and sellers own one unit of an indivisible good. Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through a Bayesian mechanism proposal game. The paper considers a market in steady state. As discounting and the fixed cost of search become small, all trade takes place at a Walrasian price. However, a robust example is presented where the limit price vector is a Walrasian price for an economy where only a strict subsets of the goods in the original economy are traded, i.e, markets are missing at the limit. Nevertheless, there exists a sequence of equilibria that converge to a Walrasian equilibria for the whole economy where all markets are open.Conditional CAPM

Does the Conditional CAPM Work? Evidence from the Istanbul Stock Exchange

This paper tests whether the conditional CAPM accurately prices assets utilizing data from the Istanbul Stock Exchange (ISE) over the time period from February 1997 to April 2008. In our empirical analysis, we closely follow the methodology introduced in Lewellen and Nagel (2006). Our results show that the conditional CAPM fairs no better than the static counterpart in pricing assets. Although market betas do vary significantly over time, the intertemporal variation is not nearly large enough to drive average conditional alphas to zero.Conditional CAPM

Reputation in Long-Run Relationships

We model a long-run relationship as an infinitely repeated game played by two equally patient agents. In each period, the agents play an extensive-form game of perfect information. There is incomplete information about the type of player 1 while player 2’s type is commonly known. We show that a sufficiently patient player 1 can leverage player 2’s uncertainty about his type to secure his highest payoff in any perfect Bayesian equilibrium of the repeated game.Repeated Games, Reputation, Equal Discount Factor, Long-run Players. JEL Classification Numbers: C73, D83

Reputation in the Long-Run with Imperfect Monitoring

We study an infinitely repeated game where two players with equal discount factors play a simultaneous-move stage game. Player one monitors the stagegame actions of player two imperfectly, while player two monitors the pure stagegame actions of player one perfectly. Player one’s type is private information and he may be a “commitment type,” drawn from a countable set of commitment types, who is locked into playing a particular strategy. Under a full-support assumption on the monitoring structure, we prove a reputation result for games with locally nonconflicting interests or games with strictly conflicting interests: if there is positive probability that player one is a particular type whose commitment payoff is equal to player one’s highest payoff, consistent with the players’ individual rationality, then a patient player one secures this type’s commitment payoff in any Bayes-Nash equilibrium of the repeated game. In contrast, if the type’s commitment payoff is strictly less than player one’s highest payoff consistent with the players’ individual rationality, then the worst perfect Bayesian equilibrium payoff for a patient player one is equal to his minimax payoff.Repeated Games, Reputation, Equal Discount Factor, Long-run Players,imperfect Observation, Complicated Types, Finite Automaton JEL Classification Numbers: C73, D83

Bargaining and Reputation in Search Markets

In a two-sided search market agents are paired to bargain over a unit surplus. The matching market serves as an endogenous outside option for agents in a bargaining relationship. Behavioral agents are (strategically inflexible) commitment types that demand a constant portion of the unit surplus. The steady state frequency of behavioral types in the market is determined in equilibrium. We show, even if behavioral types are negligible, they substantially effect the terms of trade and efficiency. In an unbalanced market where the entering flow of one side is short, bargaining follows equilibrium play in a bargaining game with one-sided reputation, the terms of trade are determined by the commitment types on the short side, and commitment types improve efficiency. In a balanced market where the entering flows of the two sides are equal, bargaining follows equilibrium play in a bargaining game with two-sided reputation and commitment types cause inefficiency. An inefficient equilibrium with persistent delays and break-ups is constructed. The magnitude of inefficiency is determined by the inflexible demands of the commitment types and is independent of the fraction of the commitment types entering the market.Bargaining, Reputation, Search, Dynamic Matching, War-of-Attrition. JEL Classification Numbers: C78, D83

Orthogonal Projections Based on Hyperbolic and Spherical n-Simplex

In this paper, orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal projection. It is also given the perpendicular foots from a point to k-plane of hyperbolic and spherical n-space.Comment: 13 page

Runaway collisions in young star clusters. II. Numerical results

We present a new study of the collisional runaway scenario to form an intermediate-mass black hole (IMBH, MBH > 100 Msun) at the centre of a young, compact stellar cluster. The first phase is the formation of a very dense central core of massive stars (Mstar =~ 30-120 Msun) through mass segregation and gravothermal collapse. Previous work established the conditions for this to happen before the massive stars evolve off the main sequence (MS). In this and a companion paper, we investigate the next stage by implementing direct collisions between stars. Using a Monte Carlo stellar dynamics code, we follow the core collapse and subsequent collisional phase in more than 100 models with varying cluster mass, size, and initial concentration. Collisions are treated either as ideal, ``sticky-sphere'' mergers or using realistic prescriptions derived from 3-D hydrodynamics computations. In all cases for which the core collapse happens in less than the MS lifetime of massive stars (~3 Myr), we obtain the growth of a single very massive star (VMS, Mstar =~ 400-4000 Msun) through a runaway sequence of mergers. Mass loss from collisions, even for velocity dispersions as high as sigma1D ~ 1000 km/s, does not prevent the runaway. The region of cluster parameter space leading to runaway is even more extended than predicted in previous work because, in clusters with sigma1D > 300 km/s, collisions accelerate (and, in extreme cases, drive) core collapse. Although the VMS grows rapidly to > 1000 Msun in models exhibiting runaway, we cannot predict accurately its final mass. This is because the termination of the runaway process must eventually be determined by a complex interplay between stellar dynamics, hydrodynamics, and the stellar evolution of the VMS. [abridged]Comment: 23 pages, 24 figures. For publication in MNRAS. Paper revised to follow requests and suggestions of referee. Companion paper to Freitag, Rasio & Baumgardt 200