Dynamic matching and bargaining games: A general approach

This paper presents a new characterization result for competitive allocations in quasilinear economies. This result is informed by the analysis of non-cooperative dynamic search and bargaining games. Such games provide models of decentralized markets with trading frictions. A central objective of this literature is to investigate how equilibrium outcomes depend on the level of the frictions. In particular, does the trading outcome become Walrasian when frictions become small? Existing specifications of such games provide divergent answers. The characterization result is used to investigate what causes these differences and to generalize insights from the analysis of specific search and bargaining games.Dynamic Matching and Bargaining, Decentralized Markets, Non-cooperative Foundations of Competitive Equilibrium, Search Theory

Stable marriages and search frictions

Stable matchings are the primary solution concept for two-sided matching markets with nontransferable utility. We investigate the strategic foundations of stability in a decentralized matching market. Towards this end, we embed the standard marriage markets in a search model with random meetings. We study the limit of steady-state equilibria as exogenous frictions vanish. The main result is that convergence of equilibrium matchings to stable matchings is guaranteed if and only if there is a unique stable matching in the underlying marriage market. Whenever there are multiple stable matchings, sequences of equilibrium matchings converging to unstable, inefficient matchings can be constructed. Thus, vanishing frictions do not guarantee the stability and efficiency of decentralized marriage markets

Dynamic Matching and Bargaining Games : Towards a General Perspective

"Nature makes no jumps," according to a famous saying - but what about economies? Is economic welfare continuous in the size of the frictions of trading and do the welfare theorems hold approximately when frictions are small? We will look at a specific institution - a decentralized market - and at a specific problem in decentralized markets that might be induced by frictions - market power. We will ask: When frictions in the decentralized market are small, will the trading outcome be approximately efficient? Suppose you are looking for a job that pays a good wage. Most likely, you will have to exert effort to find some vacancies - these are the frictions of trade. Once you have found some vacancies, you will have to bargain with each single employer separately - this is the decentralized nature of the market: Despite the fact that there are potentially hundreds of other employers and workers in the market, within each negotiation, you will find yourself in a bilateral, one-on-one relationship. In this relationship, each of you might enjoy some market power and the outside option of searching for a new partner is of limited help since search is costly. In addition, both of you might not know how important a deal is to the other, and both of you are probably low-balling: The employer offers only low wages (since, unfortunately, he can hardly afford a new employee), while you ask for a high wage (since, actually, you do not really need the job right now). Is there reason to believe that a labor market can nevertheless be well approximated by a general equilibrium model, which assumes that wages will be market clearing and which predicts that the trading outcome is efficient? Situations as described before can be modeled as dynamic matching and bargaining games, which have been introduced by Gale (1987). This description is taken from the introduction of Chapter 1. He considers bilateral trade between one buyer and one seller and embeds it into a larger dynamic market game as follows: There is a continuum of buyers and sellers who are matched into pairs at the beginning of each period. Within each pair, they bargain over the terms of trade. The pairs are connected by allowing an unsuccessful trader to be matched with another partner in a new pair in the next period. However, there is a friction that makes waiting for the next period costly, so the integration of the market is not perfect. Here, this friction is an exogeneous probability δ ∈ (0,1) that a trader cannot enter the next period and exits (dies). Formally, we will look at the limit of the equilibrium outcomes of such setups when δ converges to zero. The first chapter of this thesis illustrates how market power in the bilateral bargaining situation can make the overall trading outcome inefficient. We show that if sellers can observe the valuation of the buyers, i.e., if information is symmetric, and if sellers make price offers, then the overall surplus is increasing in the size of frictions δ. In particular, the outcome does not become efficient when d converges to zero. The second chapter shows that the outcome does become efficient if sellers can not observe the valuation of the buyers, i.e., contrary to intuition, asymmetric information makes trading more efficient. We relate the positive convergence result in this second chapter to the informal reasoning that prices must be market clearing (implying an efficient trading outcome) since otherwise sellers would be rationed, giving them an incentive to offer lower prices. The third and final chapter of this thesis explores the general structure of the first two results. We observe that each specification of a dynamic matching and bargaining game together with a decreasing sequence of frictions defines a sequence of trading outcomes. We will discuss structural properties of such sequences, which on the one hand ensure that its limit is efficient, while relating on the other hand to economic properties of the underlying games. Thereby, we highlight a common cause behind existing positive convergence results, e.g., those by Gale (1987) and Satterthwaite and Shneyerov (2007). We also illustrate the structural properties of some other specifications for which trading outcomes fail to converge to efficiency, e.g., Serrano (2002) and DeFraja and Sakovics (2001). Although we will concentrate on the characterization of trading outcomes in the limit, it should not go unnoticed that the first two chapters provide characterizations of trading outcomes for every level of frictions. The first main result is that asymmetric information, i.e., consumer privacy, can be good for e¢ ciency in a market: In contrast to bilateral interaction, in a market the distribution of rents between the trading partner matters, and this distribution of rents is influenced by the degree of information. The second main result is the provision of a generalized Lerner formula for dynamic markets in which buyers can time their purchases. We show that the markup of prices over costs is proportional to the dynamic elasticity of demand. Nevo and Hendel (2006) empirically analyse the market for laundry detergents and show that the possibility to store these goods makes demand more elastic. Both results of these chapters are of direct relevance for economic policy evaluation

Stable Marriages and Search Frictions

We embed a two-sided matching market with non-transferable utility, a marriage market, into a random search model. We study steadystate equilibria and characterize the limit of the corresponding equilibrium matchings as exogenous search frictions become small. The central question is whether the set of such limit matchings coincides with the set of stable matchings for the underlying marriage market. We show that this is the case if and only if there is a unique stable matching. Otherwise, the set of limit matchings contains the set of all stable deterministic matchings, but also contains unstable random matchings. These unstable random matchings are Pareto dominated. Thus, vanishing frictions do not guarantee the eciency of decentralized marriage markets

Existence of steady-state equilibria in matching models with search frictions

We prove existence of steady-state equilibrium in a class of matching models with search frictions

Dynamic matching and bargaining games: A general approach

This paper presents a new characterization result for competitive allocations in quasilinear economies. This result is informed by the analysis of non-cooperative dynamic search and bargaining games. Such games provide models of decentralized markets with trading frictions. A central objective of this literature is to investigate how equilibrium outcomes depend on the level of the frictions. In particular, does the trading outcome become Walrasian when frictions become small? Existing specifications of such games provide divergent answers. The characterization result is used to investigate what causes these differences and to generalize insights from the analysis of specific search and bargaining games

Dynamic matching and bargaining games: A general approach

This paper presents a new characterization result for competitive allocations in quasilinear economies. This result is informed by the analysis of non-cooperative dynamic search and bargaining games. Such games provide models of decentralized markets with trading frictions. A central objective of this literature is to investigate how equilibrium outcomes depend on the level of the frictions. In particular, does the trading outcome become Walrasian when frictions become small? Existing specifications of such games provide divergent answers. The characterization result is used to investigate what causes these differences and to generalize insights from the analysis of specific search and bargaining games

The Balance Condition in Search-and-Matching Models

Most of the literature that studies frictional search-and-matching models with heterogeneous agents and random search investigates steady state equilibria. Steady state equilibrium requires, in particular, that the flows of agents into and out of the population of unmatched agents balance. We investigate the structure of this balance condition, taking agents' matching behavior as given. Building on the "fundamental matching lemma" for quadratic search technologies in Shimer and Smith (2000), we establish existence, uniqueness, and comparative statics properties of the solution to the balance condition for any search technology satisfying minimal regularity conditions. Implications for the existence and structure of steady state equilibria in the Shimer-Smith model and extensions thereof are noted. These reinforce the point that much of the structure of search-and-matching models with quadratic search technologies carries over to more general search technologies

Comprehensive Comparison of Various Techniques for the Analysis of Elemental Distributions in Thin Films

The present work shows results on elemental distribution analyses in Cu(In,Ga)Se2 thin films for solar cells performed by use of wavelength-dispersive and energy-dispersive X-ray spectrometry (EDX) in a scanning electron microscope, EDX in a transmission electron microscope, X-ray photoelectron, angle-dependent soft X-ray emission, secondary ion-mass (SIMS), time-of-flight SIMS, sputtered neutral mass, glow-discharge optical emission and glow-discharge mass, Auger electron, and Rutherford backscattering spectrometry, by use of scanning Auger electron microscopy, Raman depth profiling, and Raman mapping, as well as by use of elastic recoil detection analysis, grazing-incidence X-ray and electron backscatter diffraction, and grazing-incidence X-ray fluorescence analysis. The Cu(In,Ga)Se2 thin films used for the present comparison were produced during the same identical deposition run and exhibit thicknesses of about 2 μm. The analysis techniques were compared with respect to their spatial and depth resolutions, measuring speeds, availabilities, and detection limit