Double Implementation in a Market for Indivisible Goods with a Price Constraint

I consider the problem of assigning agents to objects where each agent must pay the price of the object he gets and prices must sum to a given number. The objective is to select an assignment-price pair that is envy-free with respect to the true preferences. I prove that the proposed mechanism will implement both in Nash and strong Nash the set of envy-free allocations. The distinguishing feature of the mechanism is that it treats the announced preferences as the true ones and selects an envy-free allocation with respect to the announced preferences.Indivisible Goods, Envy-Freeness, Implementation, Strong Nash Equilibrium

Repeated implementation with overlapping generations of agents

We study repeated implementation in a model with overlapping generations of agents. A social choice function selects an alternative in each period as a function of preferences of those agents who are alive in that period. When the agents’ preferences do not change during their lifetime, we show that any social choice function satisfying a mild unanimity condition is repeatedly implementable in subgame perfect equilibrium if there are at least three agents and they live sufficiently long. When the agents’ preferences change every period, we show that only efficient social choice functions can be repeatedly implementable if the agents live sufficiently long

Flat Tax Reform.The Baltics 2000 – 2007.

The paper presents an endogenous growth economy with a representation of the tax rate system in the Baltic countries. Assuming that government spending is a given fraction of output, the papershows how a flat tax system balanced between labor and corporate tax rates can be second best optimal. It then computes how actual Baltic tax reforms from 2000 to 2007 affect the growth rate and welfare, including transition dynamics. Comparing the actual reform effects to hypothetical tax experiments, it results that equal flat tax rates on personal and corporate income would have increased welfare in all three Baltic countries by 24% more on average than the actual reforms. This shows how equal, balanced, flat rate taxes can be optimal in both theory and practice. Further, movement towards a more equal balance between labor and capital tax rates, through changing just one tax rate, achieved almost as high or higher utility gains as in actual law for all three countries under both open and closed economy cases. This shows benefits of moving towards the optimum.tax reform, endogenous growth, transitional dynamics, flat taxes

Information disclosure by a seller in sequential first-price auctions

I study sequential first-price auctions where two items are sold to two bidders with private binary valuations. A seller, prior to the second auction, can publicly disclose some information about the outcome of the first auction. I characterize equilibrium strategies for various disclosure rules when the valuations of bidders are either perfectly positively or perfectly negatively correlated across items. I establish outcome equivalence between different disclosure rules. I find that it is optimal for the seller to disclose some information when the valuations are negatively correlated, whereas it is optimal not to disclose any information when the valuations are positively correlated. For most of the parameter values, the seller’s expected revenue is higher if the losing bid is disclosed. When only the winner’s identity is disclosed, the equilibrium is efficient whether the valuations are positively or negatively correlated

Repeated implementation with overlapping generations of agents

We study repeated implementation in a model with overlapping ge- nerations of agents. It is assumed that the preferences of agents do not change during their lifetime. A social choice function selects an alternative in each period as a function of the preferences of agents who are alive in that period. We show that any social choice function satisfying mild necessary conditions is repeatedly implementable in subgame perfect equilibrium if there are at least three agents and they live sufficiently long

Repeated Implementation

We prove that a social choice function is repeatedly implementable if and only if it is dynamically monotonic when the number of agents is at least three. We show how to test dynamic monotonicity by building an associated repeated game. It follows that a weaker version of Maskin monotonicity is necessary and sufficient among the social choice functions that are efficient. As an application, we show that utilitarian social choice functions, which can only be one-shot implemented with side-payments, are repeatedly implementable, as continuation payoffs can play the role of transfers. Under some additional assumptions, our results also apply when the number of agents is two

Taxation and the sustainability of collusion: ad valorem versus specific taxes

Assuming constant marginal cost, it is shown that a switch from specific to ad valorem taxation that results in the same collusive price has no effect on the critical discount factor required to sustain collusion. This result is shown to hold for Cournot oligopoly when collusion is sustained with Nash-reversion strategies or optimal-punishment strategies. In a Cournot duopoly model with linear demand and quadratic costs, it is shown that the critical discount factor is lower with an ad valorem tax than with a specific tax that results in the same collusive price. However, in contrast to Colombo and Labrecciosa (2013) it is shown that the revenue is always higher with an ad valorem tax than with a specific tax

Repeated implementation with overlapping generations of agents

We study repeated implementation in a model with overlapping ge- nerations of agents. It is assumed that the preferences of agents do not change during their lifetime. A social choice function selects an alternative in each period as a function of the preferences of agents who are alive in that period. We show that any social choice function satisfying mild necessary conditions is repeatedly implementable in subgame perfect equilibrium if there are at least three agents and they live sufficiently long

Essays on implementation and auctions

Consultable des del TDXTítol obtingut de la portada digitalitzadaAparte del primer capítulo que es la introducción, la tesis consiste de tres ensayos. En el segundo capítulo estoy analizando el problema de implementación en el mercado de bienes indivisibles. El modelo trata de asignar un conjunto de bienes indivisibles a los agentes donde cada agente tiene que pagar el precio por el bien que reciba y la suma de los precios tiene que ser igual a un valor determinado. Un ejemplo estándar es el problema de inquilinos donde ha de determinar quien recibe que habitación y que precio tiene que pagar dado que la suma de los precios de las habitaciones que los inquilinos pagan por un piso tiene que ser igual al arriendo. El objetivo consiste en, desconociendo las verdaderas valoraciones de los bienes que tengan los agentes, seleccionar la asignación de los bienes y los precios correspondientes que sea eficaz y que los agentes no tengan envidia. En general, los agentes no tendrán los incentivos para revelar sus verdaderas valuaciones sino otras que permitirían conseguir una asignación más favorable. Como consecuencia, los criterios de eficiencia y sin-envidia no estarán logrados. Sin embargo, he demostrado que las posibilidades de los agentes manipular las asignaciones y los precios están limitadas en el equilibrio. Es decir, he demostrado que seleccionando la asignación con los precios correspondientes que sea eficaz y sin-envidia con respecto a las valoraciones anunciadas, y no necesariamente verdaderas, asegura que en los equilibrios de Nash y Nash Fuerte la asignación seleccionada también es eficaz y sin-envidia con respecto a las valoraciones verdaderas. El tercer capítulo se trata de subastas cuando hay un comprador dominante que desalienta la participación de otros compradores en la subasta, y como la consecuencia los precios suban poco. El objetivo consiste en comparar varias formas de subastas que han sido diseñadas para fomentar la participación. En literatura se han propuesto una mezcla de la subasta inglesa y holandesa. El uso de la subasta holandesa beneficia a los participantes desfavorecidos y por lo tanto aumenta su participación y los ingresos del vendedor. Eso ocurre a coste de eficiencia, se puede ganar la subasta no teniendo la valoración más alta entre los compradores. Nosotros hemos propuesto una subasta alternativa para fomentar la participación y que consiste de la subasta inglesa en dos etapas. En la primera etapa se fija un precio de reserva y si nadie está dispuesto a pagarlo hay la segunda etapa sin precio de reserva. Los participantes potenciales en la segunda etapa aprenden que los que ya han entrado en la primera etapa no tienen las valoraciones altas, por lo tanto tienen mayor probabilidad de ganar. Eso, en vez, atrae mayor participación. Eligiendo un precio de reserva apropiado genera al vendedor más ingresos y además es más eficaz que la otra subasta. El último capítulo consiste del análisis empírico de las subastas que lleva a cabo la compañía «Bosques Estatales de Letonia» para vender el derecho de talar los árboles en los bosques del estado a empresas privadas. La compañía en cada subasta ofrece varios lotes de bosque, y los lotes se venden en secuencia. Los compradores que estén interesados en la dicha lote, compiten en la subasta inglesa. La teoría económica sugiere que el orden en que se venden los lotes es importante cuando los lotes son heterogéneos - los ingresos del vendedor son mayores si empiezan con los lotes más valiosos y venden en el orden decreciente por valor. Mi objetivo es contrastar la dicha hipótesis. El análisis econométrico prosigue en dos etapas. Primero, dado el supuesto que se vende la lote siempre y cuando su valor supera el precio inicial que el vendedor ha fijado, he estimado un modelo de Probit para inferir las valuaciones de los lotes. En la segunda etapa yo contrasto la hipótesis que el orden de la venta no afecta los ingresos del vendedor y no encuentro la evidencia para rechazar la dicha hipótesis.Besides the introductory chapter, my thesis consists of three essays. In the first essay of my thesis I consider the problem of assigning agents to indivisible objects in which each agent must pay the price of the object he gets and prices must sum to a given number. A standard example is the housemate problem where a group of tenants is sharing an apartment and they must decide who gets which room and how much each must pay, subject to the constraint that the sum of their contributions must equal the rent of the apartment. Previous research concentrated on mechanisms that select an assignment-price pair, which is envy-free and efficient, assuming the knowledge of agents' valuations. However, it is well known that for any mechanism agents have incentives to misrepresent their true valuations if it leads to higher utility. I treat the assignment problem as a game and prove that the mechanism, in which agents are simply required to announce their (possibly false) valuations and an envy-free allocation is selected with respect to these announced valuations, will implement the set of envy-free allocations both in Nash and strong Nash. This means that, in equilibrium, the selected allocation will be envy-free also with respect to the true preferences. I demonstrate that by choosing an efficient and envy-free allocation a social planner does not need to worry about strategic issues, that is, the scope for agents to manipulate the allocations is limited in equilibrium. This result provides a justification on strategic grounds for the use of social choice functions selecting envy-free allocations. The second essay studies auctions when the presence of a strong buyer deters the entry of other potential bidders, preventing competition in the auction and leading to a low sales price. For example, the issue arose during third-generation mobile communication licenses auctions where incumbent firms could effectively discourage entry by threatening to outbid new entrants. As a response, the so-called Anglo-Dutch auction has been proposed to promote entry since the Dutch auction favors weak bidders relative to a pure English auction. However, that is achieved at the cost of efficiency. We propose an alternative two-stage English auction in order to encourage entry. In the first stage there is a reserve price, and if nobody bids at that price, then a second stage is conducted without the reserve price. Potential entrants of the second stage learn that those who entered in the first stage but did not bid have low valuations. This provides incentives for weak bidders to enter in the second stage. We show that by setting an appropriate reserve price it is possible to generate higher revenues for the seller than in the Anglo-Dutch auction and at the same time maintain efficiency. The latter implies that the two-stage English auction is superior to the Anglo-Dutch auction both from the seller's perspective and from a social welfare point of view. Many real life auctions sell more than one object; objects are usually different and often are sold sequentially; hence the questions arise of how the order of sales affects revenue and what the optimal order of sales is. The last essay addresses these issues. It consists of an empirical analysis of auctions conducted by the Latvian state company selling rights to harvest timber in state forests. In each auction the company offers several lots of forest, and they are sold sequentially through oral, ascending price auctions. Theory suggests that the revenues of the seller are highest when objects are sold in the order of decreasing value. My objective is to test empirically this hypothesis. Since we do not observe the valuations of lots the bidders have, first I estimate them, using a discrete choice model, based on the assumption that a lot will be sold if and only if its valuation exceeds the reserve price. Next, I test the order of sales effect on the revenues of the seller. I do not reject the hypothesis that the order does not have effect on the revenues of seller