Essays in Mechanism Design

This thesis addresses problems in the area of mechanism design. In many settings in winch collective decisions are made, individuals' actual preferences are not publicly observable. As a result, individuals should be relied on to reveal this information. We are interested in an important application of mechanism design, which is the construction of desirable procedures for deciding upon resource allocation or task assignment. We make two main contributions. First, we propose a new mechanism for allocating a divisible commodity between a number of buyers efficiently and fairly. Buyers are assumed to behave as price-anticipators rather than as price-takers. The proposed mechanism is as parsimonious as possible, in the sense that it requires participants to report a one-dimensional message (scalar strategy) instead of an entire utility function, as required by Vickrey-Clarke-Groves (VCG) mechanisms. We show that this mechanism yields efficient allocations in Nash equilibria and moreover, that these equilibria are envy-free. Additionally, we present distinct results that this mechanism is the only simple scalar strategy mechanism that both implements efficient Nash equilibria and satisfies the no envy axiom of fairness. The mechanism's Nash equilibria are proven to satisfy the fairness properties of both Ranking and Voluntary Participation. Our second contribution is to develop optimal VCG mechanisms in order to assign identical economic "bads" (for example, costly tasks) to agents. An optimal VCG mechanism minimizes the largest ratio of budget imbalance to efficient surplus over all cost profiles. The optimal non-deficit VCG mechanism achieves asymptotic budget balance, yet the non-deficit requirement is incompatible with reasonable welfare bounds. If we omit the non-deficit requirement, individual rationality greatly changes the behavior of surplus loss and deficit loss. Allowing a slight deficit, the optimal individually rational VCG mechanism becomes asymptotically budget balanced. Such a phenomenon cannot be found in the case of assigning economic "goods.

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study.

07261 Abstracts Collection -- Fair Division

From 24.06. to 29.06.2007, the Dagstuhl Seminar 07261 % generate automatically ``Fair Division\u27\u27 % generate automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Truthful implementation and preference aggregation in restricted domains

In a setting where agents have quasi-linear utilities over social alternatives and a transferable commodity,we consider three properties that a social choice function may possess: truthful implementation (in dominant strategies); monotonicity in differences; and lexicographic affine maximization. We introduce the notion of a flexible domain of preferences that allows elevation of pairs and study which of these conditions implies which others in such domain. We provide a generalization of the theorem of Roberts (1979) [36] in restricted valuation domains. Flexibility holds (and the theorem is not vacuous) if the domain of valuation profiles is restricted to the space of continuous functions defined on a compact metric space, or the space of piecewise linear functions defined on an affine space, or the space of smooth functions defined on a compact differentiable manifold. We provide applications of our results to public goods allocation settings, with finite and infinite alternative sets

Algorithms for Competitive Division of Chores

We study the problem of allocating divisible bads (chores) among multiple agents with additive utilities, when money transfers are not allowed. The competitive rule is known to be the best mechanism for goods with additive utilities and was recently extended to chores by Bogomolnaia et al (2017). For both goods and chores, the rule produces Pareto optimal and envy-free allocations. In the case of goods, the outcome of the competitive rule can be easily computed. Competitive allocations solve the Eisenberg-Gale convex program; hence the outcome is unique and can be approximately found by standard gradient methods. An exact algorithm that runs in polynomial time in the number of agents and goods was given by Orlin. In the case of chores, the competitive rule does not solve any convex optimization problem; instead, competitive allocations correspond to local minima, local maxima, and saddle points of the Nash Social Welfare on the Pareto frontier of the set of feasible utilities. The rule becomes multivalued and none of the standard methods can be applied to compute its outcome. In this paper, we show that all the outcomes of the competitive rule for chores can be computed in strongly polynomial time if either the number of agents or the number of chores is fixed. The approach is based on a combination of three ideas: all consumption graphs of Pareto optimal allocations can be listed in polynomial time; for a given consumption graph, a candidate for a competitive allocation can be constructed via explicit formula; and a given allocation can be checked for being competitive using a maximum flow computation as in Devanur et al (2002). Our algorithm immediately gives an approximately-fair allocation of indivisible chores by the rounding technique of Barman and Krishnamurthy (2018).Comment: 38 pages, 4 figure

Essays on auction mechanisms and information in regulating pollution

Environmental regulation often has to be designed using asymmetric and incomplete information. Polluting firms, for instance, are normally privately better informed than the regulator with regard to the costs of reducing their emissions. However, even regulated firms may not have accurate information about their own abatement costs. The regulator is eager to know this private information in order to implement the most efficient environmental policy given the information at hand. In this thesis, I study, among other things, how auction mechanisms can be used to incentivize firms to reveal their private information to the regulator. One of the central questions in pollution control theory is whether a price instrument like an emission tax or a quantity instrument like tradeable permits is better in environmental or climate policy. In climate policy, emissions trading programs have been more popular both in Europe and the U.S. Also, auctions and in particular uniform price auction formats have been used as an initial allocation method in many trading programs. In the first two essays of this thesis, I study two-stage mechanisms for controlling pollution. In the first stage, the regulator conducts a generalized multi-unit Vickrey auction in order to allocate emission permits to firms. More importantly, the auction mechanism aims to collect private information from regulated firms. In the second stage, the regulator implements a range of environmental policy instruments, in the light of the information from the auction. In the first essay, the regulator uses either a constant price regulation or a program of tradeable permits with a fixed supply of permits. I show that firms have less incentive to bid sincerely in an auction when using a tax instrument compared to emissions trading. In the second essay, the regulator implements a tradeable permits program in the second stage, where the permit supply is elastic in price. Moreover, the permit market suffers some frictions, which increase the costs of trading. I derive incentive compatibility conditions for firms to bid sincerely in the first-stage auction given the regulation in the second stage and the various information structures. In the third essay, I compare the Vickrey and uniform price auction formats in allocations of emission allowances without an allowance resale market. Firms may collude and thus coordinate their bidding behavior in auctions. The Vickrey auction is efficient but the revenues decrease the more firms collude. However, the efficiency and revenues of uniform price auctions depend heavily on the coalition game and the structure of the market.Ympäristöpolitiikan ohjauskeinot on usein suunniteltava ilman täydellistä tietämystä päästöjen vähentämisen kustannuksista tai hyödyistä. Vaikka saastuttavien yritysten käsitys mahdollisista päästövähennysteknologioistaan voi olla epävarmaa, saattaa yrityksillä olla viranomaista parempi ymmärrys niiden kustannuksista. Viranomainen haluaisi saada yritysten tiedon käyttöönsä suunnitellakseen ohjauskeinot paremmin. Tässä väitöskirjassa tutkin muun muassa, miten huutokauppamekanismeja voidaan hyödyntää yritysten palkitsemiseksi, jotta ne paljastaisivat totuudenmukaisesti tietämyksensä viranomaiselle. Yksi keskeisimmistä ympäristökontrollin teoriaan liittyvistä kysymyksistä on perinteisesti ollut, tulisiko saastuttamista ohjata hintainstrumentilla kuten veroilla vai määräinstrumentilla kuten kaupattavilla päästöoikeuksilla. Ilmastopolitiikassa päästöoikeuksien kauppaohjelmat ovat olleet suositumpia niin Euroopassa kuin Yhdysvalloissa. Huutokauppaa on sovellettu monessa kauppaohjelmassa päästöoikeuksien alkujakomenetelmänä. Väitöskirjan kahdessa ensimmäisessä esseessä tutkin kaksivaiheista ympäristöohjausta. Ensimmäisessä vaiheessa viranomainen huutokauppaa päästöoikeuksia saastuttaville yrityksille hyödyntäen Vickrey huutokauppaa. Huutokauppamekanismin avulla viranomainen oppii yritysten puhdistuskustannuksista. Ohjausmekanismin toisessa vaiheessa viranomainen asettaa yrityksille erilaisia ympäristöpolitiikan ohjauskeinoja hyödyntäen oppimaansa. Ensimmäisessä esseessä viranomainen valitsee joko kiinteän hintaohjauksen tai päästöoikeuksien kaupan, jossa markkinoille jaettavien päästöoikeuksien määrä on kiinteä. Osoitan, että yritysten halukkuus paljastaa tietonsa totuudenmukaisesti huutokaupassa on rajoittuneempaa, kun käytössä on vero-ohjaus, kuin jos varsinaiseksi ohjauskeinoksi valitaan päästökauppa. Toisessa esseessä viranomainen valitsee toisen vaiheen ohjauskeinoksi päästöoikeuksien kaupan, jossa päästöoikeuksien tarjonta on joustava hinnan suhteen. Lisäksi päästöoikeusmarkkinoiden toimintaan liittyy kaupankäynnin kustannuksia lisäävää kitkaa. Johdan ehdot tietorakenteelle, jolloin yritykset paljastavat tietonsa totuudenmukaisesti huutokaupassa. Kolmannessa esseessä vertailen Vickrey huutokauppaa ja mm. EU:n päästökaupassa sovellettua yhtenäishinnoittelun huutokauppaa, kun yritykset eivät voi käydä kauppaa päästöoikeuksien jälkimarkkinoilla. Yritykset voivat kuitenkin koordinoida käyttäytymistään päästöoikeuksien huutokaupassa. Vickrey huutokauppa jakaa päästöoikeudet tehokkaasti, mutta huutokaupan tuotot alenevat yritysten koordinoidessa käyttäytymistään. Yhtenäishinnoittelun huutokaupan tulokset ovat riippuvaisia markkinarakenteesta ja koalitionmuodostuksen luonteesta

Some alternative approaches to persistent environmental problems and the measurement of inequality

Throughout this thesis, I assume consumption is an unstoppable economic force that limits policy intervention even when the level of consumption is destructive to the environment. A result is that traditional policy interventions – caps, trading schemes, and many taxes and subsidies directly on polluting outcomes are too costly to implement in terms of political, social, or measured economic costs. However, I also assume that a limited regulator still seeks to reduce the environmental fallout. I then study some policy options that fit within the consumer’s limited expectations of regulatory reach. Deciding to use limited policy interventions is not intended to replace other efforts. I explore part of what could be a joint effort and emphasise perhaps short-term, stopgap responses to opposition. This is proposed because not all environmental problems can wait for justice or the environmental Kuznets curve to turn in their favour. Once we are free from trying to devise ways to implement first-best environmental policies, various alternatives emerge. First, I explore environmental regulation when some pollutant is necessary. Necessity restricts policy to determining where it must occur, and the analysis becomes one of whether clustering or dispersion of an activity leads to less total damages. A revision to current regulatory approaches results. I then discuss improving recycling, a necessity to transition to a circular economy model. I find there is an optimal division of effort between producers and recyclers and propose an incentive structure to improve product design for recyclability. I then review how U.S. coal power plants use technology to reduce sulphur dioxide emissions. The objective is to derive lessons for the next great energy transition. Finally, I include a foray into economic growth, inequality, and their measurement in two chapters on the premise that there is a link between the fate of the environment and ours