Matching Items (5)

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School choice: Mixed strategy Nash equilibrium as a way to predict preference reporting

Description

Since Abdulkadiroglu and Sonmez’s influential paper in 2003 that
merges school choice and mechanism design, research in the rapidly
growing school choice literature has been mainly focused on the
design

Since Abdulkadiroglu and Sonmez’s influential paper in 2003 that
merges school choice and mechanism design, research in the rapidly
growing school choice literature has been mainly focused on the
design of mechanisms with desirable properties or more realistic
assumptions. However, lab experiments often show that subjects do
not report preferences according to the experimenters’ expectation,
and the experiments rarely provide an in-depth analysis of why the
subjects behave in such confounding ways. My thesis formulates
preference reporting in school choice as a game by incorporating a
payoff schedule and proposes mixed strategy Nash equilibrium as a
way to predict preference reporting.

Contributors

Agent

Created

Date Created
  • 2019-05

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Three essays in economics

Description

This dissertation presents three essays in economics. Firstly, I study the problem of allocating an indivisible good between two agents under incomplete information. I provide a characterization of mechanisms that

This dissertation presents three essays in economics. Firstly, I study the problem of allocating an indivisible good between two agents under incomplete information. I provide a characterization of mechanisms that maximize the sum of the expected utilities of the agents among all feasible strategy-proof mechanisms: Any optimal mechanism must be a convex combination of two fixed price mechanisms and two option mechanisms. Secondly, I study the problem of allocating a non-excludable public good between two agents under incomplete information. An equal-cost sharing mechanism which maximizes the sum of the expected utilities of the agents among all feasible strategy-proof mechanisms is proved to be optimal. Under the equal-cost sharing mechanism, when the built cost is low, the public good is provided whenever one of the agents is willing to fund it at half cost; when the cost is high, the public good is provided only if both agents are willing to fund it. Thirdly, I analyze the problem of matching two heterogeneous populations. If the payoff from a match exhibits complementarities, it is well known that absent any friction positive assortative matching is optimal. Coarse matching refers to a situation in which the populations into a finite number of classes, then randomly matched within these classes. The focus of this essay is the performance of coarse matching schemes with a finite number of classes. The main results of this essay are the following ones. First, assuming a multiplicative match payoff function, I derive a lower bound on the performance of n-class coarse matching under mild conditions on the distributions of agents' characteristics. Second, I prove that this result generalizes to a large class of match payoff functions. Third, I show that these results are applicable to a broad class of applications, including a monopoly pricing problem with incomplete information, as well as to a cost-sharing problem with incomplete information. In these problems, standard models predict that optimal contracts sort types completely. The third result implies that a monopolist can capture a large fraction of the second-best profits by offering pooling contracts with a small number of qualities.

Contributors

Agent

Created

Date Created
  • 2011

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Fundamental limits in data privacy: from privacy measures to economic foundations

Description

Data privacy is emerging as one of the most serious concerns of big data analytics, particularly with the growing use of personal data and the ever-improving capability of data analysis.

Data privacy is emerging as one of the most serious concerns of big data analytics, particularly with the growing use of personal data and the ever-improving capability of data analysis. This dissertation first investigates the relation between different privacy notions, and then puts the main focus on developing economic foundations for a market model of trading private data.

The first part characterizes differential privacy, identifiability and mutual-information privacy by their privacy--distortion functions, which is the optimal achievable privacy level as a function of the maximum allowable distortion. The results show that these notions are fundamentally related and exhibit certain consistency: (1) The gap between the privacy--distortion functions of identifiability and differential privacy is upper bounded by a constant determined by the prior. (2) Identifiability and mutual-information privacy share the same optimal mechanism. (3) The mutual-information optimal mechanism satisfies differential privacy with a level at most a constant away from the optimal level.

The second part studies a market model of trading private data, where a data collector purchases private data from strategic data subjects (individuals) through an incentive mechanism. The value of epsilon units of privacy is measured by the minimum payment such that an individual's equilibrium strategy is to report data in an epsilon-differentially private manner. For the setting with binary private data that represents individuals' knowledge about a common underlying state, asymptotically tight lower and upper bounds on the value of privacy are established as the number of individuals becomes large, and the payment--accuracy tradeoff for learning the state is obtained. The lower bound assures the impossibility of using lower payment to buy epsilon units of privacy, and the upper bound is given by a designed reward mechanism. When the individuals' valuations of privacy are unknown to the data collector, mechanisms with possible negative payments (aiming to penalize individuals with "unacceptably" high privacy valuations) are designed to fulfill the accuracy goal and drive the total payment to zero. For the setting with binary private data following a general joint probability distribution with some symmetry, asymptotically optimal mechanisms are designed in the high data quality regime.

Contributors

Agent

Created

Date Created
  • 2016

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Essays in Mechanism Design

Description

I study split-pie bargaining problems between two agents. In chapter two, the types of both agents determine the value of outside options -- I refer to these as interdependent outside

I study split-pie bargaining problems between two agents. In chapter two, the types of both agents determine the value of outside options -- I refer to these as interdependent outside options. Since a direct mechanism stipulates outcomes as functions of agents' types, a player can update beliefs about another player’s type upon receiving a recommended outcome. I term this phenomenon as information leakage. I discuss binding arbitration, where players must stay with a recommended outcome, and non-binding arbitration, where players are not obliged to stay with an allocation. The total pie is reduced if the outcome is an outside option. With respect to efficiency, I derive a necessary and sufficient condition for first best mechanisms. These are mechanisms that assign zero probability to outside options for every report received. The condition describes balanced forces in conflict (outside options) and is the same in the cases of binding and non-binding arbitration. I also show a strong link between conflict and information: when conflict exists, information leakage occurs. Hence, non-binding arbitration may seem more restrictive than binding arbitration. To analyze why this is the case, I solve for second best mechanisms with binding arbitration and find a condition under which they can be implemented under non-binding arbitration. Thus, I show that non-binding arbitration can be as effective as binding arbitration in terms of efficiency. I also examine whether the equivalence between binding and non-binding arbitration can cease to hold, and provide analysis of why this happens. In chapter three, the bargaining problem entails no uncertainty but rather envy. Players can feel envy about the allocation of the other player. The Nash Bargaining solution is obtained in this context and some comparative statics are shown. The introduction of envy makes the more envious party a tougher negotiator.

Contributors

Agent

Created

Date Created
  • 2020

Development of horizontal coordination mechanisms for planning agricultural production

Description

Agricultural supply chains are complex systems which pose significant challenges beyond those of traditional supply chains. These challenges include: long lead times, stochastic yields, short shelf lives and a highly

Agricultural supply chains are complex systems which pose significant challenges beyond those of traditional supply chains. These challenges include: long lead times, stochastic yields, short shelf lives and a highly distributed supply base. This complexity makes coordination critical to prevent food waste and other inefficiencies. Yet, supply chains of fresh produce suffer from high levels of food waste; moreover, their high fragmentation places a great economic burden on small and medium sized farms.

This research develops planning tools tailored to the production/consolidation level in the supply chain, taking the perspective of an agricultural cooperative—a business model which presents unique coordination challenges. These institutions are prone to internal conflict brought about by strategic behavior, internal competition and the distributed nature of production information, which members keep private.

A mechanism is designed to coordinate agricultural production in a distributed manner with asymmetrically distributed information. Coordination is achieved by varying the prices of goods in an auction like format and allowing participants to choose their supply quantities; the auction terminates when production commitments match desired supply.

In order to prevent participants from misrepresenting their information, strategic bidding is formulated from the farmer’s perspective as an optimization problem; thereafter, optimal bidding strategies are formulated to refine the structure of the coordination mechanism in order to minimize the negative impact of strategic bidding. The coordination mechanism is shown to be robust against strategic behavior and to provide solutions with a small optimality gap. Additional information and managerial insights are obtained from bidding data collected throughout the mechanism. It is shown that, through hierarchical clustering, farmers can be effectively classified according to their cost structures.

Finally, considerations of stochastic yields as they pertain to coordination are addressed. Here, the farmer’s decision of how much to plant in order to meet contracted supply is modeled as a newsvendor with stochastic yields; furthermore, options contracts are made available to the farmer as tools for enhancing coordination. It is shown that the use of option contracts reduces the gap between expected harvest quantities and the contracted supply, thus facilitating coordination.

Contributors

Agent

Created

Date Created
  • 2015