Theses

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Start date: 2020Subject: search.filters.subject.Mechanism Design

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    Bilateral Trade and Partnership with Loss Averse Agents
    (Indian Statistical Institute,Delhi, 2023-07) Dalakoti, Harshika
    This thesis consists of three essays on bilateral trading and partnership with loss averse agents. All the three essays consider the same model where two loss averse agents (Tversky and Kahneman (1991), K ̈oszegi and Rabin (2006)) hold some shares of an asset and now want to dissolve the partnership. The first chapter shows the impossibility result for loss averse agents i.e. there does not exist a feasible, incentive compatible and individually rational mechanism which can implement an efficient outcome. The second chapter talks about the dissolution mechanism intermediated by a broker which is optimum in a sense different from ex-post efficiency. Set of all optimal mechanisms are characterised for the bilateral trade as well as partner- ship model. The third chapter shows non-existence of a dissolution mechanism which is incentive-compatible, interim individually rational, budget-balanced and efficient for equal share partnership when the degree of loss aversion exceeds a cut off, which is in contrast to Cramton et al. (1987) result
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    Essays in the theory of allocation and voting
    (Indian Statistical Institute, Delhi, 2023-10) Singh, Ankit
    This thesis consists of two essays on allocation theory and one on voting theory. The first chapter analyses preference domains (called priority domains) where every strategy proof, non-bossy and neutral allocation rule is a priority rule. It considers two versions of neutrality: unanimous profile neutrality or UPN neutrality where the neutrality axiom applies only to preference profiles where all agents have a common preference ordering and full neutrality or FN neutrality, where the neutrality axiom applies generally. We show that a very simple condition characterises priority domains under the UPN axiom. If these domains satisfy a mild richness condition, they must be the universal domain. The class of priority domains under the FN axiom is larger than those satisfying only UPN. We identify an FN-priority domain that is of order 1 n relative to the universal domain. The second chapter analyses preference domains in voting environments where every strategy proof random social choice functions satisfying unanimity is a random dictatorships. We call these random-dictatorial domains. Pramanik (2015) identifies a class of domains called P-domains which are dictatorial i.e. every deterministic strategy proof social choice functions on these domains satisfying unanimity, is dictatorial. The main result of this chapter is that P-domain is random-dictatorial. A consequence of this result is that circular domains (Sato (2010)) are also random-dictatorial. The minimum size of a random-dictatorial domain satisfying minimal richness is shown to be twice the number of alternatives. This is the same as the corresponding lower bound for dictatorial domains. Our result stands in contrast to those in Chatterji et al. (2014) who showed that linked domains are not random-dictatorial. Linked domains were shown to be dictatorial in Aswal et al. (2003). The third chapter attempts to provide a justification of the non-bossiness axiom which is pervasive in the allocation literature. It has been criticised by Thomson (2016) on the grounds that it cannot be defended by appealing to various strategic and normative criteria. We show that in some special cases, non-bossiness is a simplifying assumption that can be imposed without loss of generality by an expected welfare maximising planner in a symmetric environment. We consider the case of three objects and three agents with a planner whose goal is to maximise the expected sum of welfare with respect to a uniform prior. We show that for every strategy proof, neutral and efficient allocation rule, there exists a strategy-proof, neutral and non-bossy allocation rule which yields the same expected welfare. We conjecture that this is true for an arbitrary number of agents. For the general case, we are able to show an equivalence in terms of expected welfare for a special class of bossy allocation rules
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    Local vs Global Incentive Compatibility in Mechanism Design
    (Indian Statistical Institute, Kolkata, 2022-06) Kumar, Ujjwal
    We study models in mechanism design theory where agents have private information (called a type) which has to be elicited by the mechanism designer. The cornerstone of the theory is the collection of incentive compatibility constraints which ensure that agents do not have incentives to misreport their types (or manipulate). The standard assumption in the theory is that the proposed mechanism must be immune to all possible misreports of agents. There is, however considerable experimental evidence that agents often choose to lie credibly by only misreporting to types that are “near” or “close to” their true types. Therefore, it is natural to consider models where an agent of a particular type can only misreport to an arbitrary set of pre-specified “local” types. We consider such models and provide answers to the following question: under what circumstances is immunity to misreporting via a “local” type (local incentive compatibility) equivalent to immunity to misreporting via an arbitrary type (incentive compatibility)? This thesis consists of five chapters. We provide a brief introduction of the chapters below. Chapter 2 considers a voting model where each voter’s type is her strict preference. The type graph for a voter is a graph whose vertices are the possible types of the voter. Two vertices are connected by an edge in the graph if the associated types are “local”. Local-Global equivalence (LGE) is satisfied if local strategy-proofness implies strategy-proofness for deterministic social choice functions. This chapter identifies a condition on the graph that characterizes LGE. Our notion of “localness” is perfectly general - we use this feature of our model to identify notions of localness according to which various models of multi-dimensional voting satisfy LGE. Finally, we show that LGE for deterministic social choice functions does not imply LGE for random social choice functions. Chapter 3 considers the same voting framework as in Chapter 2 except that each agent’s type is her weak preference, that is, preferences that can admit indifference. We provide a condition that is sufficient for LGE and another condition that is necessary. Moreover, the “gap” between the two conditions is small (in the sense that both conditions boil down to the single condition identified in Chapter 2 that characterizes LGE for the case of strict preferences). We use the sufficiency result to propose notions of localness according to which environments with the domain of single-plateaued preferences and the domain of all weak preferences, satisfies LGE. Chapter 4 identifies a condition on preference domains that ensures that every locally strategy- proof and unanimous random social choice function is also strategy-proof. Furthermore every unanimous, locally strategy-proof deterministic social choice function is also group strategy-proof. The condition identified is significantly weaker than the characterization condition for local-global equivalence without unanimity in Chapter 2. Chapter 5 considers standard mechanism design problem where a set of agents have valuations for each alternative in a finite set of alternatives. Based on these valuations, the planner has to select an alternative to be shared by all the agents and some payment for each agent. Such a decision scheme is called a 2 mechanism. Agents evaluate their net utilities by means of quasilinear utility functions. A mechanism is incentive compatible (IC) if no agent can increase his/her net utility by misreporting his/her type. We explore the equivalence of pointwise local incentive compatibility (PLIC) (as defined in Carroll [12]) and incentive compatibility (IC) in non-convex type-spaces. We provide a sufficient condition on a type-space called minimal richness for the said equivalence. Using this result, we show that PLIC and IC are equivalent on large class of non-convex type-spaces such as type-spaces perturbed by modularity and concave-modularity. The gross substitutes type-space and the generalized gross substitutes and complements type-space are important examples of type-spaces perturbed by modularity and concave-modularity, respectively. Finally, we provide a geometric property consisting of three conditions for the equivalence of PLIC and IC, and show that all the conditions are indispensable. Chapter 6 studies standard mechanism design problems when agents have quasi linear utility function. We consider ordinal type-spaces, that is, possible valuations of each agent come from an underlying preference structure. This chapter explores the relation between different notions of local incentive compatibility (LIC) and incentive compatibility (IC) on ordinal type-spaces. In this context, we introduce the notion of ordinal local global equivalent (OLGE) and cardinal local global equivalent (CLGE) environments. First, we establish the equivalence between the two environments on strict ordinal type-spaces. Next, we consider ordinal type-spaces admitting indifference. We introduce the notion of almost everywhere IC and strong LIC, and provide a necessary and sufficient condition on ordinal type spaces for their equivalence. Finally, we provide results on how to (minimally) check the IC property of a given mechanism on any ordinal type-space and show that local types along with the boundary types form a minimal set of incentive constraints that imply full incentive compatibility.
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    Essays in Multidimensional Mechanism Design
    (Indian Statistical Institute,Delhi, 2021-05) Paramahamsa, Kolagani
    This thesis analyzes three problems where a monopolistic seller is selling to an agent with multidimensional private information. While our understanding of such problems is comprehensive if the agent's private information is one-dimensional, problems with multidimensional private information are known to be ubiquitous but analytically notorious. The three chapters in this thesis make progress in understanding optimal mechanism design in such multidimensional screening problems. In the first problem, the seller is selling an object to an agent who exhibits behavioral preferences, in a departure from the standard rational models. Behavioral preferences arise because the agent is budget constrained and needs approval from a manager for outcomes beyond the budget. Such lexicographic decision-making and dierent preferences of the agent and the manager make this a two-dimensional mechanism design problem where the agent's aggregate choice shows intransitivity. We characterize the expected revenue-maximizing mechanism of the seller in this problem. In the second problem, the seller is selling a pair of goods to the agent. The agent demands two goods in a particular ratio; the bundle's valuation and the ratio are the buyer's private information. We characterize the expected revenue-maximizing mechanism of the seller in this problem. In the third model, a seller is selling an object with an inherent value and an attribute value to the agent. The value of the attribute depends on the level of the attribute, which is commonly observed by the seller and the agent, and is contractible. Since the attribute's level is not known when signing the contract, the seller can o er contingent contracts. We characterize the expected revenue-maximizing contingent contract. In particular, we show that the expected revenue-maximizing contract is deterministic under reasonable restrictions on priors.