Economics

Auction theories are believed to provide a better selling opportunity for the resources to be allocated. Various organizations have taken measures to increase trust among participants towards their auction system, but trust alone cannot ensure a high level of participation. We propose a new type of auction system which takes advantage of lucky draw and gambling addictions to increase the engagement level of candidates in an auction. Our system makes use of security features present in existing auction systems for ensuring fairness and maintaining trust among participants.

Sanctioned by its constitution, India is home to an elaborate affirmative action program for allocation of public jobs, where historically discriminated groups are protected with vertical reservations implemented as "set asides," and other disadvantaged groups are protected with horizontal reservations implemented as "minimum guarantees." Concurrent implementation of these two policies with overlapping beneficiaries makes this program more complex than others elsewhere. An allocation mechanism mandated by the Supreme Court judgement Anil Kumar Gupta vs. Uttar Pradesh (1995) suffers from a number of anomalies, including disadvantaged candidates losing positions to privileged candidates of lower merit, triggering countless litigations and disarray in the country. Foretelling a recent reform in India, we propose an alternative mechanism that resolves all anomalies, and uniquely characterize it with desiderata reflecting the laws of India. Subsequently reinvented with an August 2020 High Court judgement and mandated for the state of Gujarat, our mechanism is endorsed for India with a December 2020 judgement of the Supreme Court.

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling.

In social-learning settings where individuals receive private signals and observe network neighbors' actions, the network structure often obstructs information aggregation. We consider sequential social learning with rational agents and Gaussian signals and ask how the efficiency of signal aggregation changes with the network. Rational actions in our model admit a signal-counting interpretation of accuracy, which lets us compare the aggregative efficiency of social learning across networks. Learning is very inefficient in a class of networks where agents move in generations and observe the previous generation. Generations after the first contribute very little additional information, even when generations are arbitrarily large.

We explore an application of all-pay auctions to model trade wars and territorial annexation. Specifically, in the model we consider the expected resource, production, and aggressive (military/tariff) power are public information, but actual resource levels are private knowledge. We consider the resource transfer at the end of such a competition which deprives the weaker country of some fraction of its original resources. In particular, we derive the quasi-equilibria strategies for two country conflicts under different scenarios. This work is relevant for the ongoing US-China trade war, and the recent Russian capture of Crimea, as well as historical and future conflicts.

In an auction each party bids a certain amount and the one which bids the highest is the winner. Interestingly, auctions can also be used as models for other real-world systems. In an all pay auction all parties must pay a forfeit for bidding. In the most commonly studied all pay auction, parties forfeit their entire bid, and this has been considered as a model for expenditure on political campaigns. Here we consider a number of alternative forfeits which might be used as models for different real-world competitions, such as preparing bids for defense or infrastructure contracts.

In this paper, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows a hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed recently in [1], we prove that although the marketers are in competition and therefore create tension in the network, the network reaches a consensus. Exploiting this key result, we propose a coopetition marketing strategy which combines the one-shot Nash equilibrium actions and a policy of no advertising. Under reasonable sufficient conditions, it is proved that the proposed coopetition strategy profile Pareto-dominates the one-shot Nash equilibrium strategy. This is a very encouraging result to tackle the much more challenging problem of designing Pareto-optimal and equilibrium strategies for the considered dynamical marketing game.

This work deals with the implementation of social choice rules using dominant strategies for unrestricted preferences. The seminal Gibbard-Satterthwaite theorem shows that only few unappealing social choice rules can be implemented unless we assume some restrictions on the preferences or allow monetary transfers. When monetary transfers are allowed and quasi-linear utilities w.r.t. money are assumed, Vickrey-Clarke-Groves (VCG) mechanisms were shown to implement any affine-maximizer, and by the work of Roberts, only affine-maximizers can be implemented whenever the type sets of the agents are rich enough. In this work, we generalize these results and define a new class of preferences: Preferences which are positive-represented by a quasi-linear utility. That is, agents whose preference on a subspace of the outcomes can be modeled using a quasi-linear utility. We show that the characterization of VCG mechanisms as the incentive-compatible mechanisms extends naturally to this domain. Our result follows from a simple reduction to the characterization of VCG mechanisms. Hence, we see our result more as a fuller more correct version of the VCG characterization. This work also highlights a common misconception in the community attributing the VCG result to the usage of transferable utility. Our result shows that the incentive-compatibility of the VCG mechanisms does not rely on money being a common denominator, but rather on the ability of the designer to fine the agents on a continuous (maybe agent-specific) scale. We think these two insights, considering the utility as a representation and not as the preference itself (which is common in the economic community) and considering utilities which represent the preference only for the relevant domain, would turn out to fruitful in other domains as well.

Kasher and Rubinstein (1997) introduced the problem of classifying the members of a group in terms of the opinions of their potential members. This involves a finite set of agents N={1,2,…,n} , each one having an opinion about which agents should be classified as belonging to a specific subgroup J. A Collective Identity Function (CIF) aggregates those opinions yielding the class of members deemed J . Kasher and Rubinstein postulate axioms, intended to ensure fair and socially desirable outcomes, characterizing different CIFs. We follow their lead by replacing their liberal axiom by other axioms, constraining the spheres of influence of the agents. We show that some of them lead to different CIFs while in another instance we find an impossibility result.

Models of updating a set of priors either do not allow a decision maker to make inference about her priors (full bayesian updating or FB) or require an extreme degree of selection (maximum likelihood updating or ML). Therefore I characterize a general method for updating a set of priors, partial bayesian updating (PB), in which the decision maker (i) utilizes a threshold to determine whether a prior is likely enough, conditional on observed information, and then (ii) applies Bayes' rule to the sufficiently likely priors. I show that PB nests FB and ML and explore its behavioral properties.