Sarvesh Bandhu

Contact : sarvesh.bandhu@iimb.ac.in

Bandhu, Sarvesh and Rohit Kumar. "A characterization of unanimity with status quo: Fixed vs variable population." Economics Letters (2024) [Link]

Abstract: This paper provides a characterization of a recent rule called the unanimity with status quo. The rule designates a specific alternative as the status quo, selecting it in all profiles except where another alternative is unanimously ranked first by all agents, in which case the unanimous alternative is chosen. Our characterization relies on the solidarity axiom of welfare dominance under preference replacement, in combination with unanimity and tops-only. The significance of this characterization lies in the demonstration of the axioms’ independence and the tightness of the characterization, meaning that weakening any axiom results in the emergence of additional rules. We also characterize the rule in the dynamic settings where new agents may enter the economy. Additionally, we examine the relationship between the two versions of solidarity axioms and the fairness axiom of anonymity.

Bandhu, Sarvesh, Abhinaba Lahiri, and Anup Pramanik. "Stochastic same-sidedness in the random voting model." Social Choice and Welfare (2023). [Link]

Abstract: We study the implications of stochastic same-sidedness (SSS) axiom in the random voting model. At a given preference profile if one agent changes her preference ordering to an adjacent one by swapping two consecutively ranked alternatives, then SSS imposes two restrictions on the lottery selected by a voting rule before and after the swap. First, the sum of probabilities of the alternatives which are ranked strictly higher than the swapped pair should remain the same. Second, the sum of probabilities assigned to the swapped pair should also remain the same. We show that every random social choice function (RSCF) that satisfies efficiency and SSS is a random dictatorship provided that there are two voters or three alternatives. For the case of more than two voters and atleast four alternatives, every RSCF that satisfies efficiency, tops-onlyness and SSS is a random dictatorship. 

Bandhu, Sarvesh, and Ratul Lahkar. "Survival of altruistic preferences in a large population public goods game". Economics Letters (2023) [Link]

Abstract: A large population of agents play a public goods game. Agents’ subjective payoff differs according to their level of altruism. More altruistic agents generate greater positive externality in Nash equilibrium. The strength of institutions determines the extent to which agents can materially benefit from the positive externalities they generate. Therefore, stronger institutions confer evolutionary advantage on more altruistic preferences, enabling such preferences to survive and proliferate.

Bandhu, Sarvesh, and Ratul Lahkar. "Evolutionary robustness of dominant strategy implementation." Economic Theory (2022) [Link]

Abstract: We consider dominant strategy implementation in a large population aggregative game. The model has strategic complementarities which generates multiple Nash equilibria. Moreover, externalities are positive due to which, all equilibria are socially inefficient. The planner, therefore, constructs a direct mechanism and assigns efficient strategies and transfer levels to agents. Truthful revelation then becomes strictly dominant, which implements efficiency. In our new evolutionary approach to this mechanism, the reported type distribution evolves under dynamics satisfying monotone percentage growth. Such dynamics eliminate dominated strategies thereby ensuring convergence to truthful revelation by all agents. Dominant strategy implementation is, therefore, robust under such evolutionary dynamics. Our evolutionary approach differs from existing models of evolutionary implementation based on potential games. That approach may fail to implement efficiency under strategic complementarities as a Pareto inferior Nash equilibrium can remain asymptotically stable under evolutionary dynamics. Our evolutionary approach is effective even under such strategic complementarities.

Bandhu, Sarvesh, Bishwajyoti Mondal, and Anup Pramanik. "Strategy-proofness of the unanimity with status-quo rule over restricted domains." Economics Letters (2021) [Link]

Abstract: In this paper, we provide a complete characterization of preference domains on which the Unanimity with Status-quo rule is strategy-proof. Further, we introduce a notion of “conflicting preference domains” and show that the Unanimity with Status-quo rule defined over these domains is strategy-proof. 

Bandhu, Sarvesh, Abhinaba Lahiri, and Anup Pramanik. "A characterization of status quo rules in the binary social choice model." Economics Letters (2020) [Link]

Abstract: This paper characterizes status quo rules in the binary social choice environment. We consider the full preference domain which allows for indifference. We show that status quo rules are the only rules that satisfy ontoness, strategy-proofness and a solidarity property. The solidarity property that we consider, positively correlates the welfare of a voter to rest of the voters in case of her improvement. It is independent from the usual solidarity axiom of welfare dominance under preference replacement used in the literature. 

"A Large Population Approach to Implementing Efficiency with Minimum Inequality" April 2022. (with Ratul Lahkar) [SSRN Link] 

Abstract: We consider the implementation of efficiency with minimum inequality in a large population model of negative externalities. Formally, the model is one of tragedy of the commons with the aggregate strategy at the efficient state being lower than at the Nash equilibrium. A planner can restore efficiency by imposing an externality equivalent tax and then redistribute the tax revenue as transfers to lower inequality. We characterize the transfer vector that minimizes inequality at the efficient state subject to incentive compatibility and budget balance. We then construct a mechanism that implements efficiency with minimum inequality in dominant strategies. We also show that minimizing inequality at the efficient state maximizes the minimum payoff at efficiency. But it is not equivalent to implementing the Rawlsian social choice function.

"Digital Transformation, Risky Investments and Hosting Platform Rivals" Sep 2022. (with Shiva Shekhar and Marshall W. Van Alstyne) [SSRN Link] 

Abstract: In this paper, we study the decision of traditional firms to pursue a digital transformation strategy. While digital transformation enhances value through external value creation, it also makes investments risky. We show that when the investments are very risky (after digital transformation) and the value of cross-network interactions is not very high, firms should avoid transforming to a platform and remain as a traditional firm, otherwise digital transformation is profitable. Interestingly, when firms transform into a platform, we show that inviting rivals onto their platform can be profitable in most cases. Furthermore, in some cases, the platform may even pay rivals to join its platform. Apart from the benefit of enhancing the volume of cross-sided network interactions, inviting rivals onto their proprietary platforms lowers the rival's aggressiveness. This is a novel strategic rationale for inviting rivals onto the platform elicited in this paper. Instead, when the value of cross-sided network benefits is very high and investments are almost certain, the platform may choose not to invite rivals. We provide clear managerial implications of our results.

"Voting with Lying Costs: A behavioral Approach to Overcoming Gibbard-Satterthwaite Theorem" Jan 2021. [Link] 

Abstract: The standard assumption in the mechanism design is that if a voter has any opportunity to gain (howsoever small) she will manipulate. It implicitly assumes that there is no cost of lying. But there is a large experimental literature that suggests that agents are averse to lying - see for instance, Lundquist et al. (2007), Lundquist et al. (2009), Gneezy et al. (2013),

Kajackaite and Gneezy (2015) and Abeler et al. (2019). The main contribution of this paper is the introduction of a cost of lying in the ordinal voting environment. Through a novel approach of measuring the cost of lying in terms of ranks (as there is no money involved), we have been able to overcome the negative result of Gibbard-Satterthwaite Theorem. We say

that a SCF is K-manipulable (K ≥ 1) if the voter can improve by at least K ranks in her true preference ordering by lying. It captures the idea that a voter manipulates only when the gains from lying are “substantial” and exceed the cost of lying. 

Our main result is that we have been able to overcome the negative result of Gibbard-Satterthwaite Theorem by introducing two new class of rules for selecting an outcome which are efficient, minimally fair and satisfy the K-strategy-proofness in the presence of lying costs. For sufficiently large number of alternatives, we also provide a (partial) characterization of unanimous and K-strategy-proof rules which we call K-dictatorial rules. We provide two extensions by allowing for voters to have different cost of lying and when cost of lying is relative instead of fixed cost of lying. We also show that the well-known equivalence of ontoness, unanimity and efficiency for strategy-proof SCFs breaks down when strategy-proofness is replaced by K-strategy-proofness. We conclude the paper with few results on the lower bound of number of alternatives required for K-dictatorial SCF.

''Random Strategy-Proof Voting with Lexicographic Extension'' Jan 2021. [Link]

Abstract : An important issue in the random strategic models is that preferences are ordinal rankings while the outcome is a probability distribution over alternatives.1. Hence to compare the outcomes it requires a lottery extension from an ordinal preference ordering to lotteries. The standard notion of strategy-proofness in random environment is proposed by Gibbard (1977). According to Gibbard, a RSCF is sd-strategy-proof if the truth telling lottery stochastically dominates all lotteries obtained via misrepresentation. Gibbard (1977) showed that all sd-strategy-proof RSCFs which satisfy the additional (mild) property of unanimity, must be a random dictatorship. We replace the sd-extension by two simple lottery extensions based on lexicographic comparisons. The first is the downward lexicographic or dl-extension and the second is the upward lexicographic or ul-extension. While comparing two lotteries under dl-extension, the voter will prefer the lottery which has the higher probability on the first-ranked alternative If they are the same, the voter will consider probabilities assigned to the second-ranked alternative, preferring the lottery which has the higher probability. If they are the same, she will consider the third-ranked alternative and so on till the last ranked alternative. In contrast, while comparing two lotteries using ul-extension, voters prefers the one which has lower probability on the last ranked alternative. If they are same, she will consider the alternative that is ranked second-last and so on.

There are two broad sets of results in this paper. The first concerns ul-strategy-proofness. We show that the Gibbard (1977) random dictatorship result continues to hold, i.e. every RSCF satisfying ul-strategy-proofness and unanimity must be a random dictatorship. This is rather surprising in view of the fact ul-strategy-proofness is significantly weaker than sd-strategyproofness. The second set of results concerns RSCFs that satisfy dl-strategy-proofness. We show that a dl-strategy-proof RSCFs in conjunction with efficiency must be a top-support rules, i.e. they can give strictly positive probability in a profile only to alternatives that are ranked first by some voter. We show that a class of RSCFs that we call top-weight rules, are characterized by dl-strategy-proofness, efficiency and the an additional but familiar property of tops-onlyness. We also provide a new characterization of random dictatorship using dl-strategy-proofness. We conclude the paper by discussing a generalization of top-weight rules.