arXiv subjects

Sumit Goel

Publications and source records attributed to Sumit Goel.

11 recordsLinked to original sources

arXiv2025

Feedback in Dynamic Contests: Theory and Experiment

We study the effect of interim feedback policies in a dynamic all-pay auction where two players bid over two stages to win a common-value prize. We show that sequential equilibrium outcomes are characterized by Cheapest Signal Equilibria, wherein stage 1 bids are such that one player bids zero while the other chooses a cheapest bid consistent with some signal. Equilibrium payoffs for both players are always zero, and the sum of expected total bids equals the value of the prize. We conduct an experiment with four natural feedback policy treatments -- full, rank, and two cutoff policies -- and while the bidding behavior deviates from equilibrium, we fail to reject the hypothesis of no treatment effect on total bids. Further, stage 1 bids induce sunk costs and head starts, and we test for the resulting sunk cost and discouragement effects in stage 2 bidding.

econ.TH↗

arXiv2025

Swap Bounded Envy

We study fairness in the allocation of discrete goods. Exactly fair (envy-free) allocations are impossible, so we discuss notions of approximate fairness. In particular, we focus on allocations in which the swap of two items serves to eliminate any envy, either for the allocated bundles or with respect to a reference bundle. We propose an algorithm that, under some restrictions on agents' preferences, achieves an allocation with ``swap bounded envy.''

econ.TH↗

arXiv2025

An efficiency ordering of k-price auctions under complete information

We study $k$-price auctions in a complete information environment and characterize all pure-strategy Nash equilibrium outcomes. In a setting with $n$ agents having ordered valuations, we show that any agent, except those with the lowest $k-2$ valuations, can win in equilibrium. As a consequence, worst-case welfare increases monotonically as we go from $k=2$ (second-price auction) to $k=n$ (lowest-price auction), with the first-price auction achieving the highest worst-case welfare.

econ.TH↗

arXiv2025

TTC Domains

For the object reallocation problem, we study whether characterizations of Top Trading Cycles (TTC) based on individual rationality, efficiency, and strategyproofness on the unrestricted domain extend to restricted preference domains. We introduce the top-two condition and show that it offers a useful criterion for answering this question. The condition requires that, within every subset of objects, any two objects that can each be ranked first can also be ranked as the top two, in both possible orders. We first show that this condition is sufficient: on every domain satisfying the top-two condition, TTC is the unique rule satisfying the relevant axioms. We also provide a partial converse. For domains that fail the top-two condition within a small subset of objects and satisfy a mild extension condition, we construct a rule distinct from TTC satisfying these axioms. Our results provide a unifying perspective on existing findings for specific domains, such as the single-peaked and single-dipped domains, while also addressing several previously unexplored domains, including the circular and partial-agreement domains.

econ.TH↗

arXiv2024

The effect of competition in contests: A unifying approach

We study how increasing competition, by making prizes more unequal, affects effort in contests. In a finite type-space environment, we characterize the equilibrium, analyze the effect of competition under linear costs, and identify conditions under which these effects persist under general costs. Our findings reveal that competition may encourage or deter effort, depending on the relative likelihood of efficient versus inefficient types. We derive implications for the classical budget allocation problem and establish that the most competitive winner-takes-all contest is robustly optimal under linear and concave costs, thereby resolving an open question. Methodologically, our analysis of the finite type-space domain -- which includes complete information as a special case and can approximate any continuum type-space -- provides a unifying approach that sheds light on the contrasting results in these extensively studied environments.

econ.TH↗

arXiv2024

Multi-agent contract design with a budget

We study a multi-agent contract design problem with moral hazard. In our model, each agent exerts costly effort towards an individual task at which it may either succeed or fail, and the principal, who wishes to encourage effort, has an exclusive-use budget that it can use to reward the agents. A motivating application is crowdsourcing for innovation, where a fixed budget is provided to a crowdsourcing platform to use for rewarding participants based on their submissions. Our main contribution is to introduce a novel class of contracts, which we call Luce contracts, and show that there is always a Luce contract that is optimal. A (generic) Luce contract assigns weights to the agents and distributes the entire budget among the successful agents in proportion to their weights. Furthermore, we characterize effort profiles that can be implemented by Luce contracts and show that Luce contracts offer a way to mitigate the uncertainty in total payments compared to alternative contracts-such as piece-rate or bonus-pool contracts-suggesting their desirability even in environments without budget constraints.

econ.TH↗

arXiv2023

Optimal tie-breaking rules

We consider two-player contests with the possibility of ties and study the effect of different tie-breaking rules on effort. For ratio-form and difference-form contests that admit pure-strategy Nash equilibrium, we find that the effort of both players is monotone decreasing in the probability that ties are broken in favor of the stronger player. Thus, the effort-maximizing tie-breaking rule commits to breaking ties in favor of the weaker agent. With symmetric agents, we find that the equilibrium is generally symmetric and independent of the tie-breaking rule. We also study the design of random tie-breaking rules that are ex-ante fair and identify sufficient conditions under which breaking ties before the contest actually leads to greater expected effort than the more commonly observed practice of breaking ties after the contest.

econ.TH↗

arXiv2022

Optimal grading contests

We study the design of effort-maximizing grading schemes between agents with private abilities. Assuming agents derive value from the information their grade reveals about their ability, we find that more informative grading schemes induce more competitive contests. In the contest framework, we investigate the effect of manipulating individual prizes and increasing competition on expected effort, identifying conditions on ability distributions and cost functions under which these transformations may encourage or discourage effort. Our results suggest that more informative grading schemes encourage effort when agents of moderate ability are highly likely, and discourage effort when such agents are unlikely.

cs.GT↗

arXiv2022

Stable allocations in discrete exchange economies

We study stable allocations in an exchange economy with indivisible goods. The problem is well-known to be challenging, and rich enough to encode fundamentally unstable economies, such as the roommate problem. Our approach stems from generalizing the original study of an exchange economy with unit demand and unit endowments, the \emph{housing model}. Our first approach uses Scarf's theorem, and proposes sufficient conditions under which a ``convexify then round'' technique ensures that the core is nonempty. The upshot is that a core allocation exists in categorical economies with dichotomous preferences. Our second approach uses a generalization of the TTC: it works under general conditions, and finds a solution that is a version of the stable set.

econ.TH↗

arXiv2020

Optimality of the coordinate-wise median mechanism for strategyproof facility location in two dimensions

We consider the facility location problem in two dimensions. In particular, we consider a setting where agents have Euclidean preferences, defined by their ideal points, for a facility to be located in $\mathbb{R}^2$. We show that for the $p-norm$ ($p \geq 1$) objective, the coordinate-wise median mechanism (CM) has the lowest worst-case approximation ratio in the class of deterministic, anonymous, and strategyproof mechanisms. For the minisum objective and an odd number of agents $n$, we show that CM has a worst-case approximation ratio (AR) of $\sqrt{2}\frac{\sqrt{n^2+1}}{n+1}$. For the $p-norm$ social cost objective ($p\geq 2$), we find that the AR for CM is bounded above by $2^{\frac{3}{2}-\frac{2}{p}}$. We conjecture that the AR of CM actually equals the lower bound $2^{1-\frac{1}{p}}$ (as is the case for $p=2$ and $p=\infty$) for any $p\geq 2$.

cs.GT↗

arXiv2020

Project selection with partially verifiable information

We consider a principal agent project selection problem with asymmetric information. There are $N$ projects and the principal must select exactly one of them. Each project provides some profit to the principal and some payoff to the agent and these profits and payoffs are the agent's private information. We consider the principal's problem of finding an optimal mechanism for two different objectives: maximizing expected profit and maximizing the probability of choosing the most profitable project. Importantly, we assume partial verifiability so that the agent cannot report a project to be more profitable to the principal than it actually is. Under this no-overselling constraint, we characterize the set of implementable mechanisms. Using this characterization, we find that in the case of two projects, the optimal mechanism under both objectives takes the form of a simple cutoff mechanism. The simple structure of the optimal mechanism also allows us to find evidence in support of the well-known ally-principle which says that principal delegates more authority to an agent who shares their preferences.

econ.TH↗