arXiv subjects

Ilan Nehama

Publications and source records attributed to Ilan Nehama.

6 recordsLinked to original sources

arXiv2021

Evolutionary Foundation for Heterogeneity in Risk Aversion

We examine the evolutionary basis for risk aversion with respect to aggregate risk. We study populations in which agents face choices between alternatives with different levels of aggregate risk. We show that the choices that maximize the long-run growth rate are induced by a heterogeneous population in which the least and most risk-averse agents are indifferent between facing an aggregate risk and obtaining its linear and harmonic mean for sure, respectively. Moreover, approximately optimal behavior can be induced by a simple distribution according to which all agents have constant relative risk aversion, and the coefficient of relative risk aversion is uniformly distributed between zero and two.

econ.TH↗

arXiv2019

Almost Quasi-linear Utilities in Disguise: Positive-representation An Extension of Roberts' Theorem

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.

econ.TH↗

arXiv2018

Prophets and Secretaries with Overbooking

The prophet and secretary problems demonstrate online scenarios involving the optimal stopping theory. In a typical prophet or secretary problem, selection decisions are assumed to be immediate and irrevocable. However, many online settings accommodate some degree of revocability. To study such scenarios, we introduce the $\ell-out-of-k$ setting, where the decision maker can select up to $k$ elements immediately and irrevocably, but her performance is measured by the top $\ell$ elements in the selected set. Equivalently, the decision makes can hold up to $\ell$ elements at any given point in time, but can make up to $k-\ell$ returns as new elements arrive. We give upper and lower bounds on the competitive ratio of $\ell$-out-of-$k$ prophet and secretary scenarios. These include a single-sample prophet algorithm that gives a competitive ratio of $1-\ell\cdot e^{-\Theta\left(\frac{\left(k-\ell\right)^2}{k}\right)}$, which is asymptotically tight for $k-\ell=\Theta(\ell)$. For secretary settings, we devise an algorithm that obtains a competitive ratio of $1-\ell e^{-\frac{k-8\ell}{2+2\ln \ell}} - e^{-k/6}$, and show that no secretary algorithm obtains a better ratio than $1-e^{-k}$ (up to negligible terms). In passing, our results lead to an improvement of the results of Assaf et al. [2000] for $1-out-of-k$ prophet scenarios. Beyond the contribution to online algorithms and optimal stopping theory, our results have implications to mechanism design. In particular, we use our prophet algorithms to derive {\em overbooking} mechanisms with good welfare and revenue guarantees; these are mechanisms that sell more items than the seller's capacity, then allocate to the agents with the highest values among the selected agents.

cs.GT↗

arXiv2018

Manipulation-resistant facility location mechanisms for ZV-line graphs

In many real-life scenarios, a group of agents needs to agree on a common action, e.g., on the location for a public facility, while there is some consistency between their preferences, e.g., all preferences are derived from a common metric space. The facility location problem models such scenarios and it is a well-studied problem in social choice. We study mechanisms for facility location on graphs, which are resistant to manipulations (strategy-proof, abstention-proof, and false-name-proof) by both individuals and coalitions and are efficient (Pareto optimal). We define a family of graphs, ZV-line graphs, and show a general facility location mechanism for these graphs which satisfies all these desired properties. Moreover, we show that this mechanism can be computed in polynomial time, the mechanism is anonymous, and it can equivalently be defined as the first Pareto optimal location according to some predefined order. Our main result, the ZV-line graphs family and the mechanism we present for it, unifies the few current works in the literature of false-name-proof facility location on discrete graphs, including all the preliminary (unpublished) works we are aware of. Finally, we discuss some generalizations and limitations of our result for problems of facility location on other structures.

cs.GT↗

arXiv2016

Analyzing Games with Ambiguous Player Types using the ${\rm MINthenMAX}$ Decision Model

In many common interactive scenarios, participants lack information about other participants, and specifically about the preferences of other participants. In this work, we model an extreme case of incomplete information, which we term games with type ambiguity, where a participant lacks even information enabling him to form a belief on the preferences of others. Under type ambiguity, one cannot analyze the scenario using the commonly used Bayesian framework, and therefore he needs to model the participants using a different decision model. In this work, we present the ${\rm MINthenMAX}$ decision model under ambiguity. This model is a refinement of Wald's MiniMax principle, which we show to be too coarse for games with type ambiguity. We characterize ${\rm MINthenMAX}$ as the finest refinement of the MiniMax principle that satisfies three properties we claim are necessary for games with type ambiguity. This prior-less approach we present her also follows the common practice in computer science of worst-case analysis. Finally, we define and analyze the corresponding equilibrium concept assuming all players follow ${\rm MINthenMAX}$. We demonstrate this equilibrium by applying it to two common economic scenarios: coordination games and bilateral trade. We show that in both scenarios, an equilibrium in pure strategies always exists and we analyze the equilibria.

cs.GT↗

arXiv2011

Approximate Judgement Aggregation

In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them(e.g., transitivity when describing preferences). We consider the issue of judgement aggregation from the perspective of approximation. That is, we generalize the previous results by studying approximate judgement aggregation. We relax the main two constraints assumed in the current literature, Consistency and Independence and consider mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small portion of the inputs. The main question we raise is whether the relaxation of these notions significantly alters the class of satisfying aggregation mechanisms. The recent works for preference aggregation of Kalai, Mossel, and Keller fit into this framework. The main result of this paper is that, as in the case of preference aggregation, in the case of a subclass of a natural class of aggregation problems termed `truth-functional agendas', the set of satisfying aggregation mechanisms does not extend non-trivially when relaxing the constraints. Our proof techniques involve Boolean Fourier transform and analysis of voter influences for voting protocols. The question we raise for Approximate Aggregation can be stated in terms of Property Testing. For instance, as a corollary from our result we get a generalization of the classic result for property testing of linearity of Boolean functions. An updated version (RePEc:huj:dispap:dp574R) is available at http://www.ratio.huji.ac.il/dp_files/dp574R.pdf

cs.GT↗