arXiv subjects

Eran Shmaya

Publications and source records attributed to Eran Shmaya.

14 recordsLinked to original sources

arXiv2024

Collective Upkeep

We design mechanisms for maintaining public goods which require periodic in-kind contributions, motivated by incentives problems facing crowd-sourced recommender systems. Utilitarian welfare is maximized by redistributive policies which are infeasible when group members can leave or misreport their preferences. An optimal mechanism reduces contributions for group members with low benefit-cost ratios to encourage participation; and pairs reduced contributions with restricted access to the good to ensure truthful reporting. At most two membership tiers are offered at the optimum, indicating that ecommerce and digital content platforms may benefit substantially from offering simple user-adjustable recommendation settings.

econ.TH↗

arXiv2024

Disentangling Exploration from Exploitation

Starting from Robbins (1952), the literature on experimentation via multi-armed bandits has wed exploration and exploitation. Nonetheless, in many applications, agents' exploration and exploitation need not be intertwined: a policymaker may assess new policies different than the status quo; an investor may evaluate projects outside her portfolio. We characterize the optimal experimentation policy when exploration and exploitation are disentangled in the case of Poisson bandits, allowing for general news structures. The optimal policy features complete learning asymptotically, exhibits lots of persistence, but cannot be identified by an index a la Gittins. Disentanglement is particularly valuable for intermediate parameter values.

econ.TH↗

arXiv2024

Bayesian Learning in Mean Field Games

We consider a mean-field game model where the cost functions depend on a fixed parameter, called \textit{state}, which is unknown to players. Players learn about the state from a a stream of private signals they receive throughout the game. We derive a mean field system satisfied by the equilibrium payoff of the game and prove existence of a solution under standard regularity assumptions. Additionally, we establish the uniqueness of the solution when the cost function satisfies the monotonicity assumption of Lasry and Lions at each state.

math.OC↗

arXiv2024

A Characterization of Universally Optimal Queueing Regimes

We consider an M/M/s queueing model in which customers strategically decide, based on the service reward and waiting cost, whether to join upon arrival or balk and, at any time, whether to remain in the queue or renege. Rational strategic behavior yields an equilibrium whose outcome may be socially efficient or inefficient, depending on the queueing regime. Some regimes yield an efficient equilibrium only under precise calibration to the model parameters. Others are universally optimal, meaning that their equilibrium outcome is efficient for all parameter values. Universal optimality is therefore an appealing property for a planner choosing a queueing regime. We characterize the class of universally optimal queueing regimes. A by-product of our characterization is that preemption plays an unavoidable role in universally optimal regimes.

econ.TH↗

arXiv2023

Regret-Minimizing Project Choice

An agent observes the set of available projects and proposes some, but not necessarily all, of them. A principal chooses one or none from the proposed set. We solve for a mechanism that minimizes the principal's worst-case regret. We compare the single-project environment in which the agent can propose only one project with the multiproject environment in which he can propose many. In both environments, if the agent proposes one project, it is chosen for sure if the principal's payoff is sufficiently high; otherwise, the probability that it is chosen decreases in the agent's payoff. In the multiproject environment, the agent's payoff from proposing multiple projects equals his maximal payoff from proposing each project alone. The multiproject environment outperforms the single-project one by providing better fallback options than rejection and by delivering this payoff to the agent more efficiently.

econ.TH↗

arXiv2022

Identifying the Deviator

A group of players are supposed to follow a prescribed profile of strategies. If they follow this profile, they will reach a given target. We show that if the target is not reached because some player deviates, then an outside observer can identify the deviator. We also construct identification methods in two nontrivial cases.

math.PR↗

arXiv2019

Robust Monopoly Regulation

We study the regulation of a monopolistic firm using a robust-design approach. We solve for the policy that minimizes the regulator's worst-case regret, where the regret is the difference between his complete-information payoff minus his realized payoff. When the regulator's payoff is consumers' surplus, it is optimal to impose a price cap. The optimal cap balances the benefit from more surplus for consumers and the loss from underproduction. When his payoff is consumers' surplus plus the firm's profit, he offers a piece-rate subsidy in order to mitigate underproduction, but caps the total subsidy so as not to incentivize severe overproduction.

econ.TH↗

arXiv2014

Learning the ergodic decomposition

A Bayesian agent learns about the structure of a stationary process from ob- serving past outcomes. We prove that his predictions about the near future become ap- proximately those he would have made if he knew the long run empirical frequencies of the process.

math.ST↗

arXiv2014

Rental harmony with roommates

We prove existence of envy-free allocations in markets with heterogenous indivisible goods and money, when a given quantity is supplied from each of the goods and agents have unit demands. We depart from most of the previous literature by allowing agents' preferences over the goods to depend on the entire vector of prices. Our proof uses Shapley's K-K-M-S theorem and Hall's marriage lemma. We then show how our theorem may be applied in two related problems: Existence of envy-free allocations in a version of the cake-cutting problem, and existence of equilibrium in an exchange economy with indivisible goods and money.

cs.GT↗

arXiv2014

Equivalence between Random Stopping Times in Continuous Time

Two concepts of random stopping times in continuous time have been defined in the literature, mixed stopping times and randomized stopping times. We show that under weak conditions these two concepts are equivalent, and, in fact, that all types of random stopping times are equivalent. We exhibit the significance of the equivalence relation between stopping times using stopping problems and stopping games. As a by-product we extend Kuhn's Theorem to stopping games in continuous time.

math.PR↗

arXiv2013

A prequential test for exchangeable theories

We construct a prequential test of probabilistic forecasts that does not reject correct forecasts when the data-generating processes is exchangeable and is not manipulable by a false forecaster.

math.ST↗

arXiv2012

Lipschitz Games

The Lipschitz constant of a finite normal-form game is the maximal change in some player's payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure ε-equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of pure ε-equilibrium as a function of the number of players in the game and the number of strategies of each player. Our proofs use the probabilistic method.

math.CO↗

arXiv2011

The determinacy of infinite games with eventual perfect monitoring

n infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, is determined. The proof relies on a representation of the game as a stochastic game with perfect information, in which Chance operates as a delegate for the players and performs the randomizations for them, and on Martin's Theorem about the determinacy of such games.

math.LO↗

arXiv2004

Two-player nonZero-sum stopping games in discrete time

We prove that every two-player nonzero-sum stopping game in discrete time admits an ε-equilibrium in randomized strategies for every ε>0. We use a stochastic variation of Ramsey's theorem, which enables us to reduce the problem to that of studying properties of ε-equilibria in a simple class of stochastic games with finite state space.

math.PR↗