arXiv subjects

J. Grau

Publications and source records attributed to J. Grau.

2 recordsLinked to original sources

arXiv2024

Optimal Control of Fractional Punishment in Optional Public Goods Game

Punishment is probably the most frequently used mechanism to increase cooperation in Public Goods Games (PGG); however, it is expensive. To address this problem, this paper introduces an optimal control problem that uses fractional punishment to promote cooperation. We present a series of computational experiments illustrating the effects of single and combined terms of the optimization cost function. In the findings, the optimal controller outperforms the use of constant fractional punishment and gives an insight into the period and size of the penalization to be implemented with respect to the defection in the game.

eess.SY↗

arXiv2016

A variant of the Secretary Problem: the Best or the Worst

We consider a variant of the secretary problem in which the candidates state their expected salary at the interview, which we assume is in accordance with their qualifications. The goal is for the employer to hire the best or the worst (cheapest), indifferent between the two cases. We focus on the complete information variant as well as on the cases when the number of applicants is a random variable with a uniform distribution $U[1,n]$ or with a Poisson distribution of parameter $λ$. Moreover, we also study two variants of the original problem in which we consider payoffs depending on the number of conducted interviews.

math.PR↗