Cost efficiency of institutional incentives for promoting cooperation in finite populations

Institutions can provide incentives to enhance cooperation in a population where this behaviour is infrequent. This process is costly, and it is thus important to optimize the overall spending. This problem can be mathematically formulated as a multi-objective optimization problem where one wishes to minimize the cost of providing incentives while ensuring a minimum level of cooperation, sustained over time. Prior works that consider this question usually omit the stochastic effects that drive population dynamics. In this paper, we provide a rigorous analysis of this optimization problem, in a finite population and stochastic setting, studying both pairwise and multi-player cooperation dilemmas. We prove the regularity of the cost functions for providing incentives over time, characterize their asymptotic limits (infinite population size, weak selection and large selection) and show exactly when reward or punishment is more cost efficient. We show that these cost functions exhibit a phase transition phenomenon when the intensity of selection varies. By determining the critical threshold of this phase transition, we provide exact calculations for the optimal cost of the incentive, for any given intensity of selection. Numerical simulations are also provided to demonstrate analytical observations. Overall, our analysis provides for the first time a selection-dependent calculation of the optimal cost of institutional incentives (for both reward and punishment) that guarantees a minimum level of cooperation over time. It is of crucial importance for real-world applications of institutional incentives since the intensity of selection is often found to be non-extreme and specific for a given population.

Prosecutors and their Legislatures, Legislatures and their Prosecutors

This chapter explores the often-pathological relationship between prosecutors and legislatures and considers fiscal pressure as an important antidote to the pathology. Institutional incentives between prosecutors and legislatures align in a way quite different than the classic separation of powers story. Rather, legislatures are well served to empower prosecutors as much as possible by making criminal law broad and deep. And with respect to substantive criminal law, prosecutors have been enormously empowered. Prosecutors are not merely passive recipients of such power but indeed actively lobby for it—often quite successfully. But fiscal pressures can provide a cross-cutting pressure for legislatures, particularly at the state level where many governments must balance their budgets. Thus, sentencing law sometimes finds legislatures refusing prosecutors’ requests for ever longer or mandatory minimum sentences because longer sentences are expensive; this is especially true where sentencing commissions provide legislatures with meaningful data on costs of particular proposals. Criminal procedure has recently found progressive prosecutors leading the way toward defendant-friendly reforms such as using unaffordable money bail less frequently and providing defendants with more discovery than is required by law. In these spaces, county prosecutors have provided laboratories of experimentation that led the way toward broader statewide reforms.

Cost efficiency of institutional incentives in finite populations

Institutions can provide incentives to increase cooperation behaviour in a population where this behaviour is infrequent. This process is costly, and it is thus important to optimize the overall spending. This problem can be mathematically formulated as a multi-objective optimization problem where one wishes to minimize the cost of providing incentives while ensuring a desired level of cooperation within the population. In this paper, we provide a rigorous analysis for this problem. We study cooperation dilemmas in both the pairwise (the Donation game) and multi-player (the Public Goods game) settings. We prove the regularity of the (total incentive) cost function, characterize its asymptotic limits (infinite population, weak selection and large selection) and show exactly when reward or punishment is more efficient. We prove that the cost function exhibits a phase transition phenomena when the intensity of selection varies. We calculate the critical threshold in regards to the phase transition and study the optimization problem when the intensity of selection is under and above the critical value. It allows us to provide an exact calculation for the optimal cost of incentive, for a given intensity of selection. Finally, we provide numerical simulations to demonstrate the analytical results. Overall, our analysis provides for the first time a selection-dependent calculation of the optimal cost of institutional incentives (for both reward and punishment) that guarantees a minimum amount of cooperation. It is of crucial importance for real-world applications of institutional incentives since intensity of selection is specific to a given population and the underlying game payoff structure.In this Supplementary Information, we provide detailed calculations and proofs as well as illustrative figures for the analytical results in the main text of the present paper.

INTERACTION OF THE STATE AND BUSINESS – A KEY FACTOR OF EFFECTIVE INNOVATIVE DEVELOPMENT OF INDUSTRIAL ENTERPRISES

The article shows the relevance of the national strategy of innovative development, which is actively implemented by regional authorities throughout the country. It provides comprehensive guidelines for the development and implementation of innovation policies in different regions. Institutional incentives and constraints for local authorities to implement this strategy are considered.

ACTUALIZATION OF THE CENTRAL EURASIAN POSITION OF THE ALTAI REPUBLIC IN TOURISM SPECIALIZATION

The Altai Republic is one of the most ultra-continental places in the world. At a potentially accessible distance for tourists, there are several other loosely connected states and regions. Having analysed the main economic and geographical indicators of those close to them and specialization in national tourism. Conclusion on the geo-economic efficiency of the development of the Territory by financial and institutional incentives for transport, logistics and business relations with border areas.