arXiv subjects

Shengxian Wang

Publications and source records attributed to Shengxian Wang.

6 recordsLinked to original sources

arXiv2026

Efficiency of cooperation incentives in evolutionary population games under payoff-observation errors

Traditional studies on evolutionary dynamics of cooperation have concentrated on an idealized game setup free of payoff-observation errors. However, in real-world scenarios, individuals frequently encounter errors when observing the payoffs of their opponents during game interactions, resulting from unintentional mistakes, such as data misrecording, overlooking critical details, and miscalculations. This gap between idealized error-free game models and the error-prone real-world game interactions leads to the lack of insight into the impact of payoff-observation errors on the evolutionary dynamics of population games, in particular the efficiency of cooperation incentives. In this paper, we construct a research framework for population games with payoff-observation errors, which enables us to investigate the effects of errors on the evolutionary dynamics of cooperation in the evolutionary Prisoner's Dilemma game with combined incentives. To quantify the implementation costs of incentives in the presence of errors, we devise an index function and employ optimal control theory to derive the optimal incentive protocols. Our theoretical and numerical results reveal that payoff-observation errors can lower the costs compared to error-free cases, and we also derive the theoretical conditions for these results. Finally, we formulate an optimization problem to explore the cost difference between the optimal incentive protocols with and without errors, and further design an algorithm to obtain the numerical solution that minimizes this difference.

math.OC↗

arXiv2023

Optimally combined incentive for cooperation among interacting agents in population games

Combined prosocial incentives, integrating reward for cooperators and punishment for defectors, are effective tools to promote cooperation among competing agents in population games. Existing research concentrated on how to adjust reward or punishment, as two mutually exclusive tools, during the evolutionary process to achieve the desired proportion of cooperators in the population, and less attention has been given to exploring a combined incentive-based control policy that can steer the system to the full cooperation state at the lowest cost. In this work we propose a combined incentive scheme in a population of agents whose conflicting interactions are described by the prisoner's dilemma game on complete graphs and regular networks, respectively. By devising an index function for quantifying the implementation cost of the combined incentives, we analytically construct the optimally combined incentive protocol by using optimal control theory. By means of theoretical analysis, we identify the mathematical conditions, under which the optimally combined incentive scheme requires the minimal amount of cost. In addition to numerical calculations, we further perform computer simulations to verify our theoretical results and explore their robustness on different types of network structures.

math.OC↗

arXiv2023

Evolutionary dynamics under periodic switching of update rules on regular networks

Microscopic strategy update rules play an important role in the evolutionary dynamics of cooperation among interacting agents on complex networks. Many previous related works only consider one \emph{fixed} rule, while in the real world, individuals may switch, sometimes periodically, between rules. It is of particular theoretical interest to investigate under what conditions the periodic switching of strategy update rules facilitates the emergence of cooperation. To answer this question, we study the evolutionary prisoner's dilemma game on regular networks where agents can periodically switch their strategy update rules. We accordingly develop a theoretical framework of this periodically switched system, where the replicator equation corresponding to each specific microscopic update rule is used for describing the subsystem, and all the subsystems are activated in sequence. By utilizing switched system theory, we identify the theoretical condition for the emergence of cooperative behavior. Under this condition, we have proved that the periodically switched system with different switching rules can converge to the full cooperation state. Finally, we consider an example where two strategy update rules, that is, the imitation and pairwise-comparison updating, are periodically switched, and find that our numerical calculations validate our theoretical results.

math.OC↗

arXiv2023

Optimization of institutional incentives for cooperation in structured populations

The application of incentives, such as reward and punishment, is a frequently applied way for promoting cooperation among interacting individuals in structured populations. However, how to properly use the incentives is still a challenging problem for incentive-providing institutions. In particular, since the implementation of incentive is costly, to explore the optimal incentive protocol, which ensures the desired collective goal at a minimal cost, is worthy of study. In this work, we consider the positive and negative incentives respectively for a structured population of individuals whose conflicting interactions are characterized by a prisoner's dilemma game. We establish an index function for quantifying the cumulative cost during the process of incentive implementation, and theoretically derive the optimal positive and negative incentive protocols for cooperation on regular networks. We find that both types of optimal incentive protocols are identical and time-invariant. Moreover, we compare the optimal rewarding and punishing schemes concerning implementation cost and provide a rigorous basis for the usage of incentives in the game-theoretical framework. We further perform computer simulations to support our theoretical results and explore their robustness for different types of population structures, including regular, random, small-world, and scale-free networks.

cs.GT↗

arXiv2019

Exploring optimal institutional incentives for public cooperation

Prosocial incentive can promote cooperation, but providing incentive is costly. Institutions in human society may prefer to use an incentive strategy which is able to promote cooperation at a reasonable cost. However, thus far few works have explored the optimal institutional incentives which minimize related cost for the benefit of public cooperation. In this work, in combination with optimal control theory we thus formulate two optimal control problems to explore the optimal incentive strategies for institutional reward and punishment respectively. By using the approach of Hamilton-Jacobi-Bellman equation for well-mixed populations, we theoretically obtain the optimal positive and negative incentive strategies with the minimal cumulative cost respectively. Additionally, we provide numerical examples to verify that the obtained optimal incentives allow the dynamical system to reach the desired destination at the lowest cumulative cost in comparison with other given incentive strategies. Furthermore, we find that the optimal punishing strategy is a cheaper way for obtaining an expected cooperation level when it is compared with the optimal rewarding strategy.

physics.soc-ph↗

arXiv2018

Evolutionary dynamics in the public goods games with switching between punishment and exclusion

Pro-social punishment and exclusion are common means to elevate the level of cooperation among unrelated individuals. Indeed, it is worth pointing out that the combined use of these two strategies is quite common across human societies. However, it is still not known how a combined strategy where punishment and exclusion are switched can promote cooperation from the theoretical perspective. In this paper, we thus propose two different switching strategies, namely peer switching that is based on peer punishment and peer exclusion, and pool switching that is based on pool punishment and pool exclusion. Individuals adopting the switching strategy will punish defectors when their numbers are below a threshold and exclude them otherwise. We study how the two switching strategies influence the evolutionary dynamics in the public goods game. We show that an intermediate value of the threshold leads to a stable coexistence of cooperators, defectors and players adopting the switching strategy in a well-mixed population, and this regardless of whether the pool-based or the peer-based switching strategy is introduced. Moreover, we show that the pure exclusion strategy alone is able to evoke a limit cycle attractor in the evolutionary dynamics, such that cooperation can coexist with other strategies.

physics.soc-ph↗