Cheating is evolutionarily assimilated with cooperation in the continuous snowdrift game

It is well known that in contrast to the Prisoner's Dilemma, the snowdrift game can lead to a stable coexistence of cooperators and cheaters. Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals choosing to contribute in continuous degrees can result in the social diversification to a 100% contribution and 0% contribution through so-called evolutionary branching. Until now, however, game-theoretical studies have shed little light on the evolutionary dynamics and consequences of the loss of diversity in strategy. Here we analyze continuous snowdrift games with quadratic payoff functions in dimorphic populations. Subsequently, conditions are clarified under which gradual evolution can lead a population consisting of those with 100% contribution and those with 0% contribution to merge into one species with an intermediate contribution level. The key finding is that the continuous snowdrift game is more likely to lead to assimilation of different cooperation levels rather than maintenance of diversity. Importantly, this implies that allowing the gradual evolution of cooperative behavior can facilitate social inequity aversion in joint ventures that otherwise could cause conflicts that are based on commonly accepted notions of fairness.Comment: 30 pages, 3 tables, 5 figure

Spatial competitive games with disingenuously delayed positions

Citation: Soltanolkottabi, M., Ben-Arieh, D., & Wu, C.H. (2017). Spatial competitive games with disingenuously delayed positions. Manuscript, Kansas State University, Manhattan, KS.During the last decade, spatial games have received great attention from researchers showing the behavior of populations of players over time in a spatial structure. One of the main factors which can greatly affect the destiny of such populations is the updating scheme used to apprise new strategies of players. Synchronous updating is the most common updating strategy in which all players update their strategy at the same time. In order to be able to describe the behavior of populations more realistically several asynchronous updating schemes have been proposed. Asynchronous game does not use a universal and players can update their strategy at different time steps during the play. In this paper, we introduce a new type of asynchronous strategy updating in which some of the players hide their updated strategy from their neighbors for several time steps. It is shown that this behavior can change the behavior of populations but does not necessarily lead to a higher payoff for the dishonest players. The paper also shows that with dishonest players, the average payoff of players is less than what they think they get, while they are not aware of their neighbors’ true strategy

Emergence and Implications of Conservation Opinion Propagation in Dynamic Coupled Socio-Ecological Systems

Human behaviour is rarely a static phenomenon. In life, individuals are presented with choices that define the trajectories they will experience days, weeks or months later. As an example consider farmer decision-making and orchard dynamics. If an avocado orchard is well taken care of, a bountiful harvest can lead to a lower price of avocados that will more easily attract grocers to stock the product. Alternatively, if the orchard is not properly cared for, avocado prices can surge (due to their low supply) and become a greater risk for grocers, causing them to seek other suppliers. If a particular 'care' routine is developed by the farmer, this can have a significant impact on the long-term trajectories of orchard dynamics. From this simple example, it is clear how dynamic human behaviour can interact with environmental system dynamics. This motivates the potential value of capturing this interaction in mathematical modelling. In this thesis, we develop two different coupled human-environment system (CHES) models that incorporate a dynamic feedback loop mechanism to link human impact and environmental system responses and vice versa. The first model is developed using a game-theoretic approach to describe dynamics of opinion spread. The model is then coupled to a previously established coral reef ecosystem model. We investigate the effects of key factors such as social learning, social norms, and exploitation rate on the trajectories predicted by the model. We discover stable regimes that are made possible by the presence of human coupling and we identify the potentially harmful role of social norms. In the second model, we utilize a similar game-theoretic approach to couple a dynamic human component to a previously established grassland model of the Southeastern Australian grasslands. The aim of this model is to determine conditions that suppress invasive exotic grasses, in the presence of human feedback that determines how strongly the local population mitigates its own pollution. Finally, we conduct a systematic review of the CHES modelling literature between May 2009 and April 2019 using the Web of Knowledge and PUBMED databases. Results reveal an increasing trend in the number of mathematical models using a CHES approach. Results also show that these models utilize a wide range of techniques of varying complexity. In general, most work focuses on agricultural systems. We postulate that application to other environmental systems is relatively unexplored and can be implemented using techniques similar to those of the models developed in this thesis, or via adaptations of other modelling techniques from different fields of research. We suggest that including dynamic human behaviour is necessary in order to improve existing environmental policies and improve the predictive power of mathematical modelling techniques in environmental systems research