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Understanding cooperative behavior in biological and social systems constitutes a scientific challenge, being the object of intense research over the past decades. Many mechanisms have been proposed to explain the presence and persistence of cooperation in those systems, showing that there is no unique explanation, as different scenarios have different possible driving forces. In this paper, we propose a model to study situations in which voluntary participation involves an access cost to the cooperative interaction, besides the cost associated with cooperation. The proposed Costly-Access Prisoner's Dilemma, a symmetric donation game with voluntary and costly participation, breaks the symmetry between abstainers and participants of the Voluntary Prisoner's Dilemma. A mean-field approach shows that, in well-mixed populations, the dynamic always leads the system to abstention. However, depending on the return parameter, numerical simulations in structured populations display an alternating behavior between mono-strategic, multi-stable, and coexistence phases. This behavior is fully explained through a theoretical analysis of the strategic motifs, the transitions being determined by the change in stability of those motifs., Comment: 13 pages including 7 figures. Submitted for publication

Economic unions are international agreements oriented to increase economic efficiency and establishing political and cultural ties between the member countries. Becoming a member of an existing union usually requires the approval of both the candidate and members, while leaving it may require only the unilateral will of the exiting country. There are many examples of accession of states to previously consolidated economic unions, and a recent example of leaving is the withdrawal of the United Kingdom from the European Union. Motivated by the Brexit process, in this paper we propose an agent-based model to study the determinant factors driving withdrawals from an economic union. We show that both Union and local taxes promote the exits, whereas customs fees out of the Union boost cohesion. Furthermore, heterogeneity in both business conditions and wealth distribution promotes withdrawals, while countries' size diversity does not have a significant effect on them. We also deep into the individual causes that lead to dissatisfaction and, ultimately, to exits. We found that, for low Union taxes, the wealth inequality within the country is the leading cause of anti-Union opinion spreading. Conversely, for high Union taxes, the country's performance turns out to be the main driving force, resulting in a risk of wealthier countries leaving the Union. These findings will be helpful for the design of economic policies and effective informative campaigns., Comment: 7 figures, 1 table

Since Nowak & May's (1992) influential paper, network reciprocity--the fact that individuals' interactions repeated within a local neighborhood support the evolution of cooperation--has been confirmed in several theoretical models. Essentially, local interactions allow cooperators to stay protected from exploiters by assorting into clusters, and the heterogeneity of the network of contacts--the co-presence of low- and high-connected nodes--has been shown to further favor cooperation. The few available large-scale experiments on humans have however missed these effects. The reason is that, while models assume that individuals update strategy by imitating better performing neighbors, experiments showed that humans are more prone to reciprocate cooperation than to compare payoffs. Inspired by the empirical results, we rethink network reciprocity as a rational form of direct reciprocity on networks--networked rational reciprocity--indeed made possible by the locality of interactions. We show that reciprocal altruism in a networked prisoner's dilemma can invade and fixate in any network of rational agents, profit-maximizing over an horizon of future interactions. We find that networked rational reciprocity works better at low average connectivity and we unveil the role of network heterogeneity. Only if cooperating hubs invest in the initial cost of exploitation, the invasion of cooperation is boosted; it is otherwise hindered. Although humans might not be as rational as here assumed, our results could help the design and interpretation of new experiments in social and economic networks

A general procedure to formulate asexual (unstructured, deterministic) population dynamical models resulting from individual pairwise interactions is proposed. Individuals are characterized by a continuous strategy that represents all their behavioral, morphological, and functional traits. Populations group conspecific individuals with identical strategy and are measured by densities in space. Species can be monomorphic, if only one strategy is present, or polymorphic otherwise. The procedure highlights the structural properties fulfilled by the population per-capita growth rates. In particular, the effect of perturbing a set of similar strategies is proportional to the product of the corresponding densities, with a proportionality coefficient that is density-dependent only through the total density. This generalizes the law of mass action, which traditionally refers to the case in which the per-capita growth rates are linearly density-dependent and insensitive to joint strategy perturbations. Being underpinned with individual strategies, the proposed procedure is most useful for evolutionary considerations, in the case strategies are inheritable. The developed body of theory is exemplified on a Holling-type-II many-prey-one-predator system and on a model of a cannibalistic community., Comment: Submitted to Journal of Mathematical Biology on Feb. 3, 2014

This paper investigates the effects of the "uptick rule" (a short selling regulation formally known as rule 10a-1) by means of a simple stock market model, based on the ARED (adaptive rational equilibrium dynamics) modeling framework, where heterogeneous and adaptive beliefs on the future prices of a risky asset were first shown to be responsible for endogenous price fluctuations. The dynamics of stock prices generated by the model, with and without the uptick-rule restriction, are analyzed by pairing the classical fundamental prediction with beliefs based on both linear and nonlinear technical analyses. The comparison shows a reduction of downward price movements of undervalued shares when the short selling restriction is imposed. This gives evidence that the uptick rule meets its intended objective. However, the effects of the short selling regulation fade when the intensity of choice to switch trading strategies is high. The analysis suggests possible side effects of the regulation on price dynamics.

We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries characterising the system's dynamics. Rather than aiming at a complete unfolding of the three cases, which would require specific assumptions on both the class of nonsmooth system and the geometry of the involved boundary, we concentrate on the geometric features that are common to all scenarios. We show that, at a generic intersection between the smooth and discontinuity induced bifurcation curves, a third curve generically emanates tangentially to the former. This is the discontinuity induced bifurcation curve of the secondary invariant set (the other cycle, the double-period cycle, or the torus, respectively) involved in the smooth bifurcation. The result can be explained intuitively, but its validity is proven here rigorously under very general conditions. Three examples from different fields of science and engineering are also reported.