Abstract Prosocial behaviours have been extensively studied across multiple disciplines. Cooperation, requiring a personal cost for collective benefits, is widespread in nature and human society, having been explained through mechanisms such as kin selection, direct and indirect reciprocity, and network reciprocity. Institutional incentives, which reward cooperation and punish anti-social behaviour, offer a promising approach to promoting cooperation in groups of self-interested individuals. Focusing on general $$2\times 2$$ games and the collective risk game (a fundamental model for climate action), we analyse the associated cost of providing incentives under evolutionary dynamics governed by Fermi’s rule. Moreover, we explore the asymptotic behaviour of the incentive cost functions in the limits of neutral drift and strong selection. We also implement numerical simulations to study how parameters such as the intensity of selection affect the behaviour of the aforementioned cost functions.

This study examines the stability effects of strategy-dependent time delays on replicator dynamics with logistic population growth. Using a two-player snowdrift game, we incorporate social forms of delay where individuals’ payoffs are delayed, impacting offspring production. While a stable mixed-strategy equilibrium exists without delays, introducing time delays can destabilize this equilibrium through Hopf bifurcations, inducing oscillations. Employing Hopf bifurcation theory, we explore how critical delay values depend on whether delays are equal across strategies, unequal with one strategy experiencing no delay, or fully asymmetric. The analysis reveals rich phenomena, including regions where increasing a delay can transition the system between stability and instability. Our work elucidates the complex interplay between time delays, strategic dynamics, and finite population constraints.

Abstract The beer-quiche game has been used to study interactions involving bluffing. In this paper, we use a four-by-four strategic-form representation of the beer-quiche game to demonstrate five Nash equilibria of three different kinds, including pooling and hybrid equilibria. Our results show how receiver response strategies can maintain bluffing signals within communication systems. Critically, we identify a novel pooling equilibrium in which all senders use a single signal, effectively concealing positive information about themselves. This provides a plausible explanation for the strategic concealment of quality. Our findings suggest that signals conveying concealed information can exist in a wide range of interactive situations with asymmetric information, contributing to a broader understanding of signalling beyond traditional costly signalling models.

Abstract In recent years, classical evolutionary models have been extended to incorporate realistic multiplayer interactions rather than the traditional pairwise modelling approach. Several papers have introduced a new evolutionary framework involving population structure, evolutionary dynamics, multiplayer games and movement processes. The theory underlying the framework has been explored in several directions, identifying strong predictors of fixation probability, such as mean group size and temperature. A recent study developed an evolutionary model where individuals move in a coordinated manner via newly developed movement mechanisms, resulting in herding or separation within the population. This analysis demonstrated that these movement mechanisms impact the fixation probability of cooperation. This paper extends this analysis by investigating whether the previously identified predictors of fixation probability retain their strong influences under different games on complete graphs and by considering a different social dilemma in the form of the Stag-Hunt game. We show that previously defined measures of aggregation are directly related to mean group size and that these fundamental measures can be analytically calculated. In the Stag-Hunt game, we demonstrate that herding opposes the evolution of cooperation. In the Public Goods game, we demonstrate that temperature and fixation share a linear relationship regardless of the movement mechanism considered. In the Hawk-Dove game, temperature is a stronger predictor of fixation but the linear relationship breaks down for higher temperatures and a similar relationship holds as for the Stag-Hunt game.