The predator-dependent replicator dynamics

Ecological interactions are central to understanding evolution. For example, Darwin noticed that the beautiful colours of the male peacock increase the chance of successful mating. However, the colours can be a threat because of the increased probability of being caught by predators. Eco-evolutionary dynamics takes into account environmental interactions to model the process of evolution. The selection of prey types in the presence of predators may be subjected to pressure on both reproduction and survival. Here, we analyze the evolutionary game dynamics of two types of prey in the presence of predators. We call this model \textit{the predator-dependent replicator dynamics}. If the evolutionary time scales are different, the number of predators can be assumed constant, and the traditional replicator dynamics is recovered. However, if the time scales are the same, we end up with sixteen possible dynamics: the combinations of four reproduction’s games with four predation’s games. We analyze the dynamics and calculate conditions for the coexistence of prey and predator. The main result is that predators can change the equilibrium of the traditional replicator dynamics. For example, the presence of predators can induce polymorphism in prey if one type of prey is more attractive than the other, with the prey ending with a lower capture rate in this new equilibrium. Lastly, we provide two illustrations of the dynamics, which can be seen as rapid feedback responses in a predator-prey evolutionary arm’s race.

Coordination and Equilibrium Selection in Games: The Role of Local Effects

We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules – the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

Computational Behavioral Models in Public Goods Games with Migration Between Groups

In this study we have simulated numerically two models of linear Public Goods Games where players are equally distributed among a given number of groups. Agents play in their group by using two simple sets of rules that are inspired by the observed behavior of human participants in laboratory experiments. In addition, unsatisfied agents have the option of leaving their group and migrating to a new random one through probabilistic choices. Stochasticity, and the introduction of two types of players in the population, help simulate the heterogeneous behavior that is often observed in experimental work. The numerical simulation results of the corresponding dynamical systems show that being able to leave a group when unsatisfied favors contribution and avoids free-riding to a good extent in a range of the enhancement factor where defection would prevail without migration. Our numerical simulation results are qualitatively in line with known experimental data when human agents are given the same kind of information about themselves and the other players in the group. This is usually not the case with customary mathematical models based on replicator dynamics or stochastic approaches. As a consequence, models like the ones described here may be useful for understanding experimental results and also for designing new experiments by first running cheap simulations instead of doing costly preliminary laboratory work. The downside is that models and their simulation tend to be less general than standard mathematical approaches.

An Action Principle for Biological Systems

In the analysis of physical systems, the forces and mechanics of all system changes as codified in the Newtonian laws can be redefined by the methods of Lagrange and Hamilton through an identification of the governing action principle as a more general framework for dynamics. For the living system, it is the dimensional and relational structure of its biologic continuum (both internal and external to the organism) that creates the signature informational metrics and course configurations for the action dynamics associated with any natural systems phenomena. From this dynamic information theoretic framework, an action functional can be also derived in accordance with the methods of Lagrange. The experiential process of acquiring information and translating it into actionable meaning for adaptive responses is the driving force for changes in the living system. The core axiomatic procedure of this adaptive process should include an innate action principle that can determine the system’s directional changes. This procedure for adaptive system reconciliation of divergences from steady state within the biocontinuum can be described by an information metric formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback’s Principle of Minimum Discrimination Information powered by the mechanics of survival replicator dynamics. This entropic driven trajectory naturally minimizes the biocontinuum information gradient differences like a least action principle and is an inference procedure for directional change. If the mathematical expression of this process is the Lagrangian integrand for adaptive changes within the biocontinuum, then it is also considered as an action functional for the living system.

On the Strategic Complementarity of Skilled Workers and Technological Innovation: Which Determines Which?

In this document, we analyse the strategic complementarity between technological investment and investment in training by workers. We show that, beyond the importance of the answer to the question about which factor determines which, initial minimal conditions in both factors are required to start a long-run social development process. If these minimums are not met, the economy can become a self-satisfied economy, with a social mediocre performance but, at least in the short run, successful from the individual point of view. We consider that either manager of firms as workers are rational agents who make decisions about their future behaviour, considering the current state of the economy, understanding for such, the percentage of innovative and non-innovative firms in the market and the percentage of skilled and unskilled workers in the labour market. While managers decide the best way to invest, workers decide whether to invest or not in the upgrade or in the development of their skills to face the new challenges posed by technological change. The evolution of the economy is summarized in a complex dynamical system represented by a coupled dynamical system very close to the replicator dynamics considered in evolutionary game theory. In this way, we show that the initial conditions play a crucial role to understand the possibilities of future performance of the economy in each country, and, on the other hand, we analyse the conditions that make possible or necessary the intervention of the government in the economy. JEL Codes: C72, C73, O11, O55, K42