The evolution of strategic timing in collective-risk dilemmas

In collective-risk dilemmas, a group needs to collaborate over time to avoid a catastrophic event. This gives rise to a coordination game with many equilibria, including equilibria where no one contributes, and thus no measures against the catastrophe are taken. In this game, the timing of contributions becomes a strategic variable that allows individuals to interact and influence one another. Herein, we use evolutionary game theory to study the impact of strategic timing on equilibrium selection. Depending on the risk of catastrophe, we identify three characteristic regimes. For low risks, defection is the only equilibrium, whereas high risks promote equilibria with sufficient contributions. Intermediate risks pose the biggest challenge for cooperation. In this risk regime, the option to interact over time is critical; if individuals can contribute over several rounds, then the group has a higher chance to succeed, and the expected welfare increases. This positive effect of timing is of particular importance in larger groups, where successful coordination becomes increasingly difficul

Effect on Recreation Benefit Estimates from Correcting for On-Site Sampling Biases and Heterogeneous Trip Overdispersion in Count Data Recreation Demand Models (STATA)

Correction procedures (STATA commands NBSTRAT and GNBSTRAT) are applied to simultaneously account for zero-truncation, endogenous stratification, and overdispersion, and also consider heterogeneity in the overdispersion parameter. Their effect is shown on welfare estimates from previous studies, confirming that the routines perform the appropriate correction and only when endogenous stratification is expected

Introspection dynamics: a simple model of counterfactual learning in asymmetric games

Social behavior in human and animal populations can be studied as an evolutionary process.Individuals often make decisions between different strategies, and those strategies that yield afitness advantage tend to spread. Traditionally, much work in evolutionary game theory considerssymmetric games: individuals are assumed to have access to the same set of strategies, and theyexperience the same payoff consequences. As a result, they can learn more profitable strategies byimitation. However, interactions are oftentimes asymmetric. In that case, imitation may beinfeasible (because individuals differ in the strategies they are able to use), or it may be undesirable(because individuals differ in their incentives to use a strategy). Here, we consider an alternativelearning process which applies to arbitrary asymmetric games,introspection dynamics. Accordingto this dynamics, individuals regularly compare their present strategy to a randomly chosenalternative strategy. If the alternative strategy yields a payoff advantage, it is more likely adopted. Inthis work, we formalize introspection dynamics for pairwise games. We derive simple and explicitformulas for the abundance of each strategy over time and apply these results to severalwell-known social dilemmas. In particular, for the volunteer’s timing dilemma, we show that theplayer with the lowest cooperation cost learns to cooperate without delay

Cooperation in alternating interactions with memory constraints

In repeated social interactions, individuals often employ reciprocal strategies to maintain cooperation. To explore the emergence of reciprocity, many theoretical models assume synchronized decision making. In each round, individuals decide simultaneously whether to cooperate or not. Yet many manifestations of reciprocity in nature are asynchronous. Individuals provide help at one time and receive help at another. Here, we explore such alternating games in which players take turns. We mathematically characterize all Nash equilibria among memory-one strategies. Moreover, we use evolutionary simulations to explore various model extensions, exploring the effect of discounted games, irregular alternation patterns, and higher memory. In all cases, we observe that mutual cooperation still evolves for a wide range of parameter values. However, compared to simultaneous games, alternating games require different strategies to maintain cooperation in noisy environments. Moreover, none of the respective strategies are evolutionarily stable

On the designation of the patterned associations for longitudinal Bernoulli data: weight matrix versus true correlation structure?

Due to potential violation of standard constraints for the correlation for binary data, it has been argued recently that the working correlation matrix should be viewed as a weight matrix that should not be confused with the true correlation structure. We propose two arguments to support our view to the contrary for the first-order autoregressive AR(1) correlation matrix. First, we prove that the standard constraints are not unduly restrictive for the AR(1) structure that is plausible for longitudinal data; furthermore, for the logit link function the upper boundary value only depends on the regression parameter and the change in covariate values between successive measurements. In addition, for given marginal means and parameter $\alpha$, we provide a general proof that satisfaction of the standard constraints for consecutive marginal means will guarantee the existence of a compatible multivariate distribution with an AR(1) structure. The relative laxity of the standard constraints for the AR(1) structure coupled with the existence of a simple model that yields data with an AR(1) structure bolsters our view that for the AR(1) structure at least, it is appropriate to view this model as a correlation structure versus a weight matrix

Cooperation and control in multiplayer social dilemmas

Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. However, in large groups, these mechanisms may become ineffective because they require single individuals to have a substantial influence on their peers. However, the recent discovery of zero-determinant strategies in the iterated prisoner’s dilemma suggests that we may have underestimated the degree of control that a single player can exert. Here, we develop a theory for zero-determinant strategies for iterated multiplayer social dilemmas, with any number of involved players. We distinguish several particularly interesting subclasses of strategies: fair strategies ensure that the own payoff matches the average payoff of the group; extortionate strategies allow a player to perform above average; and generous strategies let a player perform below average. We use this theory to describe strategies that sustain cooperation, including generalized variants of Tit-for-Tat and Win-Stay Lose-Shift. Moreover, we explore two models that show how individuals can further enhance their strategic options by coordinating their play with others. Our results highlight the importance of individual control and coordination to succeed in large groups

Direct reciprocity between individuals that use different strategy spaces

In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate

The Overlooked Potential of Generalized Linear Models in Astronomy - I: Binomial Regression

Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific inquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper -- the first in a series aimed at illustrating the power of these methods in astronomical applications -- we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity $\approx 1.3 \times 10^{-4} Z_{\bigodot}$, an increase of $1.2 \times 10^{-2}$ in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks.Comment: 20 pages, 10 figures, 3 tables, accepted for publication in Astronomy and Computin