The Ideal Free Distribution with travel costs.

This article studies the effect of travel costs on population distribution in a patchy environment. The Ideal Free Distribution with travel costs is defined in the article as the distribution under which it is not profitable for individuals to move, i.e., the movement between patches ceases. It is shown that depending on the travel costs between patches, the Ideal Free Distribution may be unique, there may be infinitely many possible IFDs, or no Ideal Free Distribution exists. In the latter case, animal distribution can converge to an equilibrium of distributional dynamics at which individuals do disperse, but the net movement between patches ceases. Such distributional equilibrium corresponds to balanced dispersal.

The asymmetric Hawk-Dove game with costs measured as time lost.

The classic Hawk-Dove game is a symmetric game in that it does not distinguish between the winners and losers of Hawk-Hawk or Dove-Dove contests. Either of the two interacting Hawks or the two interacting Doves have the same probability to win/lose the contest. In addition, all pairwise interactions take the same time and after disbanding, the individuals pair instantaneously again. This article develops an asymmetric version of the Hawk-Dove model where all costs are measured by the time lost. These times are strategy dependent and measure the length of the conflict and, when a fight occurs between two interacting Hawks, the time an individual needs to recover and pair again. These recovery times depend on whether the Hawk won or lost the contest so that we consider an asymmetric Hawk-Dove game where we distinguish between winners and losers. However, the payoff matrix for this game does not correspond to the standard bimatrix game, because some entries are undefined. To calculate strategy payoffs we consider not only costs and benefits obtained from pairwise contests but also costs when individuals are disbanded. Depending on the interacting and recovery times, the evolutionary outcomes are: Hawk only, both Hawk and Dove, and a mixed strategy. This shows that measuring the cost in time lost leads to a new prediction since, in the classic (symmetric) Hawk-Dove model that does assume positive cost (C>0), both Hawk and Dove strategy is never an evolutionary outcome.

Reducing courtship time promotes marital bliss: The Battle of the Sexes game revisited with costs measured as time lost.

Classic bimatrix games, that are based on pair-wise interactions between two opponents belonging to different populations, do not consider the cost of time. In this article, we build on an old idea that lost opportunity costs affect individual fitness. We calculate fitnesses of each strategy for a two-strategy bimatrix game at the equilibrium distribution of the pair formation process that includes activity times. This general approach is then applied to the Battle of the Sexes game where we analyze the evolutionary outcome by finding the Nash equilibria (NE) of this time-constrained game when courtship and child rearing costs are measured by time lost. While the classic Battle of the Sexes game has either a unique strict NE (specifically, all males exhibit Philanderer behavior and either all females are Coy or all are Fast depending on model parameters), or a unique interior NE where both sexes exhibit mixed behavior, including time costs for courtship and child rearing changes this prediction. First, (Philanderer, Coy) is never a NE. Second, if the benefit of having offspring is independent of parental strategies, (Philanderer, Fast) is the unique strict NE but a second stable interior NE emerges when courtship time is sufficiently short. In fact, as courtship time becomes shorter, this mixed NE (where most males are Faithful and the Coy female population is increasing) attracts almost all initial population configurations. Third, this latter promotion of marital bliss also occurs when parents who share in child rearing receive a higher benefit from their offspring than those that don't. Finally, for courtship time of moderate duration, the same phenomenon occurs when the population size increases.

Voluntary vaccination strategy and the spread of sexually transmitted diseases.

In this work, we investigate the spread and control of sexually transmitted diseases when a game-theory based vaccination strategy is involved. An individual's decision on vaccination uptake may follow a cost-benefit analysis since the individual obtains immunity against the disease from the vaccination and, at the same time, may have some perceived side effects. Evolutionary game theory is integrated into the epidemic model to reveal the relationship between individuals' voluntary decisions on vaccination uptake and the spread and control of such diseases. We show that decreasing the perceived cost of taking vaccine or increasing the payoff from social obligation is beneficial to controlling the disease. It is also shown how the "degree of rationality" of males and females affects the disease spread through the net payoff of the game. In particular, individual awareness of the consequences of the disease on the infectives also contributes to slowing down the disease spread. By analyzing an asymmetric version of our evolutionary game, it is shown that the disease is better controlled when individuals are more sensitive to fitness differences when net payoff is positive than when it is negative.

Costly punishment does not always increase cooperation.

In a pairwise interaction, an individual who uses costly punishment must pay a cost in order that the opponent incurs a cost. It has been argued that individuals will behave more cooperatively if they know that their opponent has the option of using costly punishment. We examined this hypothesis by conducting two repeated two-player Prisoner's Dilemma experiments, that differed in their payoffs associated to cooperation, with university students from Beijing as participants. In these experiments, the level of cooperation either stayed the same or actually decreased when compared with the control experiments in which costly punishment was not an option. We argue that this result is likely due to differences in cultural attitudes to cooperation and punishment based on similar experiments with university students from Boston that found cooperation did increase with costly punishment.

Stochastic fluctuations through intrinsic noise in evolutionary game dynamics.

A one-step (birth-death) process is used to investigate stochastic noise in an elementary two-phenotype evolutionary game model based on a payoff matrix. In this model, we assume that the population size is finite but not fixed and that all individuals have, in addition to the frequency-dependent fitness given by the evolutionary game, the same background fitness that decreases linearly in the total population size. Although this assumption guarantees population extinction is a globally attracting absorbing barrier of the Markov process, sample trajectories do not illustrate this result even for relatively small carrying capacities. Instead, the observed persistent transient behavior can be analyzed using the steady-state statistics (i.e., mean and variance) of a stochastic model for intrinsic noise that assumes the population does not go extinct. It is shown that there is good agreement between the theory of these statistics and the simulation results. Furthermore, the ESS of the evolutionary game can be used to predict the mean steady state.