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This article uses game theory to investigate investor-state dispute settlement and related dispute resolution strategies through international arbitration. When deciding whether either to bring or to defend a claim rather than pursue settlement, investors and states will select strategies to maximize their respective payoffs, either by securing compensation or successfully defeating a claim for compensation. This article develops a model decision-making strategy for claimant investors and defendant states based on the observed patterns of outcomes in actual investment treaty arbitration awards. Embedding the problem in the context of utility and hence risk-aversion, it will offer a general solution for the arbitration 'game'. Four regions will be identified in the settlement space consisting of the respondent offer against claimant success probability. It will be shown that no settlement is possible in three of these four regions. The go-no-go probability of claimant victory below which it would not be reasonable for a potential claimant to proceed will be quantified. An algorithm is developed for calculating the settlement sum that the respondent may offer with a reasonable expectation of acceptance by the claimant.

Dominance hierarchies based on resource holding potential (RHP) or age are central to the social structure of many group-living animals. Nonhuman primate females and some other mammals are unusual because ranks can depend on kin support or follow an inverse age-graded pattern independent of kin. Whereas the former hierarchies are mediated by frequent coalitions leading to long-term stability, the latter are unstable due to individualistic contests and occasional revolutionary coalitions. We use mathematical modeling to investigate this variation, based on the interaction of triads, subgroups of the group consisting of 3 individuals. This produces 4 key situations, namely that relationships can be either stable or unstable, and involving coalitionary support or not. Varying the parameter values of our model and applying it to real-world examples, we conclude that the emergence of different dominance hierarchies depends on 6 major factors. In addition to RHP, reproductive skew and demography often suggested previously, we stress the importance of 1) the variance in relatedness; 2) the costs and likelihood of interventions; and 3) the value of resources and rank in different life stages, which might be tightly linked to the life history of a species. Key words: ageinversed hierarchies, ESS, evolutionary games, matrilineal hierarchies, triads. [Behav Ecol]

We consider the neglected question of how secondary defences of prey animals evolve if they are discontinuous in nature, being either present or absent, or expressible over a limited number of levels. We present a novel computer model that evaluates the conditions in which defended mutant prey may (1) fail to rise above nontrivial levels within a population, (2) reach values close to fixation, or (3) find some evolutionarily stable strategy (ESS) frequency between these two situations. Undefended prey that coexist with defended conspecifics are known as automimics. One finding is that automimicry can be an ESS over a range of conditions, but especially when prey are relatively cryptic and secondary defences are very effective at deterring predation. Evolutionarily stable automimicry emerges from the interplay between the direct benefits of costly defences in surviving individual attacks by predators and frequency-dependent benefits conferred on all prey, from a reduction in the rate of attack on all identical-looking prey. When, in contrast, secondary defences have continuous variation, the result is effectively a monomorphic state of defence across the population. Thus the degree and kind of variation that a defence takes has a profound effect on its initial evolution. We discuss the interesting possibility that mixed ESSs may help explain some examples of variation in prey secondary defences. © 2006 The Linnean Society of London, Biological Journal of the Linnean Society, 2006, 87, 393–402.

We consider the optimal behavior of a cryptic prey individual as it is approached by a predator searching for prey. Although the predator has not yet discovered the prey, it has an increasing likelihood of doing so as it gets closer to the prey. Further, the closer the predator is to the prey when it discovers it, the more likely the predator will be to capture the prey. These arguments suggest that the prey should flee before the predator discovers it. However, the act of fleeing will alert the predator to the presence of the prey and trigger an attack that might not have occurred otherwise. We capture these conflicting outcomes in a mathematical model, which we then use to predict the optimal behavior of the prey and predator. We argue that the optimal strategy for the prey is either to run as soon as they detect a predator approaching or to only flee in response to having been detected by the predator. Running as soon as the predator is detected is associated with low predator search speeds, a low nonpredation cost to running, a large advantage to the prey in initiating chases rather than reacting, limited ability to spot the predator at distance, a high ability to spot prey by the predator, and a high probability that chases will be successful. The optimal strategy for the predator depends on whether its current trajectory is taking it closer to or further from the prey. In the latter case, the predator should attack immediately on discovering the prey; in the former case, it should delay its attack until it reaches the point on its current trajectory where distance to the prey is minimized. Key words: antipredator strategies, coursing predators, crypsis, fleeing, flight, predation, predator-prey interactions, prey detection. [Behav Ecol]

We present two elaborations of the model of Broom and Ruxton that found evolutionarily stable kleptoparasitic strategies for foragers. These elaborations relax the assumption that the distribution of times required to handle discovered food items is exponential. These changes increase the complexity of the model but represent a significant improvement in biological realism. In one elaboration, handling takes a fixed interval, th, at the end of which the whole value of the food item is obtained. We liken this to peeling then consuming a small orange. The other elaboration also assumes that handling takes a fixed interval, th, but this time the reward from the food item is extracted continuously throughout the handling period. We liken this to eating an apple. Both models predict that increasing food density, the ease with which food items can be discovered, or the length of aggressive contests all act to make kleptoparasitism less common. The difference between the evolutionarily stable strategy solutions of the apple and orange models provides a clear prediction of our theory. When prey items require handling before yielding a lump sum at the end, then kleptoparasitic attacks will be focused on prey items near the end of their handling period. However, if prey items yield reward continuously during handling, then attacks should be biased toward newly discovered food items. Another key difference between the model predictions is that kleptoparasitism increases with forager density in the apple model, but decreases in the orange model. Key words: aggression, evolutionarily stable strategy, food stealing, game theory, intraspecific interference. [Behav Ecol 14:23‐33 (2003)]

We constructed a game theoretical model to predict optimal patterns of egg laying in systems where individuals lay in the nests of others as well as in their own nests. We show that decreasing the effect of position within an egg-laying sequence on the worth of an egg should lead to reduced parasitism. Indeed, parasitism can only flourish if the worth of an egg to its biological parent declines with the total number of eggs laid in that nest. Further, we found that increasing the intrinsic costs of egg production should lead to an increased propensity for conspecific brood parasitism. The model also predicts that variation in hosts' ability to reject parasitic eggs has little effect on parasitism until this ability is well developed. Copyright 2002.

Many species of animals have to perform two contradictory tasks: feeding, and avoiding becoming food for others. A large number of theoretical and empirical studies have investigated the trade-off between feeding and antipredator vigilance, especially in birds. An important factor which has been neglected in these studies is that of the area occupied by the flock. If individuals feed close together, competition increases and feeding rates decrease. However, if individuals space themselves widely, then vigilance efficiency goes down and there is an increased predation risk. We develop a vigilance model which allows birds to control the area the flock occupies as well as their vigilance rate. The optimal strategy is found for the birds under a variety of environmental conditions. In particular the effect of each environmental parameter on this optimum is considered in turn. How the model can be adapted for different bird species is also investigated.

Feeding birds must balance food gathering against predation risk. Group foraging is generally considered as a strategy for optimizing this trade-off. Previous modelling studies assumed that group sizes were static and that all group members are informed of an imminent predator attack if one of them detects it. These models implicitly assumed that birds could estimate group size, and adopt a fixed rate of anti-predator vigilance scanning. Recent empirical results suggest that group sizes are generally dynamic rather than static and the group members are often unaware of another's detection of imminent attack. It has also been observed that vigilance rates are not static but change after the arrival or departure of another. Here, we present a model which allows feeding-group size (and individuals' vigilance rates) to vary dynamically, and investigate the implications which this has for the optimum trade-off between foraging and avoiding predation. We find that newly arrived birds should generally be the most vigilant and that vigilance rates should decrease after the arrival of another into the feeding group but increase after a departure. Vigilance rates should increase as the cost of predator attack increases or if the reward rate from foraging decreases. Vigilance should increase if predator attacks are more common but decrease if predators require a longer time undetected to approach the feeding group. In common with many experimental studies, we observe that vigilance rates decrease as the average number of birds feeding together increases. Hence, the main conclusion of previous works (that foraging in groups is an effective strategy for balancing the conflicting pressures of foraging and avoiding predation) is obtained by our model, despite relaxing several previously used assumptions. Finally, we discuss some of the open questions related to group vigilance and how extensions to our modelling framework might be used to address these.