511 research outputs found
Pattern formation in a predator-prey system characterized by a spatial scale of interaction
We describe pattern formation in ecological systems using a version of the
classical Lotka-Volterra model characterized by a spatial scale which controls
the predator-prey interaction range. Analytical and simulational results show
that patterns can emerge in some regions of the parameters space where the
instability is driven by the range of the interaction. The individual-based
implementation captures realistic ecological features. In fact, spatial
structures emerge in an erratic oscillatory regime which can contemplate
predators' extinction.Comment: 5 pages, 4 figure
The asymptotic price of anarchy for k-uniform congestion games
We consider the atomic version of congestion games with affine cost functions, and analyze the quality of worst case Nash equilibria when the strategy spaces of the players are the set of bases of a k-uniform matroid. In this setting, for some parameter k, each player is to choose k out of a finite set of resources, and the cost of a player for choosing a resource depends affine linearly on the number of players choosing the same resource. Earlier work shows that the price of anarchy for this class of games is larger than 1.34 but at most 2.15. We determine a tight bound on the asymptotic price of anarchy equal to ≈1.35188. Here, asymptotic refers to the fact that the bound holds for all instances with sufficiently many players. In particular, the asymptotic price of anarchy is bounded away from 4/3. Our analysis also yields an upper bound on the price of anarchy <1.4131, for all instances
Simulated ecology-driven sympatric speciation
We introduce a multi-locus genetically acquired phenotype, submitted to
mutations and with selective value, in an age-structured model for biological
aging. This phenotype describes a single-trait effect of the environment on an
individual, and we study the resulting distribution of this trait among the
population. In particular, our simulations show that the appearance of a double
phenotypic attractor in the ecology induces the emergence of a stable
polymorphism, as observed in the Galapagos finches. In the presence of this
polymorphism, the simulations generate short-term speciation, when mating
preferences are also allowed to suffer mutations and acquire selective value.Comment: 11 pages, 5 figures, 1 table, uses package RevTe
Efficiency in Multi-objective Games
In a multi-objective game, each agent individually evaluates each overall
action-profile on multiple objectives. I generalize the price of anarchy to
multi-objective games and provide a polynomial-time algorithm to assess it.
This work asserts that policies on tobacco promote a higher economic
efficiency
Mechanisms that Govern how the Price of Anarchy varies with Travel Demand
Selfish routing, represented by the User-Equilibrium (UE) model, is known to be inefficient when compared to the System Optimum (SO) model. However, there is currently little understanding of how the magnitude of this inefficiency, which can be measured by the Price of Anarchy (PoA), varies across different structures of demand and supply. Such understanding would be useful for both transport policy and network design, as it could help to identify circumstances in which policy interventions that are designed to induce more efficient use of a traffic network, are worth their costs of implementation. This paper identifies four mechanisms that govern how the PoA varies with travel demand in traffic networks with separable and strictly increasing cost functions. For each OD movement, these are expansions and contractions in the sets of routes that are of minimum cost under UE and minimum marginal total cost under SO. The effects of these mechanisms on the PoA are established via a combination of theoretical proofs and conjectures supported by numerical evidence. In addition, for the special case of traffic networks with BPR-like cost functions having common power, it is proven that there is a systematic relationship between link flows under UE and SO, and hence between the levels of demand at which expansions and contractions occur. For this case, numerical evidence also suggests that the PoA has power law decay for large demand
Polymorphic evolution sequence and evolutionary branching
We are interested in the study of models describing the evolution of a
polymorphic population with mutation and selection in the specific scales of
the biological framework of adaptive dynamics. The population size is assumed
to be large and the mutation rate small. We prove that under a good combination
of these two scales, the population process is approximated in the long time
scale of mutations by a Markov pure jump process describing the successive
trait equilibria of the population. This process, which generalizes the
so-called trait substitution sequence, is called polymorphic evolution
sequence. Then we introduce a scaling of the size of mutations and we study the
polymorphic evolution sequence in the limit of small mutations. From this study
in the neighborhood of evolutionary singularities, we obtain a full
mathematical justification of a heuristic criterion for the phenomenon of
evolutionary branching. To this end we finely analyze the asymptotic behavior
of 3-dimensional competitive Lotka-Volterra systems
Resource Competition on Integral Polymatroids
We study competitive resource allocation problems in which players distribute
their demands integrally on a set of resources subject to player-specific
submodular capacity constraints. Each player has to pay for each unit of demand
a cost that is a nondecreasing and convex function of the total allocation of
that resource. This general model of resource allocation generalizes both
singleton congestion games with integer-splittable demands and matroid
congestion games with player-specific costs. As our main result, we show that
in such general resource allocation problems a pure Nash equilibrium is
guaranteed to exist by giving a pseudo-polynomial algorithm computing a pure
Nash equilibrium.Comment: 17 page
Designing cost-sharing methods for Bayesian games
We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players
The Perfect Family: Decision Making in Biparental Care
Background
Previous theoretical work on parental decisions in biparental care has emphasized the role of the conflict between evolutionary interests of parents in these decisions. A prominent prediction from this work is that parents should compensate for decreases in each other\u27s effort, but only partially so. However, experimental tests that manipulate parents and measure their responses fail to confirm this prediction. At the same time, the process of parental decision making has remained unexplored theoretically. We develop a model to address the discrepancy between experiments and the theoretical prediction, and explore how assuming different decision making processes changes the prediction from the theory.
Model Description
We assume that parents make decisions in behavioral time. They have a fixed time budget, and allocate it between two parental tasks: provisioning the offspring and defending the nest. The proximate determinant of the allocation decisions are parents\u27 behavioral objectives. We assume both parents aim to maximize the offspring production from the nest. Experimental manipulations change the shape of the nest production function. We consider two different scenarios for how parents make decisions: one where parents communicate with each other and act together (the perfect family), and one where they do not communicate, and act independently (the almost perfect family).
Conclusions/Significance
The perfect family model is able to generate all the types of responses seen in experimental studies. The kind of response predicted depends on the nest production function, i.e. how parents\u27 allocations affect offspring production, and the type of experimental manipulation. In particular, we find that complementarity of parents\u27 allocations promotes matching responses. In contrast, the relative responses do not depend on the type of manipulation in the almost perfect family model. These results highlight the importance of the interaction between nest production function and how parents make decisions, factors that have largely been overlooked in previous models
- …