4 Presentations

• 
  09:00 AM - 09:25 AM

  Game-theoretical modelling of a dynamically evolving network

  • Mark Broom, presenter, City University London
  • Chris Cannings, University of Sheffield

  Animal (and human) populations contain a finite number of individuals with social and geographical relationships which evolve over time, at least in part dependent upon the actions of members of the population. These actions are often not random, but chosen strategically. In this talk we introduce a game-theoretical model of a population where the individuals have an optimal level of social engagement, and form or break social relationships strategically to obtain the correct level. This builds on previous work where individuals tried to optimise their number of connections by forming or breaking random links; the difference being that here we introduce a truly game-theoretic version where they can choose which specific links to form or break. This is more realistic and makes a significant difference to the model, one consequence of which is that the analysis is much more complicated. We discuss some general results and then focus on a particular example.

• 
  09:25 AM - 09:50 AM

  Ecological feedback on diffusion dynamics

  • Hye Jin Park, presenter, Max Planck Institute for Evolutionary Biology
  • Chaitanya Gokhale, Max Planck Institute for Evolutionary Biology

  Spatial patterns are ubiquitous across different scales of organization. Animal coat pattern, spatial organization of insect colonies, and vegetation in arid areas are prominent examples from such diverse ecologies. Typically, pattern formation has been described by reaction-diffusion equations, which considers individuals dispersing between sub-populations of a global pool. This framework applied to public goods game nicely showed the endurance of populations via diffusion and generation of spatial patterns. However, how the spatial characteristics, such as diffusion, are related to the eco-evolutionary process as well as the nature of the feedback from evolution to ecology and vice versa, has been so far neglected. We present a thorough analysis of the ecologically driven evolutionary dynamics in a spatially extended version of ecological public goods games. We show how these evolutionary dynamics feedback into shaping the ecology thus together determining the fate of the system.

• 
  09:50 AM - 10:15 AM

  A game-theoretic approach to foraging dynamics

  • Theodore Galanthay, presenter, Ithaca College
  • Vlastimil Krivan, Biology center
  • Ross Cressman, Wilfrid Laurier University

  The Hawk-Dove game has been used to model the evolution of aggression in animals. This is a frequency-dependent, but density-independent, two-strategy game with well-known results. In the classical game, interactions between players take the same amount of time. R. Cressman and V. Krivan found qualitatively different results when interaction times depended on the strategies. Recent work extended this time-dependent Hawk-Dove game by incorporating foraging dynamics, from ecology, by including payoffs to singles from foraging on an implied underlying resource where resource levels were assumed to be fixed. In this talk, we present preliminary results on how predictions of aggression are affected by including resource dynamics.

• 
  10:15 AM - 10:40 AM

  Evolutionary games with interaction times and time between interactions

  • Ross Cressman, presenter, Wilfrid Laurier University

  Abstract: Evolutionary game theory was developed under a number of simplifying assumptions. One that is not often explicitly stated is that each interaction among individuals takes the same amount of time no matter what strategies these individuals use. When interaction time is strategy-dependent, it is more natural to take individual fitness as the payoff received per unit time. For instance, two Hawks interacting in the standard two-player Hawk-Dove game are assumed to engage in a fight, implying that they may be involved in fewer interactions than Doves who avoid such contests. Furthermore, there may be time and payoffs received between interactions.

  The talk will analyze how these individual fitnesses affect the game dynamics and evolutionary outcome (e.g. the evolutionarily stable strategy (ESS) and Nash equilibrium (NE)) in general two-strategy symmetric games (i.e. matrix games). The results will be applied to the Hawk-Dove game and to the repeated Prisoner’s Dilemma (PD) game when the number of rounds is under the players’ control. It is shown that cooperation can coexist with defection in the PD game, a result consistent with empirical evidence from game experiments based on the corresponding opting out game.