4 Presentations

• 
  02:00 PM - 02:25 PM

  Interaction and imitation with heterogeneous agents: A misleading evolutionary equilibrium

  • Francisco Cabo, presenter, Universidad de Valladolid
  • Ana García-González, Universidad de Valladolid

  The paper analyzes the interaction between individuals belonging to two distinct populations, who share the same strategy set but differ in their payoff matrices. A two-population evolutionary game describes this interaction, that presents a double dimension. On the one hand, agents in one population play a game against individuals within their own and also the alternative population. On the other hand, an imitative revision protocol matches together agents belonging to the same population, but also individuals from different populations. When a revising agent in one population is matched with an individual in the alternative population who plays a different strategy, switching to this new strategy gives an uncertain payoff. Given the inter-population heterogeneity, this agent's payoff diverges from the observed payoff of his pair. By assigning weights to these two components, the player constructs the expected
  payoff of switching the strategy. These weights reflect the implicit probability that the real payoff is given by either the individual's believes or by the observed payoff of his pair. And these probabilities are crucially dependent on the individual's awareness on the existence of other agents having different preferences. The mixed-strategy asymptotically stable fixed point of the evolutionary dynamics is computed as a function of these probabilities.

• 
  02:25 PM - 02:50 PM

  Heterogenous Heuristics in 3x3 Bimatrix Population Games

  • Marius Ochea, presenter, THEMA, Université Cergy-Pontoise

  We investigate population-level evolutionary dynamics resulting from individual-level, adaptive play both under homogenous ( "self-play") and heterogenous ( "mixed play") scenarios. The set of heuristics includes imitation rule, perturbed best-reply and (unconditional) regret matching. In a class of bimatrix, 3x3 normal form games (Sparrow and van Strien, 2009), that includes Rock-Paper-Scissors as a special case, rich limit behavior unfolds as the heuristics and/or underlying game parameters are varied.

• 
  02:50 PM - 03:15 PM

  Imitative dynamics and survival of dominated strategies

  • Yannick Viossat, presenter, Université Paris-Dauphine

  Under the replicator dynamics and other imitative dynamics, pure strategies dominated by other pure strategies go extinct. By contrast, such strategies may survive under a large class of innovative dynamics. We argue that the fundamental reason for these results is that innovative dynamics favour rare strategies, while currently studied imitative dynamics do not. It is however easy to imagine imitation processes favouring rare or frequent strategies. The resulting dynamics allow for survival of pure strategies strictly dominated by other pure strategies.

• 
  03:15 PM - 03:40 PM

  Experimenting with spatial assumptions in evolutionary games

  • Frank Thuijsman, presenter, Maastricht University

  We present the results of experiments with spatial assumptions in agent-based simulation studies on generalized rock-paper-scissors games. We compare studies of local interaction in discrete space and in continuous space. These studies use a finite population, consisting of individuals of finitely many types, that are initially randomly distributed in a two-dimensional space. In this population, individuals will interact with eachother according to a process of random selections. An individual selected, the so-called focal individual, does not interact with a random individual from all the population, but rather with a random individual within a certain interaction radius. This interaction will lead to a specific number of offspring that is specified in a so-called fitness matrix. The offspring will be placed within a certain dispersal radius and all offspring will be of the same type as the focal individual. Placing of offspring is only possible when density conditions permit to do so.
  We show that assumptions on the local interactions in discrete space may yield processes that are quite different from those in continuous space, while both may be different from the global interaction model as well.