Discussion Summary Week 13: Game Theory

Game Theory 4/16/13

  • Prisoner’s dilemma
    • Two rational prisoners, don’t know what the other is doing
      • Each can either cooperate or rat out the other prisoner
      • Guaranteed positive outcome with cooperation
      • If only one cooperates, the other receives harsh punishment
      • If neither cooperates, they get an intermediate punishment
  • Stock market crash example
    • Who is going to spend first?
  • Applicability to environmental systems?
    • Difficult without human actor
    • Need conscientious decision-making ability
  • Climate change
    • How powerful are stakeholders?
    • Example: Maldives
    • Reputation matters
    • Public goods games
      • Each agent has fixed asset
        • Chooses how much to contribute to public good
        • Contributions pooled and divided up
        • Largest payoff when everyone contributes
  • Typically communication amongst group
    • Different stakes for different individuals in group
    • Individual decisions depend on whether you think others will adapt or mitigate
    • Very cost-dependent
  • Defectors vs. cooperators vs. loners
    • Defectors do better than cooperators
    • Loners > defectors
    • Cooperators > loners
    • Simpson’s paradox– trend in group of data disappears when groups combined, reverse trend appears when groups divided
    • Deterministic vs. stochastic updating
      • Stochastic—neighbor randomly selected, may or may not update strategy
      • Deterministic—each site taken over by best strategy
        • Loners go extinct
    • Individuals continually update strategy
    • Voluntary participation avoids deadlock of mutual defection
  • Social diversity
    • Different groups in which people are making decisions
    • Fitness changes depending on structure
    • Weighting important
      • Iterating changes structure
    • Power law distribution of wealth (scale-free)
      • Fewer poor people when fixed individual cost
    • Need to consider network structure
    • Rock Paper Scissors games
      • Biodiversity study
        • Non-transitive community (no strict competitive hierarchy)
        • Examples
          • Side blotched lizard
            • 3 different morphs
              • Aggressive, large territory
              • Less aggressive, small territory
              • Sneakers, no territory
              • Equal fitness
              • Oscillate in a period of time
              • Each can invade other morph when it is rare, but is invade-able when common
              • E coli
                • Different forms resistance/growth rate advantages
    • State transition probabilities of focal point depend on current state and states of points within neighborhood
    • Neighborhood size matters
      • Local neighborhood; interaction and dispersal local
      • Global neighborhood- behaves like well-mixed system
    • Spatial scale allowing interaction and dispersal to occur locally can promote diversity (non-hierarchical competitive relations can promote diversity)
    • Extinction via competition
      • Resistance causes extinction
      • Evolutionary suicide—population adapts so that it can no longer persist
      • Almost impossible with symmetric competition, but asymmetric much more likely
    • Constrained movement/non-hierarchical competitive relationships dictate species dominance/equipartition
    • Regional richness explains a large portion of the variance in local richness (75%), local ~50% in regional
  • Allesina and Levine paper
    • Non-hierarchical dynamics arise from multiple limiting factors
    • Assume well-mixed patches
    • Random blind draws to determine outcome of each pairwise  competition
    • Species oscillate in predictable manner over long periods of time

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