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