Some simple game theoretic models with solutions

Solution concepts

• nash equilibrium
  • mixed nash equilibrium
  • iterated nash equilibrium
• replicator dynamics/ess
• what do humans do

Games

Prisoner's Dilemma

• Iterated version is solvable
• ESS and Axelrod experiments
• Stag hunt
  • Coordination
  • Tend to see lots of hype and bluster (aka Silicon Valley)
• Driving
  • Stag hunt but with multiple "good" outcomes
  • Schelling points
• Chicken
  • Credible commitment
  • Simultaneous vs sequential games
  • Hawks and doves replicator dynamics
• Pie slicing
  • No nash equilibrium
  • Tend to see lots of negotiating and instability
• Soccer
  • Rules
    • Simultaneous game played between the kicker and the goalie
    • Kicker kicks right or left, goalie dives right or left
    • If kicker kicks left (or right) and goalie dives left (right), the kicker wins. Otherwise the goalie wins.
  • Mixed strategies
• Lemons
  • Asymmetric information
• Nim
  • Zugzwang
• Mexican Standoff
  • Truel
• Ponzi
  • Is there a nontrivial Nash equilibrium here?
• Money auction
  • I hold an auction for a $20 bill, but you have to pay you bid whether you win or not.
• Lottery auction
  • Winner's curse
• Non zero-sum games
  • Some cash transfer will lead to the highest sum option
• Smart cow
  • conjunctive vs disjunctive victory conditions
  • FUD strategies