Saturday, July 20, 2013

Lyapunov Functions in Exchange Markets

Exchange Markets

  1. People bring stuff - some bring fish, some bring vegetables, some bring money
  2. People exchange stuff (trade)

Assumptions

  1. Each person brings a wagon of stuff
  2. People trade with others but only if each gets an increase in happiness by some amt K 

Lyapunov Function

  • Lyapunov Function
    • Sum of total happiness
  • Maximum
    • There is a maximum happiness - when everyone gets what they want
  • Each move increases value of Lyapunov Function
    • Each trade increases total happiness

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