4.8. game theory¶

  • Backward Induction – start at the ends and consider the last moves for each player until the beginning is reached

  • Dominating strategy – always gives a better payoff regardless of other player

    • Weakly dominating strategy – always at least as good

  • Mixed strategy – active randomization with given probabilities that determines players decision

  • Nash equilibrium - no player can unilaterally (without the other player changing) change his strategy and get a better payoff

  • Prisoner’s Dilllema has dominant strategy of both complying

    • in a repeated game, this inefficiency can be fixed

  • Quality choice game – provider and buyer can each offer high or low bandwidth

    • Two Nash equilibria

    • In an evolutionary game, which equilibrium is picked is based on what percentage of each the provider expects

    • Over time, the buyer will mimic whatever the provider is providing

  • Mixed strategies – compliance inspections

    • The percentage of the time that the inspector should inspect is based on the incentive / penalty that the buyer will cheat

    • It has a mixed equilibrium, based on probabilities

    • Player’s willingness for risk and other factors are considered when determining numbers for utility

  • Many games have first-mover advantage: such as firms determining how much of a product to produce

  • There are games with imperfect information- ex. Deciding whether to announce or cede

  • Bidding in auctions – one of the main uses of game theory

    • You should bid how much you are willing to pay

    • Winner’s curse – if you win an auction for something with common value, you probably overvalued it