game theory

view markdown**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