# 4.8. game theoryÂ¶

**Backward Induction**â€“ start at the ends and consider the last moves for each player until the beginning is reached**Dominating strategy**â€“ always gives a better payoff regardless of other playerWeakly dominating strategy â€“ always at least as good

**Mixed strategy**â€“ 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 payoffPrisonerâ€™s Dilllema has dominant strategy of both complying

in a repeated game, this inefficiency can be fixed

Quality choice game â€“ 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 â€“ 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

Playerâ€™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 â€“ one of the main uses of game theory

You should bid how much you are willing to pay

Winnerâ€™s curse â€“ if you win an auction for something with common value, you probably overvalued it