Book: Game Theory 101: The Basics
- Read: July 2012
- Rating: 8.0/10
Game Theory 101: The Basics by William Spaniel is a great introduction to Game Theory. If you haven’t had any game theory before, then I’d definitely recommend this book. It’s a pretty hard topic to cover, so I’ll let the book do the speaking…
Strict dominance - Strategy X strictly dominates strategy Y for a player if X provides a greater payoff for that player than Y regardless of what the other players do.
Iterated Elimination of Strictly Dominated Strategies (IESDS) - (in the prisoner’s dilemma), note that confess strictly dominates keep quiet for player A, so we removed keep quiet. Then, you can pretend that the remaining game matters, and find that confess strictly dominates keep quiet for player B.
When you are solving complex games and you find a strictly dominated strategy, eliminate it immediately.
Weak dominance - Strategy X weakly dominates strategy Y for a player if X provides at least as great of a payoff for that player regardless of what the other players do and there is at least one set of opposing strategies for which X pays greater than Y.
Nash equilibrium - A set of strategies, one for each player, such that no player has incentives to change his or her strategy given what the other players are doing.
“Outcomes are a function of preferences and not just the strategic environment”
Best response is simply the optimal strategy for a particular player given what everyone else is doing.
If IESDS reduces the game to a single outcome, that outcome is a Nash Equilibrium, and the only Nash Eq of that game.
Mied strategy Nash Equilibrium - mixed strategy refers to how we are randomizing over multiple strategies rathr than playing a single pure strategy
“Always remember: weak dominance will be the bane of your existence”