Zombie apocalypse! Anna and Ben have to cooperate while zombies attack their village. Or who knows? Maybe the right strategy for one of them is to run away. That's what we will find out in this chapter, using game theory.
The goal is to find Nash Equilibriums in pure strategy and Nash Equilibriums mixed strategy. To that aim, you'll need to understand
- Payoff Matrix — Anna and Ben's payoff, given their chosen strategies
- Best Responses — Anna's best strategy when she knows what strategy Ben chooses
- Pure Strategy Nash Equilibrium — Anna and Ben reach equilibrium if
- Anna plays a best response to Ben's strategy
- Ben plays a best response to Anna's strategy
- Expected Payoff — A player's payoffs when the other randomizes their strategy
- Mixed Strategy Nash Equilibrium — Both players might randomize their strategy, and none would have incentives to deviate
How does that relate to you?
Whenever you make a decision, you influence other people making decisions. And what they do influence you. That applies to actual games like football, zombie apocalypses, but also many many little situations in life. Think about driving, raising your hand in class, or even dating. The outcome depends on the actions of everybody involved.