Game Theory & Nash Equilibrium
Strategic interaction: dominant strategies, the Prisoner's Dilemma, and best responses.
Definition
The study of strategic interaction: players, strategies, payoffs, and equilibriumequilibriumThe point where opposing forces balance, quantity supplied equals quantity demanded, so there's no pressure for price to change. concepts, chiefly Nash equilibriumNash equilibriumA strategy profile where no player can gain by changing their choice alone., where every strategy is a best response to the others.
Key equation
Nash: s*แตข maximizes uแตข(sแตข, s*โแตข) for every player i
The intuition
In the Prisoner's Dilemma both confess even though both staying silent beats it, individually rational moves can be collectively terrible, and that gap powers everything from price wars to arms races. Solve by finding strategies that survive 'would I regret this given what they did?'
Exam tip
Check for dominant strategies first; underline best responses in the payoff matrix and Nash equilibria are the cells with both underlined.
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