A nash equilibrium for a game is a set of actions from which no agent can unilaterally profitably deviate (Osborne & Rubinstein, 1994, p. 14).
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Game theory is supposed to explain why things happen:
‘Many events and outcomes prompt us to ask: Why did that happen? [...] For example, cutthroat competition in business is the result of the rivals being trapped in a prisoners’ dilemma’ (Dixit, Skeath, & Reiley, 2014, p. 36).
This section introduces two notions that are involved in giving such explanations, dominance and Nash equilibrium.
If you understand these notions and can apply them, you can do game theory.
A Nash equilibrium for a game is a set of actions (sometimes called a ‘strategy’) from which no agent can unilaterally profitably deviate.
‘equilibrium [...] simply means that each player is using the strategy that is the best response to the strategies of the other players’ (Dixit et al., 2014, pp. 32--3)
Although not covered in this section, there is some interesting research on other ways of specifying a ‘best response’ (Misyak & Chater, 2014; Misyak & Chater, 2014). Why might you want to do so? Potential motives arise in Applications and Limits of Game Theory and What Is Team Reasoning?.
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