5. There are 10,000,000 players, each of whom has two actions: Revolt, or Not. P

Question

5. There are 10,000,000 players, each of whom has two actions: Revolt, or Not. Payoffs are as follows:

(1) If at least 2,000,000 people revolt, the revolution succeeds, and everyone gets a payoff of 1.

(2) If fewer than 2,000,000 people revolt, and individual i revolts, then i gets -1.

(3) If fewer than 2,000,000 people revolt, and individual i does not, then i gets 0.

Remember to justify your reasoning in your responses.

(a) What is this game’s Nash equilibrium?

(b) Karl Marx, in German Ideology (1845), writes: [T]his communist consciousness and... the alteration of men on a mass scale is [sic] necessary... [for] revolution.

How would you change this game to introduce Marx’s ‘class consciousness’?

(c) What is the new Nash equilibrium?

Explanation / Answer

The Nash equilibrium of this game is when atleast 2,000,000 people revolt and everyone gets a payoff of (1,1).

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