Topic: Analytical Game Theory
Table 10.4 Nash equilibrium exercises (a) (b) (c)
Find all the Nash equilibria for the games in the three tables above. Complete this for each game (a), (b), and (c). Player 1 can choose U or D. Player 2 can play L, M or R.
Draw the payoff matrix for the game ‘rock-paper-scissors’. Suppose that a win gives you 1 utile, a tie 0 utiles, and a loss -1 utiles.
For this game, using the payoff matrix you created, are there any unique pure strategy Nash equilibrium? What are they?
2 Topic: Behavioral Game Theory
For the payoffs in the prisoner’s dilemma above, solve the Nash Equilibrium with the following pure strategies:Table 11.2 Prisoners’ dilemma (in dollar terms)(a) Two egoists: U(x,y)=x2(b) Two utilitarians: U(x,y)=x2+y2(c) Two enviers: U(x,y)=x2-y2(d) Two Rawlsians: U(x,y)=min(x2,y2)
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