Question

How to do the c and d?

Player 2 A-1,-1 0,0 0,0 0,0 5,5 Player 1 B 0,0 ci 0,0 0,0 Figure 2: A 3-by-3 Game (a) (2 points) First, what category of game does this fall into (e.g. prisoner's dilemma)? (b) (3 points) Next, find all of the Nash equilibria in this game, being careful to explain (c) (5 points) Which of the Nash equilibria is the best? Which is the worst? Justify Explain. the associated beliefs your answers carefully; notice that we haven't said anything about whether we can compare payoffs across individuals here (d) (5 points) Under what situations might the best equilibrium be played? The worst? How is this related to how the Player feel about one another? How is this manifested in their beliefs? Explain.

Answer 1

Nash equilibrium of the game is (B,B) and (C,C)

c)

Best NE - (C,C)

Worst NE - (B,B)

This is so because playing (C,C) will give a payoff of 5 to each player.

(B, B) is worst NE because each player gets only a payoff of 1.

Deviating from either outcomes give a payoff of zero to that player if other players continue to act in the same way.

d)

If the row player believes that column player is trustworthy and will choose to cooperate to gain higher payoff, it will choose to do the same. Thus best NE (C,C) arises.

On the other hand, if there are low levels of trust and players have incentive to deviate or cause harm to other, it will choose to deviate too and hence (B, B) NE arises.