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Level of knowledge of rationality increases

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Consider a model where two firms choose some variable q (firm 1 chooses q 1 and firm 2 chooses q2). Their reaction curves are R1(q2)=12 - 2q2, and R2(q1)=12 - 2q1.

a) Find a Nash equilibrium for this game, and graph the reaction curves.b) Consider dynamic adjustment. Start at q1=4.1, and q2=3.8. How would firm 1 want to adjust its output taking 2's output as given? If firm 1 made that adjustment, what would firm 2 want to do? Draw these changes on a graph. Does production converge to the Nash equilibrium?c) (optional) Consider the rationalizability discussion in lecture. Suppose each player is rational, but does not necessarily know that the other is rational (level "K0" knowledge of rationality). Draw possible play on the graph and explain. Now suppose each player is rational and knows that the other player is rational. Draw possible play on the graph and explain.

Does play converge to Nash as the level of knowledge of rationality increases?

d) (optional) If the answers to "b" and "c" differ from the answers we found for the

Cournot model in class, what is the source of the difference?

Reference no: EM133082049

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