Lucy (L) and Kitty (K) are two lumberjacks working in the forest near Paradise Pond and the Mill River. Each player has a fallback position of a payoff of 12. The interaction between the two lumberjacks works as follows. Lucy and Kitty may choose between chopping wood for 12 hours and chopping wood for 6 hours. Their actions and preferences provide a normal form game as represented by the following Table
Table [[, Kitty], [, Chop 6 hours, Chop 12 hours], [, Chop 6 hours, 51, 51], [Lucy, 66, 24, 12, 12], [, Chop 12 hours, 66], [,,]]
Does either player have a strictly dominant strategy in the Game? Is there a dominant strategy equilibrium? Explain. [3 points]
What are the players’ best responses in the Game? Show all the steps. [2 points]
What is/are the Nash equilibrium/ equilibria of the game? Explain. [3 points]
Define Pareto-efficiency. What are the shortcomings of Pareto efficiency as a criterion for policy-making? [2 points]
Redraw the game as a sequential game with Lucy as the first mover and Kitty as the second mover. [5 points]
Assume that both players are Homo economicus. Show and explain how the game would be solved using backward induction. What would the Nash equilibrium of the game be? [5 points]
Now, instead of Homo economicus, assume that Kitty is still the second mover. But assume now that both Lucy and Kitty are Homo reciprocans and they like to reciprocate the actions of others. Let us test out what this would look like by giving each player an extra payoff of 2 units if they take the same action that the other player takes, but leave their payoffs unmodified if they take a different action. Draw the game tree and solve for the Nash equilibrium. Explain what happens and compare it to your answer when the two players were both Homo economicus. [5 points]
8. Aanchal and Bradyn are two self-regarding traders engaged in exchange over sour snakes (x) and peanut butter cups (y). Their utility functions are given by the following:
Aanchal: uA=(xA)14(yA)34
Bradyn: uB=(xB)14(yB)34
Aanchal has an initial endowment of 13 sour worms and 5 peanut buttercups. Bradyn has an initial endowment of 7 sour worms and 10 peanut butter cups.
i. What is Aanchal’s marginal rate of substitution of peanut butter cups for sour worms ( mrsA )? What is Bradyn’s marginal rate of substitution of peanut butter cups for sour worms (mrsg)? [5 points]
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