Econ398_HW2Solutions - It’s interesting that...

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Econ 398 Homework 2 Sketchy Solutions 1. There are four Nash Equilibria; each one involves one of the four writing down “$3”, while the other three each write down “$10”. Notice that in a strategy profile where two players, say Alice and Bertha, write down “$3” while the others write down “$10”, then that profile is not a Nash Equilibrium because each one would have been better off had they written down “$10” while everyone else continued to follow the profile. Deviations are considered one-at-a-time, and if even one player to has an incentive to deviate from the strategy profile, let alone two players, the strategy profile is not a Nash Equilibrium. That’s not to say that if both had written down “$10”, they both would have been better off. In that case, they would have gotten nothing. 2. Going North is a weakly dominant strategy for the Japanese convoy. The Nash Equilibrium is for the convoy to go North, and for the Americans to search the North first.
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Unformatted text preview: It’s interesting that understanding your opponent’s incentives helps you figure out what to do. 3. Outcomes where one player is Passive and the other is Aggressive are Nash Equilibria. 4. The Nash Equilibria are (T1,L2); and (T2,R2). Note that (B2,L2) is a Pareto improvement over each of these, so that neither is Pareto Efficient. 5. b) There are four Nash Equilibria; three involve two people contributing and one person not contributing. The fourth involves nobody contributing. c) It’s rare for contributions to public goods to spontaneously arise, except perhaps as a “prestige contribution”, say to a university, or a bequest. When is that last time you heard of people making a large contribution to an elementary school. People won’t even pick up trash along a public trail. Usually contributions to a public good are coordinated through a club which helps make everyone’s effort publicly observable which helps verify that no one is shirking....
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