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Question: hi im pretty much struggling with nash equilibrium of advanced...

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I'm pretty much struggling with Nash Equilibrium of advanced level of Game Theory, yet I need to make progress anyway while catching up the concepts.

It would be great if you enlighten me any techniques or tips to solve these questions.

Thanks in advanced.

1. Find a Nash equilibrium for the peer-effects game in which u,(s,,s-i) =-(ai-Si)2-λ, . (s,-$2)2 for i = 1,2 Notice that the equilibrium will be a function of the given parameters 2. There are two individuals with one unit of resources each. Let x i be the amount that individual i devotes to consumption and 1-x i the amount donated towards a public good, so the amount of public good provided is The individuals utility for private consumption and public good is Each individual chooses the value of E 10, 1 simultaneously. Write their payoffs as a function of their actions only and compute a Nash equilibrium for this game. 3. Compute a Nash equilibrium of the Cournot-duopoly game when C2 >c>0 and a+c2-2c>0> ac-2c2 Remember that quantities must be positive quantities: 9142 10,+oo The payoff functions are as we say in class 14(4-4-i) = (α-β(ql + q2) _ c:) . qì, for i = 1.2.

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