Consider a game played by two lobbyists 1 and 2 sponsoring two distinct versions of a...

 

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Consider a game played by two lobbyists 1 and 2 sponsoring two distinct versions of a bill. The value of having version i = {1, 2} approved equals v; to lobbyist i and equals 0 to lobbyist j, for some v₂ > 0. Lobbyists choose how many resources, r; € [0, ∞), to invest to sway the parliament to support their preferred version. The probability that the policy preferred by lobbyist i is approved is given by the following function of the resources invested by the two lobbyists 1/2 if riTj Pi(ri, Tj): ri/(ri+rj) if ri ‡ rj Resources are however costly and the payoff of lobbyist i amounts to ui(ri, Tj) = Pi(ri, Tj ) vi – Ti Tj = The payoff is concave and single peaked in r, for any value rj. Find the best response for each of the two lobbyists. Find the Nash equilibria of this game. Is there always an efficient equilibrium? = Consider a game played by two lobbyists 1 and 2 sponsoring two distinct versions of a bill. The value of having version i = {1, 2} approved equals v; to lobbyist i and equals 0 to lobbyist j, for some v₂ > 0. Lobbyists choose how many resources, r; € [0, ∞), to invest to sway the parliament to support their preferred version. The probability that the policy preferred by lobbyist i is approved is given by the following function of the resources invested by the two lobbyists 1/2 if riTj Pi(ri, Tj): ri/(ri+rj) if ri ‡ rj Resources are however costly and the payoff of lobbyist i amounts to ui(ri, Tj) = Pi(ri, Tj ) vi – Ti Tj = The payoff is concave and single peaked in r, for any value rj. Find the best response for each of the two lobbyists. Find the Nash equilibria of this game. Is there always an efficient equilibrium? =

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Answer Solution Thus best response function for player i necessarily satis... View the full answer