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will post c and d as a separate question
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answerhappygod
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will post c and d as a separate question
will post c and d as a separate question
3. Recall the "Lions and Antelopes" game. There are two antelopes with sizes a and B, where a > B. Each lion choosses an antelope to chase. If more than one lion chases the same antelope they share the prize. The payoff matrix when there are two lions is therefore a/ A= = [ 062 812 812] (a) For what values of a and B is there a symmetric pure strategy Nash equilibrium? When is there an asymmetric Nash equilibrium? (b) When is there a mixed strategy Nash equilibrium? Is it an ESS? (c) Write down the replicator equations for this model, i.e., find p'(t) where p(t) = fraction of lions that chase the big antelope. Find the equilibria, i.e., when is p'(t) = 0? Which equilibria are stable and which are unstable? (d) Now suppose there are three lions (same rules). When is there a symmetric pure strategy Nash equilibrium? Find the mixed strategy Nash equilibrium, when it exists.
3. Recall the "Lions and Antelopes" game. There are two antelopes with sizes a and B, where a > B. Each lion choosses an antelope to chase. If more than one lion chases the same antelope they share the prize. The payoff matrix when there are two lions is therefore a/ A= = [ 062 812 812] (a) For what values of a and B is there a symmetric pure strategy Nash equilibrium? When is there an asymmetric Nash equilibrium? (b) When is there a mixed strategy Nash equilibrium? Is it an ESS? (c) Write down the replicator equations for this model, i.e., find p'(t) where p(t) = fraction of lions that chase the big antelope. Find the equilibria, i.e., when is p'(t) = 0? Which equilibria are stable and which are unstable? (d) Now suppose there are three lions (same rules). When is there a symmetric pure strategy Nash equilibrium? Find the mixed strategy Nash equilibrium, when it exists.
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