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Passing a bill into law in the United States requires the signature of the President of the United States, and a simple majority in both the Senate (composed of 100 Senators) and the House of Representatives (composed of 435 members), or alternatively a two-thirds majority in both the Senate and the House of Representatives required to override a presidential veto.
(a) Write down the coalitional function of the corresponding game.
(b) Is this a weighted majority game? If you answer yes, write down the quota and weights of the game. If you answer no, prove that it is not a weighted majority game.
Find all the equilibria of the following two-player game.- What are all the subgames of the two-stage game?- Find all the subgame perfect equilibria of the two-stage game.
Three students, Jim, Joan, and Jethroe are registered for the same class and attend independently to each other, Jim 95.7% of the time, Joan 92.3% of the time, and Jethroe 82.8% of the time. What is the probability that on any given day:
Construct a belief space in which the described situation is represented by a state of the world and indicate that state.
Show that in order that AA and PP yield a player the same expected payoff when her opponent uses the strategy β, we need β to assign probability (V + v)/2c to AA.
Prove that the set of equilibria of a two-player symmetric game is a symmetric set: if (s1, s2) is an equilibrium, then (s2, s1) is also an equilibrium.
Find all the equilibria of the following two-player zero-sum game.- Explain why one cannot obtain all the equilibria of the game by implementing backward induction.
The following payoff matrix represents long run payoffs for 2-duopolists faced with the option of purchasing or leasing buildings to use for production.
Find the variance of EI and of EII when there are n buyers, whose private values are independent and uniformly distributed over [0, 1].
Alternating Offers game Debby and Barack are jointly conducting a project that will pay them a total payoff of $100. - Describe given situation as an extensive-form game, and find all of its subgame perfect equilibria.
Consider the following data for a simultaneous move ggiven: If you advertise and your rival advertises, you will each earn 5 million dollar in profits.
Prove that the function that associates with every matrix A = (aij ) ∈ Mn,m the value in mixed strategies of the game that it represents is continuous in (aij ).
Manuel is a high school basketball player. He is a 70% free throw shooter. That means his probability of making a free throw is 0.70. What is the probability that Manuel makes his first free throw on his fifth shot?
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