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Let Mn,m be the space of matrices of order n × m representing two-player zero-sum games in which Player I has n pure strategies and Player II has m pure strategies.
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 ).
Remark: The sequence of matrices (Ak)k∈N in Mn,m, where to A = (aij ), if
aij = limk→∞ akij, ∀i,j.
Consider now an evolutionary game where what evolves are not strategies in a one-shot game but strategies in a repeated game without discounting
For multiple sclerosis patients we wish to estimate the mean age at which the disease was first diagnosed. We want a 90% confidence interval that is 8 years wide. If the population variance is estimated to be 85 from previous research, how large a..
Identify which player can benefit from making a strategic move, identify the natu re of the strategic move appropriate for this purpose.
Find the optimal pricing scheme for Tony. Discuss whether Tony would gain from being able to commit to not selling monitors in period 2.
How many samples would be required if we wished to obtain the maximum possible number of samples needed (i.e., we do not want to rely on the 37% estimate from above) with a 95% confidence and 0.03 error?
What is the Nash equilibrium in this game? Is there a first-mover advantage or first-mover disadvantage in this game?
Construct a game with payoffs that corresponds to situation - Can you solve the game through iterated dominance?
Do you have enough information to calculate the probability that player 2 selects X in equilibrium? If so, what is this probability?
Generalize the argument that no ESS in the game in Figure 1 assigns positive probability to AP or to PA, to show the following result.
Illustrate this game in a game table. Identify any dominant strategies in the game and solve for the Nash equilibrium.
Suppose this reliability cannot be met, and the actual median is 20,000. So the company instead implements a preventive maintenance policy with a maintenance cycle of 4,000 hours. What is the new reliability at 10,000 hours?
1. capm numerical exercise consider the following three assetswrite a computer program for example using matlab to
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