Consider player n in a sequential game.
a. If the player can play 2 actions from a single node, how many pure strategies does he have?
b. Suppose he can play 2 actions at each of two different nodes. How many pure strategies does he have now?
c. Suppose he can play 2 actions at each of three different nodes. How many pure strategies does he have now?
d. Suppose he can play 2 actions at each of four different nodes. How many pure strategies does he have now?
e. Suppose he can play 2 actions at each of k different nodes. How many pure strategies does he have now?
What will be an ideal response?
b. Suppose the actions at each node are L and R. Then his strategies are (L,L), (L,R), (R,L), (R,R) -- so he has 4 possible strategies.
c. We now have to specify an action for each of 3 nodes. The portions of the strategies for the last two nodes are the same as the strategies in (b) -- but now he combines those with either playing L or R in the first stage. Thus, we now have 8 possible strategies.
d. The portions of the strategies for the last 3 nodes are now the same as the strategies if there were only 3 nodes -- i.e. there are 8 of those (as determined in (c)). But now the player has to combine these with either L or R in the first stage -- giving us 16 possible strategies.
e. Following the pattern developed in (a) through (d), the number of strategies is now
.You might also like to view...
Which of the following is likely among the most concentrated industries in the United States?
A) printing and publishing B) soft drinks C) tobacco products D) household vacuum cleaners
On account of a massive construction boom in a country, the demand for iron ore increases substantially. This causes iron ore prices to escalate. Producers increase iron ore mining considerably in the short run, in spite of knowing that this will adversely affect future availability of ore. Which of the following is most similar to the scenario described above?
a. Corn producers hoard their supplies in order to induce a price hike. b. Petroleum manufacturers increase extraction in response to sky-rocketing fuel prices. c. The government of a country makes aforestation mandatory for lumber firms. d. Impressive revenue generation induces the government of a country to impose additional fuel surcharge. e. To discourage smoking, the government of a country increases sales tax on cigarettes.
Frequent substantial fluctuations in the exchange rate can ____________ international trade with an economy.
a. disrupt b. stabilize c. support d. encourage
The dual-control approach refers to
a. dual trading programs, one for sulfur dioxide and one for nitrogen oxides b. different standards used in PSD areas versus nonattainment areas c. the netting program and the offset program d. state control of existing sources and federal control of new or modified sources