Problem 2

Problem 2Suppose we are analyzing an equilibrium in which the MMs’ strategy is to not acquire information (pn = 0 for n = 1, 2). Argue that in this case, bn = 1/2 in equilibrium.
Lack of value information implies that both players are bound to make a bid that is defined by the expectation of the market. In essence, the prospect of attaining bn-V would remain equally distributed among the two market markers. Arguably, the attribute of the trader stands dismissed along the implication of noise. Considering the input of the two market markers, n1 and n2, their ability to achieve bn when the value is unknown would be split evenly
MMn1 = bn – V
MMn2 = bn – V
But V = 0 (since v is undisclosed)
Thus, gains from bid would equate to bn.
The probability of attaining bn for each player would be 50%,
Thus, at equilibrium, bn = ½
Suppose MMn chooses never to become informed (pn = 0), and MMm chooses always to become informed (pm = 1). Suppose the uninformed MM sets prices 0 < bn ≤ an < 1. Argue that in this case, the informed MM should optimally set bid (ask) price marginally above (below) the informed MM’s bid (ask) price whenever V = 1 (V = 0). As for the ask (bid) price when V = 1 (V = 0), any price such that the informed MM will not sell (buy) the asset is optimal.
Price setting for MMn is bound by their comprehension of the market. In the case of MMn1 assuming ignorance of the value, the modelling of the pricing for both ask and bid would be:
0 < bn ≤ an < 1
The trading price model is guided by the impression of the value remaining unknown, and the possibility of settling at 1 as its optimal.

Assuming MMn2 is informed of the value, then the guiding model would be guided by the established information. The new model would indicate:
1 < bn ≤ an > 1
In the pricing model for the informed MM, the bid price is beyond that the uninformed MM, while the asking price is below that of the informed counterpart.
Show that the lowest c such that no MM becomes informed in equilibrium is c = 1/4. That is to say, MMs will be uninformed for c > 1/4, but informed (pn > 0 for at least one MM) for c < 1/4.
The probability of learning V is defined by the number of the interested parties. In essence, of the two MMs, only one can learn V, and at a cost of C
Thus, each MM has a 50% chance of accessing C. Arguably, C = ½
Determining the party with the C in either case would involve finding the probability of both players securing the disclosure of the V value. In that case, MMn1 has ½ chances and MMn2 has ½ prospects. Cumulatively, they both have the product of their respective prospects, implying ¼ chances. On assumption, that would be the lowest possible value of C when reflected from the chances shared by the market.
Suppose MM1 becomes informed for sure (p1 = 1) whereas MM2 does not become informed (p2 = 0). Calculate the bid price set by MM2 in this case (calculate b2) and argue that p1 = 1 and p2 = 0 can never be an equilibrium