I am doing a game theory assignment. I am currently answering a question on different types of equilibria (pooling, separating and semi-seperating) and must answer questions dependant on the probability of tudors low cost being 'z'. I have now been asked what is the lowest value z could such that this would be considered a pooling equilibrium.
AGE AutoSave ON AGT CW - Saved Home Insert Draw Design Layout References Mailings Review View ? Tell me Share Comments Cover Page v 2 SmartArt v Get Add-ins W v A v 4 Blank Page Chart Table Pictures Shapes Icons 3D Media Links Comment Header Footer Page Text Box WordArt Drop Equation Advanced Page Break o My Add-ins v Wikipedia Models 4 Screenshot v Number Cap Symbol 2) How many pure-strategy equilibria are there when z = 0? What type of equilibrium (separating, pooling, or semiseparating) occurs when z = 0? Explain. Fordor Regardless (11) Conditional (OI) Bluff (LL) 22, 5 44, 0 Tudor Honest (LH) 28, 5 28, 5 When z = 0, the best responses are highlighted. There is one pure-strategy Nash equilibrium at (Honest, Regardless). Furthermore, there is a separating equilibrium at z=0 because Tudor's honesty means that the previously uniformed Fordor learns everything about Tudor after observing an equilibrium move. Tudor therefore no longer has asymmetric 3) How many pure-strategy equilibria are there when z = 1? What type of equilibrium (separating, pooling, or semiseparating) occurs when z = 1? Explain. Fordo Regardless (I1) Conditional (OI) Bluff (LL) 31, -15 112,0 Honest (LH) 31, -1 112, C There are 2 pure-strategy Nash equilibria at (Bluff, Conditional) and (Honest, Conditional). These are semi-separating equilibria because neither types take the same actions 4) What is the lowest value of z such that there is a pooling equilibrium? Pooling equilibrium is when both types would take the same action. Pooling equilibrium would take place at (Bluff, Conditional) 59z + 22, 10z + 5 Page 3 of 5 1263 words English (United Kingdom) Focus E 115%EAv QEAutoSavam : Horne Insert Draw Design Layout References Mailings Review View l3 Share Cl Comments mm m w - r: a v e v m l: v n O lj Blank Page Pictures Shapes Icons SD M Add? Wikipedia Comment Header Footer Page Text Box WordArt Drop Equation Advanced w Ins v ,_' Page Break Models Screenshot v V Number Cap 4 v symbol 4) In the case when Republicans move first, is it possible for Democrats to achieve an outcome that is better than the rollback equilibrium outcome by credibly declaring a strategic move in the pregame? If not, why not? And if so, what sort of strategic move would the Democrats use, and how might they phrase their declaration? U4 Return to the TudorFordor problem from Section Sac, when Tudor's low per-unit production cost is 10. Let 2 be the probability that Tudor actually has a low per-unit cost. 1) Rewrite the table in Figure 9.8 in terms of z. Regardless (ll) Conditional (Oi) Bluff (Ll) 591 + 22. 101 + 5 681 + 44. 0 Honest (LH) 531+28. 101+5 841+ 28,51+5 2) How many pure-strategy equilibria are there when 1 = 0? What type of equilibrium (separating, pooling, or semisegarating occurs when 2 = 0? Explain. 55m; Regardless (II) Conditional (Oi) Page 2 of 5 i26' s (United kingdom)
