UADPhilEcon Ec10 Strategic Choices Lecture 3 The Refinement Project continued Dynamic Games Two dynamic games 20 matches on the table. Two players take turns to collect one or two at a time. The one collecting the 20 th wins!
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The Refinement Project continued
NBI equivalent to CAB
An alternative, non-equilibrium, logic
Node 2: [p½2000 + p½800 + (1-p)800] > 1000 That is, p is at least equal to ⅓.
Node 1: Worth a bluff if p will exceed ⅓ with prob 1 in 2000!
Pr(a3|R is rational) = 0 Pr(d3|R is rational) = 1
Pr(a3|R is irrational) = ½ Pr(d3|R is irrational) = ½
ERC(a2) = 2000[½ p2] + 800[½ p2 + (1-p2)]
So, for C to lean toward a2 ERC(a2) must exceed the sure 1000 pay-off from d2: i.e. 2000[½ p2] + 800[½ p2 + (1-p2)] ≥ 1000 or, p2 ≥ ⅓.
Stage 1: q=Pr(p2 ≥ ⅓| a1). If q is large enough, this means that R feels that the prospects of a successful bluff are good.
In sequential equilibrium: p2=⅓. Why?
Suppose p2>⅓ This is tantamount to saying that R managed to force C to play pure strategy ‘across’ (a2) at stage 2 of the game. But how can this be?
And vice versa