A bankruptcy problem and an information trading problem: by Driessen T. PDF

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L-u/) for the Hider. The user can adjust the number of points plotted, the number of searches made and the scale of the graph. The line x = y is also plotted on the graph and the point of intersection of the graph and the line is approximated. SEARCH4 plots points (Ul. y) where Ul is the probability that the Hider will hide at location 1 and y is the expected search time provided that the Seeker uses the optimal strategy against (Ul, 1 - uI) as determined by the Fundamental Minimality Criterion.

6), the pure strategy f makes the sum Ei=1 'UjS(f)j a minimum if and only if the following condition holds: For each i we have f(i) = x only if (1 - P:r:)c(J,:r:,i-l) is the largest of the quantities (1- Py)c(J,y,i-l), y = 1,2, ... , n. 6) is that it is the optimal strategy for the Hider in the case when all of the Pj are equal. The following result is found in [Ruckle, 1983]. Using Bram's Theory and the Fundamental Minimality Criterion we can give a substantially easier proof. 3 Theorem: If in the DSG all Pj are equal to p, then (a) an optimal strategy for the Hider is to hide at point i with probability lin for each i= 1,2, ...

1) Then cp(z) ~ V for 0 ::5 z ::5 W. 2) forW V and that y = f (x) where 0 < x < W. Then the probability that I is telling the truth is g(y), where g(y) = P(X = ylY = y) = f'(x)/U'(x) + 1). 23 Models for the Game of Liar's Dice If II challenges y, then P(I winslY = y) = g(y). If II accepts y, then P(I winslY = y) = g(y)(l- ip(O)) + (1- g(y))(I- ip((y - x)/(I- x))). Hence it is optimal for II to challenge y if and only if g(y) ::; g(y)(l- ip(O)) + (1- g(y))(I- ip((y - x)/(I- x))) or, equivalently, ip(O)f'(x) ::; 1- ip((y - x)/(I- x)).

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A bankruptcy problem and an information trading problem: Applications to k-convex games by Driessen T.

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