157 research outputs found
On "Indifference" and Backward Induction in Games with Perfect Information
Indifference of a player with respect to two distinct outcomes of a game
cannot be handled by small perturbations, because the actual choice may have
significant impact on other players, and cause them to act in a way that has
significant impact of the indifferent player. It is argued that ties among
rational choices can be resolved by refinements of the concept of rationality
based on the utilities of other players. One such refinement is the concept of
Tit-for-Tat
Remarks on Utility in Repeated Bets
The use of von Neumann -- Morgenstern utility is examined in the context of
multiple choices between lotteries. Different conclusions are reached if the
choices are simultaneous or sequential. It is demonstrated that utility cannot
be additive
An Efficient Interior-Point Method for Online Convex Optimization
A new algorithm for regret minimization in online convex optimization is
described. The regret of the algorithm after time periods is - which is the minimum possible up to a logarithmic term. In
addition, the new algorithm is adaptive, in the sense that the regret bounds
hold not only for the time periods but also for every sub-interval
. The running time of the algorithm matches that of newly
introduced interior point algorithms for regret minimization: in
-dimensional space, during each iteration the new algorithm essentially
solves a system of linear equations of order , rather than solving some
constrained convex optimization problem in dimensions and possibly many
constraints
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