Given a prediction of opponent behavior in a generalsum two-player normal form game, it is difficult to select a strategy that balances the opportunity to use the prediction to inform one’s action with the risk of becoming predictable. We propose Restricted Stackelberg Response with Safety (RSRS), a novel way of generating such a strategy. RSRS uses an r-safe Stackelberg equilibrium in a modifi...

Given a prediction of opponent behavior in a general-sum two-player normal form game, it is difficult to select a strategy that balances the opportunity to use the prediction to inform one’s action with the risk of becoming predictable. We propose Restricted Stackelberg Response with Safety (RSRS), a novel way of generating such a strategy. RSRS uses an r-safe Stackelberg equilibrium in a modif...

Skewed trees constitute a two-parameter family of recursively constructed trees. Recently, Willemson proved that suitably picked skewed trees are space-optimal for interval time-stamping. At the same time, Willemson proposed a practical but suboptimal algorithm for nonrecursive traversal of skewed trees. We describe an alternative, extremely efficient traversal algorithm for skewed trees. The n...

We consider a general reinforcement learning problem and show that carefully combining the Bayesian optimal policy and an exploring policy leads to minimax sample-complexity bounds in a very general class of (history-based) environments. We also prove lower bounds and show that the new algorithm displays adaptive behaviour when the environment is easier than worst-case.

We investigate the worst-case behavior of the simplex algorithm on linear programs with 3 variables, that is, on 3-dimensional simple polytopes. Among the pivot rules that we consider, the “random edge” rule yields the best asymptotic behavior as well as the most complicated analysis. All other rules turn out to be much easier to study, but also produce worse results: Most of them show essentia...

We prove matching lower and upper bounds on the worst-case OBDD size of a Boolean function, revealing an interesting oscillating behavior.

Coalition formation is one of the key problems in mul-tiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions , but often the number of coalition structures is too large to allow exhaustive search for the optimal one. This paper focuses on nding a worst case bound on how good the optimal coalition structure is compared to the best coalition...

In a system where noncooperative agents share a common resource, we propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model where several agents share a very simple network leads to some interesting mathematics, results, and open...

A continuous tension exists between the day to day requirements for a new product and the requirements in exceptional cases. The System Architect must understand both requirements and be able to discuss them in terms of value in order to make a balanced product. This article gives some handles to tackle this problem. This article builds upon the paper "Requirements Capturing by the System Archi...

The AB game is a two-player game, where the codemaker has to choose a secret code and the codebreaker has to guess it in as few questions as possible. It is a variant of the famous Mastermind game, with the only difference that all pegs in both, the secret and the questions must have distinct colors. In this work, we consider the Generalized AB game, where for given arbitrary numbers p, c with ...