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Register a new userOptimal Strategies in Sequential Bidding
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Added by
Krzysztof R. Apt
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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We are interested in mechanisms that maximize social welfare. In [1] this problem was studied for multi-unit auctions with unit demand bidders and for the public project problem, and in each case social welfare undominated mechanisms in the class of feasible and incentive compatible mechanisms were identified. One way to improve upon these optimality results is by allowing the players to move sequentially. With this in mind, we study here sequentia
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We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong link between these two classes.
We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the hardness results on the computation of normal-form correlated equilibria, we introduce the notion of normal-form coarse correlated equilibrium, extending the definition of coarse correlated equilibrium to sequential games. We show that, in two-player games without chance moves, an optimal (e.g., social welfare maximizing) normal-form coarse correlated equilibrium can be computed in polynomial time, and that in general multi-player games (including two-player games with Chance), the problem is NP-hard. For the former case, we provide a polynomial-time algorithm based on the ellipsoid method and also propose a more practical one, which can be efficiently applied to problems of considerable size. Then, we discuss how our algorithm can be extended to games with Chance and games with more than two players.
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of the two hypotheses is made after each test. Under the constraint that the number of samples is bounded, either in expectation or with high probability, we exhibit adaptive strategies that minimize both types of misidentification errors. Namely, we show that these errors decrease exponentially (in the stopping time) with decay rates given by the measured relative entropies between the two states. Moreover, if we allow joint measurements on multiple samples, the rates are increased to the respective quantum relative entropies. We also fully characterize the achievable error exponents for non-adaptive strategies and provide numerical evidence showing that adaptive measurements are necessary to achieve our bounds under some additional assumptions.
We prove that optimal strategies exist in every perfect-information stochastic game with finitely many states and actions and a tail winning condition.
Most analyses of manipulation of voting schemes have adopted two assumptions that greatly diminish their practical import. First, it is usually assumed that the manipulators have full knowledge of the votes of the nonmanipulating agents. Second, analysis tends to focus on the probability of manipulation rather than its impact on the social choice objective (e.g., social welfare). We relax both of these assumptions by analyzing optimal Bayesian manipulation strategies when the manipulators have only partial probabilistic information about nonmanipulator votes, and assessing the expected loss in social welfare (in the broad sense of the term). We present a general optimization framework for the derivation of optimal manipulation strategies given arbitrary voting rules and distributions over preferences. We theoretically and empirically analyze the optimal manipulability of some popular voting rules using distributions and real data sets that go well beyond the common, but unrealistic, impartial culture assumption. We also shed light on the stark difference between the loss in social welfare and the probability of manipulation by showing that even when manipulation is likely, impact to social welfare is slight (and often negligible).
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