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Felix Fischer

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14 papers
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14

NeurIPS Conference 2025 Conference Paper

Impartial Selection with Predictions

  • Javier Cembrano
  • Felix Fischer
  • Max Klimm

We study the selection of agents based on mutual nominations, a theoretical problem with many applications from committee selection to AI alignment. As agents both select and are selected, they may be incentivized to misrepresent their true opinion about the eligibility of others to influence their own chances of selection. Impartial mechanisms circumvent this issue by guaranteeing that the selection of an agent is independent of the nominations cast by that agent. Previous research has established strong bounds on the performance of impartial mechanisms, measured by their ability to approximate the number of nominations for the most highly nominated agents. We study to what extent the performance of impartial mechanisms can be improved if they are given a prediction of a set of agents receiving a maximum number of nominations. Specifically, we provide bounds on the consistency and robustness of such mechanisms, where consistency measures the performance of the mechanisms when the prediction is correct and robustness its performance when the prediction is incorrect. For the general setting where up to $k$ agents are to be selected and agents nominate any number of other agents, we give a mechanism with consistency $1-O\big(\frac{1}{k}\big)$ and robustness $1-\frac{1}{e}-O\big(\frac{1}{k}\big)$. For the special case of selecting a single agent based on a single nomination per agent, we prove that $1$-consistency can be achieved while guaranteeing $\frac{1}{2}$-robustness. A close comparison with previous results shows that (asymptotically) optimal consistency can be achieved with little to no sacrifice in terms of robustness.

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JAIR Journal 2015 Journal Article

Possible and Necessary Winners of Partial Tournaments

  • Haris Aziz
  • Markus Brill
  • Felix Fischer
  • Paul Harrenstein
  • Jerome Lang
  • Hans Georg Seedig

We study the problem of computing possible and necessary winners for partially specified weighted and unweighted tournaments. This problem arises naturally in elections with incompletely specified votes, partially completed sports competitions, and more generally in any scenario where the outcome of some pairwise comparisons is not yet fully known. We specifically consider a number of well-known solution concepts---including the uncovered set, Borda, ranked pairs, and maximin---and show that for most of them, possible and necessary winners can be identified in polynomial time. These positive algorithmic results stand in sharp contrast to earlier results concerning possible and necessary winners given partially specified preference profiles.

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AAMAS Conference 2012 Conference Paper

Possible and Necessary Winners of Partial Tournaments

  • Haris Aziz
  • Markus Brill
  • Felix Fischer
  • Paul Harrenstein
  • J
  • eacute; r
  • ocirc; me Lang
  • Hans Georg Seedig

We study the problem of computing possible and necessary winners for partially specified weighted and unweighted tournaments. This problem arises naturally in elections with incompletely specified votes, partially completed sports competitions, and more generally in any scenario where the outcome of some pairwise comparisons is not yet fully known. We specifically consider a number of well-known solution concepts---including the uncovered set, Borda, ranked pairs, and maximin---and show that for most of them possible and necessary winners can be identified in polynomial time. These positive algorithmic results stand in sharp contrast to earlier results concerning possible and necessary winners given partially specified preference profiles.

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AAAI Conference 2012 Conference Paper

The Price of Neutrality for the Ranked Pairs Method

  • Markus Brill
  • Felix Fischer

The complexity of the winner determination problem has been studied for almost all common voting rules. A notable exception, possibly caused by some confusion regarding its exact definition, is the method of ranked pairs. The original version of the method, due to Tideman, yields a social preference function that is irresolute and neutral. A variant introduced subsequently uses an exogenously given tie-breaking rule and therefore fails neutrality. The latter variant is the one most commonly studied in the area of computational social choice, and it is easy to see that its winner determination problem is computationally tractable. We show that by contrast, computing the set of winners selected by Tideman’s original ranked pairs method is NP-complete, thus revealing a trade-off between tractability and neutrality. In addition, several known results concerning the hardness of manipulation and the complexity of computing possible and necessary winners are shown to follow as corollaries from our findings.

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AAMAS Conference 2010 Conference Paper

Minimal Retentive Sets in Tournaments

  • Felix Brandt
  • Markus Brill
  • Felix Fischer
  • Paul Harrenstein

Many problems in multiagent decision making can be addressed using tournament solutions, i. e. , functions that associate with each completeand asymmetric relation on a set of alternatives a non-empty subset of the alternatives. For any given tournemant solution $S$, there is another tournament solution $\dot{S}$, which returns the union of all inclusion-minimal sets that satisfy S-retentiveness, a natural stability criterion with respect to S. Schwartz's tournament equilibrium set ($TEQ$) is then defined as $TEQ = T\dot{E}Q$. Due to this unwieldy recursive definition, preciously little is known about $TEQ$. Contingent on a well-known conjecture about $TEQ$, we show that $\dot{S}$ inherits a number of important and desirable properties from $S$. We thus obtain an infinite hierarchy of attractive and efficiently computable tournament solutions that "approximate" $TEQ$, which itself is intractable. This hierarchy contains well-known tournament solutions such as the top cycle ($TC$) and the minimal covering set ($MC$). We further pove a weaker version of the conjecture mentioned above, which establishes $\dot{T}C$ as an attractive new tournament solution.

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AAMAS Conference 2009 Conference Paper

Computational Aspects of Shapley's Saddles

  • Felix Brandt
  • Markus Brill
  • Felix Fischer
  • Paul Harrenstein

Game-theoretic solution concepts, such as Nash equilibrium, are playing an ever increasing role in the study of systems of autonomous computational agents. A common criticism of Nash equilibrium is that its existence relies on the possibility of randomizing over actions, which in many cases is deemed unsuitable, impractical, or even infeasible. In work dating back to the early 1950s Lloyd Shapley proposed ordinal setvalued solution concepts for zero-sum games that he refers to as strict and weak saddles. These concepts are intuitively appealing, they always exist, and are unique in important subclasses of games. We initiate the study of computational aspects of Shapley’s saddles and provide polynomial-time algorithms for computing strict saddles in normal-form games and weak saddles in a subclass of symmetric zero-sum games. On the other hand, we show that certain problems associated with weak saddles in bimatrix games are NP-hard. Finally, we extend our results to mixed refinements of Shapley’s saddles introduced by Duggan and Le Breton.

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IJCAI Conference 2007 Conference Paper

  • Felix Brandt
  • Felix Fischer
  • Paul Harrenstein
  • Yoav Shoham

This paper is a comparative study of game-theoretic solution concepts in strictly competitive multiagent scenarios, as commonly encountered in the context of parlor games, competitive economic situations, and some social choice settings. We model these scenarios as ranking games in which every outcome is a ranking of the players, with higher ranks being preferred over lower ones. Rather than confining our attention to one particular solution concept, we give matching upper and lower bounds for various comparative ratios of solution concepts within ranking games. The solution concepts we consider in this context are security level strategies (maximin), Nash equilibrium, and correlated equilibrium. Additionally, we also examine quasi-strict equilibrium, an equilibrium refinement proposed by Harsanyi, which remedies some apparent shortcomings of Nash equilibrium when applied to ranking games. In particular, we compute the price of cautiousness, i. e. , the worst-possible loss an agent may incur by playing maximin instead of the worst (quasi-strict) Nash equilibrium, the mediation value, i. e. , the ratio between the social welfare obtained in the best correlated equilibrium and the best Nash equilibrium, and the enforcement value, i. e. , the ratio between the highest obtainable social welfare and that of the best correlated equilibrium.

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AAMAS Conference 2007 Conference Paper

Commitment and Extortion

  • Paul Harrenstein
  • Felix Brandt
  • Felix Fischer

Making commitments, e. g. , through promises and threats, enables a player to exploit the strengths of his own strategic position as well as the weaknesses of that of his opponents. Which commitments a player can make with credibility depends on the circumstances. In some, a player can only commit to the performance of an action, in others, he can commit himself conditionally on the actions of the other players. Some situations even allow for commitments on commitments or for commitments to randomized actions. We explore the formal properties of these types of (conditional) commitment and their interrelationships. So as to preclude inconsistencies among conditional commitments, we assume an order in which the players make their commitments. Central to our analyses is the notion of an extortion, which we define, for a given order of the players, as a profile that contains, for each player, an optimal commitment given the commitments of the players that committed earlier. On this basis, we investigate for different commitment types whether it is advantageous to commit earlier rather than later, and how the outcomes obtained through extortions relate to backward induction and Pareto efficiency.

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