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Article
Open AccessA Mathematical Analysis of an Election System Proposed by Gottlob Frege
In 1998 a long-lost proposal for an election law by Gottlob Frege (1848–1925) was rediscovered in the Thüringer Universitäts- und Landesbibliothek in Jena, Germany. The method that Frege proposed for the election...
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Article
Open AccessRational verification: game-theoretic verification of multi-agent systems
We provide a survey of the state of the art of rational verification: the problem of checking whether a given temporal logic formula ϕ is satisfied in some or all game-theoretic equilibria of a multi-agent system...
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Article
Extending tournament solutions
An important subclass of social choice functions, so-called majoritarian (or C1) functions, only take into account the pairwise majority relation between alternatives. In the absence of majority ties—e.g., when t...
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Article
Hard and Soft Preparation Sets in Boolean Games
A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify gam...
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Article
A note on the McKelvey uncovered set and Pareto optimality
We consider the notion of Pareto optimality under the assumption that only the pairwise majority relation is known and show that the set of necessarily Pareto optimal alternatives coincides with the McKelvey u...
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Article
Minimal retentive sets in tournaments
Tournament solutions, i.e., functions that associate with each complete and asymmetric relation on a set of alternatives a nonempty subset of the alternatives, play an important role in the mathematical social...
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Article
On the Rate of Convergence of Fictitious Play
Fictitious play is a simple learning algorithm for strategic games that proceeds in rounds. In each round, the players play a best response to a mixed strategy that is given by the empirical frequencies of act...
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Chapter and Conference Paper
Boolean Games with Epistemic Goals
We introduce and formally study games in which the goals of players relate to the epistemic states of players in the game. For example, one player might have a goal that another player knows a certain proposit...
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Article
On the Complexity of Iterated Weak Dominance in Constant-Sum Games
In game theory, an action is said to be weakly dominated if there exists another action of the same player that, with respect to what the other players do, is never worse and sometimes strictly better. We inve...
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Chapter and Conference Paper
Pareto Optimality in Coalition Formation
A minimal requirement on allocative efficiency in the social sciences is Pareto optimality. In this paper, we identify a far-reaching structural connection between Pareto optimal and perfect partitions that ha...
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Article
Characterization of dominance relations in finite coalitional games
McGarvey (Econometrica, 21(4), 608–610, 1953) has shown that any irreflexive and anti-symmetric relation can be obtained as a relation induced by majority rule. We address the analogous issue for dominance rel...
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Article
A computational analysis of the tournament equilibrium set
A recurring theme in the mathematical social sciences is how to select the “most desirable” elements given a binary dominance relation on a set of alternatives. Schwartz’s tournament equilibrium set (TEQ) ranks a...
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Chapter and Conference Paper
On the Rate of Convergence of Fictitious Play
Fictitious play is a simple learning algorithm for strategic games that proceeds in rounds. In each round, the players play a best response to a mixed strategy that is given by the empirical frequencies of act...
-
Chapter and Conference Paper
On the Complexity of Iterated Weak Dominance in Constant-Sum Games
In game theory, a player’s action is said to be weakly dominated if there exists another action that, with respect to what the other players do, is never worse and sometimes strictly better. We investigate the...
