253,371 research outputs found
The Ranking Problem of Alternatives as a Cooperative Game
This paper considers the ranking problem of candidates for a certain position
based on ballot papers filled by voters. We suggest a ranking procedure of
alternatives using cooperative game theory methods. For this, it is necessary
to construct a characteristic function via the filled ballot paper profile of
voters. The Shapley value serves as the ranking method. The winner is the
candidate having the maximum Shapley value. And finally, we explore the
properties of the designed ranking procedure
Reducing the Effects of Unequal Number of Games on Rankings
Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In such settings, the standard derivations of the methods can produce nonsensical rankings. This paper introduces the idea of including a super-user into the rankings and considers the effect of this fictitious player on the ratings. We apply such techniques to rank batters and pitchers in Major League baseball, professional tennis players, and participants in a free online social game. The ideas introduced in this paper can further the scope that such methods are applied and the depth of insight they offer
Convergence of Learning Dynamics in Information Retrieval Games
We consider a game-theoretic model of information retrieval with strategic
authors. We examine two different utility schemes: authors who aim at
maximizing exposure and authors who want to maximize active selection of their
content (i.e. the number of clicks). We introduce the study of author learning
dynamics in such contexts. We prove that under the probability ranking
principle (PRP), which forms the basis of the current state of the art ranking
methods, any better-response learning dynamics converges to a pure Nash
equilibrium. We also show that other ranking methods induce a strategic
environment under which such a convergence may not occur
Price of Competition and Dueling Games
We study competition in a general framework introduced by Immorlica et al.
and answer their main open question. Immorlica et al. considered classic
optimization problems in terms of competition and introduced a general class of
games called dueling games. They model this competition as a zero-sum game,
where two players are competing for a user's satisfaction. In their main and
most natural game, the ranking duel, a user requests a webpage by submitting a
query and players output an ordering over all possible webpages based on the
submitted query. The user tends to choose the ordering which displays her
requested webpage in a higher rank. The goal of both players is to maximize the
probability that her ordering beats that of her opponent and gets the user's
attention. Immorlica et al. show this game directs both players to provide
suboptimal search results. However, they leave the following as their main open
question: "does competition between algorithms improve or degrade expected
performance?" In this paper, we resolve this question for the ranking duel and
a more general class of dueling games.
More precisely, we study the quality of orderings in a competition between
two players. This game is a zero-sum game, and thus any Nash equilibrium of the
game can be described by minimax strategies. Let the value of the user for an
ordering be a function of the position of her requested item in the
corresponding ordering, and the social welfare for an ordering be the expected
value of the corresponding ordering for the user. We propose the price of
competition which is the ratio of the social welfare for the worst minimax
strategy to the social welfare obtained by a social planner. We use this
criterion for analyzing the quality of orderings in the ranking duel. We prove
the quality of minimax results is surprisingly close to that of the optimum
solution
On top coalitions, common rankings, and semistrict core stability
The top coalition property of Banerjee et al. (2001) and the common ranking property of Farrell and Scotchmer (1988) are sufficient conditions for core stability in hedonic games. We introduce the semistrict core as a stronger stability concept than the core, and show that the top coalition property guarantees the existence of semistrictly core stable coalition structures. Moreover, for each game satisfying the common ranking property, the core and the semistrict core coincide.coalition formation, common ranking property, hedonic games, semistrict core, top coalition property
A network-based dynamical ranking system for competitive sports
From the viewpoint of networks, a ranking system for players or teams in
sports is equivalent to a centrality measure for sports networks, whereby a
directed link represents the result of a single game. Previously proposed
network-based ranking systems are derived from static networks, i.e.,
aggregation of the results of games over time. However, the score of a player
(or team) fluctuates over time. Defeating a renowned player in the peak
performance is intuitively more rewarding than defeating the same player in
other periods. To account for this factor, we propose a dynamic variant of such
a network-based ranking system and apply it to professional men's tennis data.
We derive a set of linear online update equations for the score of each player.
The proposed ranking system predicts the outcome of the future games with a
higher accuracy than the static counterparts.Comment: 6 figure
A Lexicographic Public Good Ranking
In this paper, we consider the consistency of the desirability relation with
the ranking of the players in a simple game provided by some well-known
solutions, in particular the Public Good Index [12] and the criticality-based
ranking [1]. We define a new ranking solution, the lexicographic Public Good
ranking (LPGR), strongly related to the Public Good Index being rooted in the
minimal winning coalitions of the simple game, proving that it is monotonic
with respect to the desirability relation [15], when it holds. A suitable
characterization of the LPGR solution is provided. Finally, we investigate the
relation among the LPGR solution and the criticality-based ranking, referring
to the dual game
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