Picking the winners

We analyze the problem of choosing the w contestants who will win a competition within a group of n > w competitors when all jurors commonly observe who the w best contestants are, but they may be biased. We study conditions on the configuration of the jury so that it is possible to induce the jurors to always choose the best contestants, whoever they are. If the equilibrium concept is dominant strategies, the condition is very strong: there must be at least one juror who is totally impartial, and the planner must have some information about who this juror is. If the equilibrium concept is Nash (or subgame perfect) equilibria the condition is less demanding: for each pair of contestants, the planner must know that there is a number of jurors who are not biased in favor/against any of them and he must have some information about who these jurors are. Furthermore, the latter condition is also necessary for any other equilibrium concept.     

Recognizing graphic matroids

There is no polynomially bounded algorithm to test if a matroid (presented by an “independence oracle”) is binary. However, there is one to test graphicness. Finding this extends work of previous authors, who have given algorithms to test binary matroids for graphicness. Our main tool is a new result that ifM′ is the polygon matroid of a graphG, andM is a different matroid onE(G) with the same rank, then there is a vertex ofG whose star is not a cocircuit ofM.     

On Tutt's Characterization of graphic matroids—a graphic proof

In this paper we present a relatively simple proof of Tutt's characterization of graphic matroids. The proof uses the notion of ‘signed graph’ and it is ‘graphic’ in the sense that it can be presented almost entirely by drawing (signed) graphs. © 1995 John Wiley & Sons, Inc.     

Silent-noisy marksmanship contest with random termination

We consider a marksmanship contest in which Player I has one silent bullet, whereas Player II has one noisy bullet, the first contestant to hit his target wins, and the contest is to be terminated at a random timeT with cdfH(t). The model is a silent-noisy version of our previous paper (Ref. 8), and an extension of silent-noisy duel to nonzero-sum games of timing under an uncertain environment. It is shown that the uncertainty on the termination of the contest has influence on the equilibrium strategies and the equilibrium values, but the silent player has no advantages over the noisy one, in such a nonzero-sum model.The author thanks Professor M. Sakaguchi, Osaka University, who contributed to the research on mathematical decision-making problems and expresses appreciation for his continuous encouragement and guidance. The author also thanks Professor G. Kimeldorf, The University of Texas at Dallas, who invited the author to his university. Finally, the author expresses appreciation to Professors K. Sugahara and W. Fukui, Himeji Institute of Technology, for their encouragement and support.     

Selecting contestants for a rent-seeking contest

In this paper, a contest designer derives profits from aggregate effort exerted by the contestants. I develop a revelation mechanism that enables the contest designer to select a subset of contestants from a pool of candidates in a way that maximizes her profits, even though she is uninformed about the candidates’ valuations for the contest prize. I prove the existence of an incentive compatible and individually rational mechanism. I solve the designer’s problem by using a three-stage game. At Stage 0, the designer designs a mechanism. At Stage 1, candidates participate in the mechanism then a subset of candidates become contestants. Lastly, at Stage 2, information is revealed and the contestants participate in a contest. I show that the optimal size of a contest depends on contestants’ types, the cost of the prize to the designer and on the marginal cost that a contestant imposes on the designer. Contrary to models in which an entry fee s access to the contest, the designer can elicit truthful revelations by imposing revelation costs, and in turn is able to select the optimal subset of contestants.