Evolutionarily Stable Preferences in Contests

We define an indirect evolutionary approach formally and apply it to (Tullock) contests. While it is known (Leininger, 2003) that the direct evolutionary approach in the form of finite population ESS (Schaffer, 1988) yields more aggressive behavior than in Nash equilibrium, it is now shown that the indirect evolutionary approach yields the same more aggressive behavior, too. This holds for any population size N, if evolution of preferences is determined by behavior in two-player contests. The evolutionarily stable preferences (ESP) of the indirect approach turn out to be negatively interdependent, thereby ”rationalizing” the more aggressive behavior.contests, preference evolution, evolutionary stability

Fending off one Means Fending off all: Evolutionary Stability in Submodular Games (new title: Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games)

The implications of evolutionarily stable behavior in finite populations have recently been explored for a variety of aggregative games. This note proves an intimate relationship between submodularity and global evolutionary stability of strategies for these games, which -apart from being of independent interest - accounts for a number of results obtained in the recent literature: we show that any evolutionarily stable strategy (ESS) of a submodular aggregative game must also be globally stable. I.e. if one mutant cannot successfully invade a population, any number of mutants can even less do so.

Evolutionarily Stable Preferences in Contests

We define an indirect evolutionary approach formally and apply it to (Tullock)contests. While it is known (Leininger, 2003) that the direct evolutionary approach in the form of finite population ESS (Schaffer, 1988) yields more aggressive behavior than in Nash equilibrium, it is now shown that the indirect evolutionary approach yields the same more aggressive behavior, too. This holds for any population size N, if evolution of preferences is determined by behavior in two-player contests. The evolutionarily stable preferences (ESP) of the indirect approach turn out to be negatively interdependent, thereby “rationalizing” the more aggressive behavior.

Multivarable nyquist array method with application to turbofan engine control

Extensions to the multivariable Nyquist array (MNA) method are used to design a feedback control system for the quiet clean shorthaul experimental engine. The results of this design are compared with those obtained from the deployment of an alternate control system design on a full scale nonlinear, real time digital simulation. The results clearly demonstrate the utility of the MNA synthesis procedures for highly nonlinear sophisticated design applications

On the number and location of short geodesics in moduli space

A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.Comment: 23 pages, 1 figur

Finite rigid sets in curve complexes

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex X of the curve complex C(S) such that every locally injective simplicial map from X into C(S) is the restriction of an element of Aut(C(S)), unique up to the (finite) point-wise stabilizer of X in Aut(C(S)). Furthermore, if S is not a twice-punctured torus, then we can replace Aut(C(S)) in this statement with the extended mapping class group.Comment: 19 pages, 12 figures. v2: small additions to improve exposition. v3: conclusion of Lemma 2.5 weakened, and proof of Theorem 3.1 adjusted accordingly. Main theorem remains unchange