Brodgar Downhole Gauge Analysis with Deconvolution

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Coalitional Equilibria of Strategic Games

Let N be a set of players, C the set of permissible coalitions and G an N-playerstrategic game. A profile is a coalitional-equilibrium if no coalition permissible coalition in C has a unilateral deviation that profits to all its members. Nash-equilibria consider only single player coalitions and Aumann strong-equilibria permit all coalitions to deviate. A new fixed point theorem allows to obtain a condition for the existence of coalitional equilibria that covers Glicksberg for the existence of Nash-equilibria and is related to Ichiishi's condition for the existence of Aumann strong-equilibria.Fixed point theorems, maximum of non-transitive preferences, Nash and strong equilibria, coalitional equilibria

Equilibrium in Two-Player Non-Zero-Sum Dynkin Games in Continuous Time

We prove that every two-player non-zero-sum Dynkin game in continuous time admits an epsilon-equilibrium in randomized stopping times. We provide a condition that ensures the existence of an epsilon-equilibrium in non-randomized stopping times

Rank Bounded Hibi Subrings for Planar Distributive Lattices

Let $L$ be a distributive lattice and $R[L]$ the associated Hibi ring. We show that if $L$ is planar, then any bounded Hibi subring of $R[L]$ has a quadratic Gr\"obner basis. We characterize all planar distributive lattices $L$ for which any proper rank bounded Hibi subring of $R[L]$ has a linear resolution. Moreover, if $R[L]$ is linearly related for a lattice $L$, we find all the rank bounded Hibi subrings of $R[L]$ which are linearly related too.Comment: Accepted in Mathematical Communication

Stopping games in continuous time

We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing literature, we do not assume any conditions on the relations between the payoff processes. We also show that both players have simple epsilon- optimal randomized stopping times; namely, randomized stopping times which are small perturbations of non-randomized stopping times.Comment: 21 page

Inertial game dynamics and applications to constrained optimization

Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied "heavy ball with friction" optimization method. By exploiting a well-known link between the replicator dynamics and the Shahshahani geometry on the space of mixed strategies, the dynamics are stated in a Riemannian geometric framework where trajectories are accelerated by the players' unilateral payoff gradients and they slow down near Nash equilibria. Surprisingly (and in stark contrast to another second-order variant of the replicator dynamics), the inertial replicator dynamics are not well-posed; on the other hand, it is possible to obtain a well-posed system by endowing the mixed strategy space with a different Hessian-Riemannian (HR) metric structure, and we characterize those HR geometries that do so. In the single-agent version of the dynamics (corresponding to constrained optimization over simplex-like objects), we show that regular maximum points of smooth functions attract all nearby solution orbits with low initial speed. More generally, we establish an inertial variant of the so-called "folk theorem" of evolutionary game theory and we show that strict equilibria are attracting in asymmetric (multi-population) games - provided of course that the dynamics are well-posed. A similar asymptotic stability result is obtained for evolutionarily stable strategies in symmetric (single- population) games.Comment: 30 pages, 4 figures; significantly revised paper structure and added new material on Euclidean embeddings and evolutionarily stable strategie

Judge:Don't Vote!

This article explains why the traditional model of the theory of social choice misrepresents reality, it cannot lead to acceptable methods of ranking and electing in any case, and a more realistic model leads inevitably to one method of ranking and electing—majority judgment—that best meets the traditional criteria of what constitutes a good method.Arrow's paradox ; Condorcet's paradox ; Majority judgment ; Skating ; Social choice ; Strategic manipulation ; Voting