Journal of Dynamics and Games: latest papers Latest articles for selected journal On repeated games with imperfect public monitoring: From discrete to continuous time Mathias Staudigl and Jan-Henrik Steg Sun, 1 Jan 2017 08:00:00 GMT Global analysis of solutions on the Cournot-Theocharis duopoly with variable marginal costs Iraklis Kollias, Elias Camouzis and John Leventides Sun, 1 Jan 2017 08:00:00 GMT Price of anarchy for graph coloring games with concave payoff     In our generalization, payoff is computed by determining the distance of the player's color to the color of each neighbor, applying a concave function $f$ to each distance, and then summing up the resulting values. This is motivated, e.g., by spectrum sharing, and includes the payoff functions suggested by Kun et al. (2013) for future work as special cases.
    Denote $f^*$ the maximum value that $f$ attains on {${0,\ldots,k-1}$}. We prove an upper bound of $2$ on the price of anarchy if $f$ is non-decreasing or assumes $f^*$ somewhere in {${0,\ldots,⌊\frac{k}{2}⌋}$}. Matching lower bounds are given for the monotone case and if $f^*$ is assumed in $\frac{k}{2}$ for even $k$. For general concave $f$, we prove an upper bound of $3$. We use a new technique that works by an appropriate splitting $\lambda = \lambda_1 + \cdots + \lambda_k$ of the bound $\lambda$ we are proving. ]]>
Lasse Kliemann, Elmira Shirazi Sheykhdarabadi and Anand Srivastav Sun, 1 Jan 2017 08:00:00 GMT Control systems of interacting objects modeled as a game against nature under a mean field approach game against nature according to the mean field theory; that is, we introduce a game model associated to the proportions of the objects in each class, whereas the values of the unknown parameter are now considered as "actions" selected by an opponent to the controller (the nature). Then, letting $N\rightarrow\infty$ (the mean field limit) and considering a discounted optimality criterion, the objective for the controller is to minimize the maximum cost, where the maximum is taken over all possible strategies of the nature. ]]> Carmen G. Higuera-Chan, Héctor Jasso-Fuentes and J. Adolfo Minjárez-Sosa Sun, 1 Jan 2017 08:00:00 GMT Discretized best-response dynamics for the rock-paper-scissors game Peter Bednarik and Josef Hofbauer Sun, 1 Jan 2017 08:00:00 GMT