Fixed points of the (most) refined best reply correspondence, introduced in Balkenborg, Hofbauer, and Kuzmics (2013), in the agent normal form of extensive form games with perfect recall have a remarkable property. They induce fixed points of the same correspondence in the agent normal form of...

This paper studies the dynamic construction of a blockchain by competitive miners. In contrast to the literature, we assume a finite time horizon. It is shown that popular mining strategies such as adherence to conservative mining or to the longest-chain rule constitute pure-strategy Nash...

It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a...

A technique to determine closed-loop Nash equilibria of n-player differential games is developed when their dynamic state-control system is composed of decoupled ODEs. In particular, the theory of Lie point symmetries is exploited to achieve first integrals of such systems.

We propose a model of discrete time dynamic congestion games with atomic players and a single source-destination pair. The latencies of edges are composed by free-flow transit times and possible queuing time due to capacity constraints. We give a precise description of the dynamics induced by...

In this paper a procedure is described that computes for a given bimatrix game all stable sets in the sense of Kohlberg and Mertens (1986). Further the procedure is refined to find the strictly perfect equilibria (if any) of such a game. Keywords and Phrases: Bimatrix game, Computation, Stable...

In this paper, we provide a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game. The algorithm is based on the calculation of the eigenstructure of a certain matrix. The analysis follows the lines of the approach taken by...

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a...

In this note we generalize a numerical algorithm presented in [9] to calculate all solutions of the scalar algebraic Riccati equations that play an important role in finding feedback Nash equilibria of the scalar N-player linear affine-quadratic differential game. The algorithm is based on...