Tropical Linear Regression and Mean Payoff Games: Or, How to Measure the Distance to Equilibria

Tropical linear programming and parametric mean payoff games

Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, the tropical analogues of classical linear programming results need to be developed. This motivation leads us to study a general tropical linear programming problem. We construct an associated parametric mean payoff game problem, and show that the optimality of a given ...

Tropical linear-fractional programming and parametric mean payoff games

Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to study the tropical analogue of the classical linear-fractional programming problem. We construct an associated parametric mean payoff game problem, and show that...

Tropical Polyhedra are Equivalent to mean Payoff Games

Mean Payoff Games and Linear Complementarity

We suggest new pseudopolynomial and subexponential algorithms for Mean Payoff Games (MPGs). The algorithms are based on representing the MPG decision problem in the forms of non-standard and standard Linear Complementarity Problems (LCPs): find w, z ≥ 0 satisfying w = Mz + q and w · z = 0, (1.1) and monotonic iterative propagation of slack updates.

The correspondence between tropical convexity and mean payoff games

We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum, two player game problems. In particular, we set up an equivalence between the external representation of tropical convex sets and zero-sum stochastic games, in which tropical polyhedra correspond to deterministic games with finite action spaces. Then, we show that the winning initi...