1 research outputs found
On terminating improvement in two-player games
A real-valued game has the finite improvement property (FIP), if starting
from an arbitrary strategy profile and letting the players change strategies to
increase their individual payoffs in a sequential but non-deterministic order
always reaches a Nash equilibrium. E.g., potential games have the FIP. Many of
them have the FIP by chance nonetheless, since modifying even a single payoff
may ruin the property. This article characterises (in quadratic time) the class
of the finite games where FIP not only holds but is also preserved when
modifying all the occurrences of an arbitrary payoff. The characterisation
relies on a pattern-matching sufficient condition for games (finite or
infinite) to enjoy the FIP, and is followed by an inductive description of this
class.
A real-valued game is weakly acyclic if the improvement described above can
reach a Nash equilibrium. This article characterises the finite such games
using Markov chains and almost sure convergence to equilibrium. It also gives
an inductive description of the two-player such games.Comment: The proof of Proposition 2 (p 11-12) was incomplete in the first
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