1,745 research outputs found
Projections and functions of Nash equilibria
We show that any non-empty compact semi-algebraic subset of mixed action profiles on a fixed player set can be represented as the projection of the set of equilibria of a game in which additional binary players have been added. Even stronger, we show that any semi-algebraic continuous function, or even any semi-algebraic upper-semicontinuous correspondence with non-empty convex values, from a bounded semi-algebraic set to the unit cube can be represented as the projection of an equilibrium correspondence of a game with binary players in which payoffs depend on parameters from the domain of the function or correspondence in a multi-affine way. Some extensions are also presented
Distributivity breaking and macroscopic quantum games
Examples of games between two partners with mixed strategies, calculated by
the use of the probability amplitude as some vector in Hilbert space are given.
The games are macroscopic, no microscopic quantum agent is supposed. The reason
for the use of the quantum formalism is in breaking of the distributivity
property for the lattice of yes-no questions arising due to the special rules
of games. The rules of the games suppose two parts: the preparation and
measurement. In the first part due to use of the quantum logical
orthocomplemented non-distributive lattice the partners freely choose the wave
functions as descriptions of their strategies. The second part consists of
classical games described by Boolean sublattices of the initial non-Boolean
lattice with same strategies which were chosen in the first part. Examples of
games for spin one half are given. New Nash equilibria are found for some
cases. Heisenberg uncertainty relations without the Planck constant are written
for the "spin one half game"
Payoff Performance of Fictitious Play
We investigate how well continuous-time fictitious play in two-player games
performs in terms of average payoff, particularly compared to Nash equilibrium
payoff. We show that in many games, fictitious play outperforms Nash
equilibrium on average or even at all times, and moreover that any game is
linearly equivalent to one in which this is the case. Conversely, we provide
conditions under which Nash equilibrium payoff dominates fictitious play
payoff. A key step in our analysis is to show that fictitious play dynamics
asymptotically converges the set of coarse correlated equilibria (a fact which
is implicit in the literature).Comment: 16 pages, 4 figure
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