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 whic...

This paper proposes the Fictitious Reference Iterative Tuning-Particle Swarm Optimization (PSO-FRIT) method to design PID controllers for control systems. The proposed method is an offline PID parameter tuning method and it is not necessary to derive any mathematical models of objected control systems. The proposed method is demonstrated by comparing with the FRIT method in numerical examples. ...

A learning process is belief affirming if the difference between a player's expected payoff in the next period, and the average of his or her past payoffs converges to zero. We show that every smooth discrete fictitious play and every continuous fictitious play is belief affirming. We also provide conditions under which general averaging processes are belief affirming. Journal of Economic Liter...

In the last lecture, we defined several variants of fictitious play. In this lecture we will discuss some examples that reveal the behavior of fictitious play, and then recap the key results on convergence. We will also prove convergence in two cases: two-player zero sum games under the PCTFP dynamic, and N -player games of identical interest under the CTFP dynamic. We use the same notation and...

We combine the controllability and fictitious domain methods to compute time-periodic solution for a wave equation describing scattering by an obstacle. The fictitious domain method uses distributed Lagrange multipliers to satisfy the Dirichlet boundary condition on the scatterer. The controllability technique leads to an optimization problem which we solve with a preconditioned conjugate gradi...

Analysis of the fictitious domain method with L 2-penalty for elliptic and parabolic problems Abstract. The fictitious domain method with L 2-penalty for elliptic and parabolic problems are considered, respectively. The regularity theorems and a priori estimates for L 2-penalty problems are given. We derive error estimates for penalization and finite element interpolation with P 1-element. Nume...

In this paper the Non-Intrusive Polynomial Chaos Method coupled to a Fictitious Domain approach has been applied to oneand twodimensional elliptic problems with geometric uncertainties, in order to demonstrate the accuracy and convergence of the methodology. The main advantage of non-intrusive formulation is that existing deterministic solvers can be used. A new Least-Squares Spectral Element m...

When objects carry the same or different label(s), our perception of the similarity of the objects changes. How does this happen? In two experiments, pictures of animal tissues were presented with fictitious labels and participants judged the similarity of the pictures. The perceived similarity increased when the fictitious labels highlight the interrelatedness of features; this effect of label...

It is known that every continuous time fictitious play process approaches equilibrium in every nondegenerate 2×2 and 2×3 game, and it has been conjectured that convergence to equilibrium holds generally for 2×n games. We give a simple geometric proof of this. As a corollary, we obtain the same result for the discrete fictitious play process. Journal of Economic Literature classification numbers...