Recent studies of the method of auxiliary sources (MAS) and the method of fundamental solutions (MFS) have shown that it is possible to have convergence of the field, which is the finally desired quantity, together with divergence of the fictitious sources, which are intermediate quantities. The aforementioned studies concern a simple scattering problem, where the scattered field satisfies the ...

The present article explores how factual and fictional media portrayals may activate culturally shared racial and gender stereotypes and influence subsequent judgments involving members of stereotyped groups. In line with previous research (Power, Murphy, and Coover 1996), new data are presented that demonstrate that exposure to a stereotypic or counterstereotypic portrayal primes consistent in...

Fictitious play, an algorithm to predict the opponents next move based on the observed history of play, is one of the oldest simple yet very effective algorithms in game theory. Although using pattern recognition as a more sophisticated way to analyze the history of play seems a logical step, there is little research available on this subject. In this paper we will examine two different types o...

Although the Internet provides an excellent infrastructure for executing combinatorial auctions, we must consider the possibility of new types of cheating. For example, a bidder may try to profit from submitting false bids under fictitious names such as multiple e-mail addresses. Such an action is very difficult to detect since identifying each participant on the Internet is virtually impossibl...

It is shown by example that learning rules of the fictitious play type fail to converge in certain kinds of coordination games. Variants of fictitious play in which past actions are eventually forgotten and that incorporate small stochastic perturbations are better behaved for this class of games: over the long run, players coordinate with probability one. Journal of Economic Literature Classif...

In this lecture we define several variants of the fictitious play dynamic, and study some of the properties of fictitious play. Throughout the section we consider a finite N -player game, where each player i has a finite pure action set Ai. We let ai denote a pure action for player i, and let si ∈ ∆(Ai) denote a mixed action for player i. We will typically view si as a vector in Ri , with si(ai...

In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop learning theory algorithms for computing Nash equilibrium asymmetric $N$-player non-zero-sum stochastic differential games, which refer as \emph{deep play}, a multi-stage process. Specifically at each stage, propose strategy letting individual player optimize her own payoff subject other playe...