Structure of Extreme Correlated Equilibria: a Zero-Sum Example and its Implications

We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure of its extreme points can be quite complicated. In finite games the ratio of extreme correlated to extreme Nash equilibria can be greater than exponential in the size of the strategy spaces. In polynomial games there can exist extreme correlated equilibria which are not finitely supported; we construct a large family of examples using techniques from ergodic theory. We show that in general the set of correlated equilibrium distributions of a polynomial game cannot be described by conditions on finitely many moments (means, covariances, etc.), in marked contrast to the set of Nash equilibria which is always expressible in terms of finitely many moments

Separable and Low-Rank Continuous Games

In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in separable games. We show that these games admit finitely supported Nash equilibria. Motivated by the bounds on the supports of mixed equilibria in two-player finite games in terms of the ranks of the payoff matrices, we define the notion of the rank of an n-player continuous game and use this to provide bounds on the cardinality of the support of equilibrium strategies. We present a general characterization theorem that states that a continuous game has finite rank if and only if it is separable. Using our rank results, we present an efficient algorithm for computing approximate equilibria of two-player separable games with fixed strategy spaces in time polynomial in the rank of the game

Non-zero-sum Dresher inspection games

Dedicated to the memory of Eckhard Hopnger (1941{1990

Morphological Alternations at the Intonational Phrase Edge

This article develops an analysis of a pair of morphological alternations in K\u27ichee\u27 (Mayan) that are conditioned at the right edge of intonational phrase boundaries. I propose a syntax-prosody mapping algorithm that derives intonational phrase boundaries from the surface syntax, and then argue that each alternation can be understood in terms of output optimization. The important fact is that a prominence peak is always rightmost in the intonational phrase, and so the morphological alternations occur in order to ensure an optimal host for this prominence peak. Finally, I consider the wider implications of the analysis for the architecture of the syntax-phonology interface, especially as it concerns late-insertion theories of morphology

Can Machines Think? Interaction and Perspective Taking with Robots Investigated via fMRI

Krach S, Hegel F, Wrede B, Sagerer G, Binkofski F, Kircher T. Can Machines Think? Interaction and Perspective Taking with Robots Investigated via fMRI. PLoS ONE. 2008;3(7): e2597.Background When our PC goes on strike again we tend to curse it as if it were a human being. Why and under which circumstances do we attribute human-like properties to machines? Although humans increasingly interact directly with machines it remains unclear whether humans implicitly attribute intentions to them and, if so, whether such interactions resemble human-human interactions on a neural level. In social cognitive neuroscience the ability to attribute intentions and desires to others is being referred to as having a Theory of Mind (ToM). With the present study we investigated whether an increase of human-likeness of interaction partners modulates the participants' ToM associated cortical activity. Methodology/Principal Findings By means of functional magnetic resonance imaging (subjects n = 20) we investigated cortical activity modulation during highly interactive human-robot game. Increasing degrees of human-likeness for the game partner were introduced by means of a computer partner, a functional robot, an anthropomorphic robot and a human partner. The classical iterated prisoner's dilemma game was applied as experimental task which allowed for an implicit detection of ToM associated cortical activity. During the experiment participants always played against a random sequence unknowingly to them. Irrespective of the surmised interaction partners' responses participants indicated having experienced more fun and competition in the interaction with increasing human-like features of their partners. Parametric modulation of the functional imaging data revealed a highly significant linear increase of cortical activity in the medial frontal cortex as well as in the right temporo-parietal junction in correspondence with the increase of human-likeness of the interaction partner (computer<functional robot<anthropomorphic robot<human). Conclusions/Significance Both regions correlating with the degree of human-likeness, the medial frontal cortex and the right temporo-parietal junction, have been associated with Theory-of-Mind. The results demonstrate that the tendency to build a model of another's mind linearly increases with its perceived human-likeness. Moreover, the present data provides first evidence of a contribution of higher human cognitive functions such as ToM in direct interactions with artificial robots. Our results shed light on the long-lasting psychological and philosophical debate regarding human-machine interaction and the question of what makes humans being perceived as human