Search

The paper is concerned with a zero-sum Stackelberg stochastic linear-quadratic (LQ) diferential game over fnite horizons. Under a fairly weak condition, the Stackelberg equilibrium is explicitly obtained by frst solving a forward stochastic LQ optimal control problem (SLQ problem) and then a backward SLQ problem. Two Riccati equations are derived for constructing the Stackel- berg equilibrium. An interesting fnding is that the diference of these two Riccati equations coincides with the Riccati equation associated with the zero-sum Nash stochastic LQ diferential game, which implies that under the uniform convexity-concavity condition, the Stackelberg equilibrium and the Nash equilibrium are actually identical. Consequently, the Stackelberg equilibrium admits a linear state feedback representation, and the Nash game can be solved in a leader-follower manner. [ABSTRACT FROM AUTHOR]

In this paper I discuss Magid, Fosshage and Shane's impressive overview of the contributions to Relational Self Psychology in the psychoanalytic literature, contributions they see as having emerged for the most part after Kohut's death and therefore as having been carried out almost entirely by Kohut's followers. But while the authors see Kohut's work as having hewed closely to a one-person psychology, I use my discussion to highlight what I see as the two-person themes in Kohut's own writings, suggesting that he may have been more relational in his thinking than initially meets the eye. [ABSTRACT FROM AUTHOR]

The paper studies the open-loop saddle point and the open-loop lower and upper values, as well as their relationship for two-person zero-sum stochastic linear-quadratic (LQ) differential games with deterministic coefficients. It derives a necessary condition for the finiteness of the open-loop lower and upper values and a sufficient condition for the existence of an open-loop saddle point. It turns out that under the sufficient condition, a strongly regular solution to the associated Riccati equation uniquely exists, in terms of which a closed-loop representation is further established for the open-loop saddle point. Examples are presented to show that the finiteness of the open-loop lower and upper values does not ensure the existence of an open-loop saddle point in general. But for the classical deterministic LQ game, these two issues are equivalent and both imply the solvability of the Riccati equation, for which an explicit representation of the solution is obtained. [ABSTRACT FROM AUTHOR]

Results from neuropsychological studies, and neuroimaging and behavioural experiments with healthy individuals, suggest that the imitation of meaningful and meaningless actions may be reliant on different processing routes. The left posterior middle temporal gyrus (pMTG) is one area that might be important for the recognition and imitation of meaningful actions. We studied the role of the left pMTG in imitation using repetitive transcranial magnetic stimulation (rTMS) and two-person motion-tracking. Participants imitated meaningless and emblematic meaningful hand and finger gestures performed by a confederate actor whilst both individuals were motion-tracked. rTMS was applied during action observation (before imitation) over the left pMTG or a vertex control site. Since meaningless action imitation has been previously associated with a greater wrist velocity and longer correction period at the end of the movement, we hypothesised that stimulation over the left pMTG would increase wrist velocity and extend the correction period of meaningful actions (i.e., due to interference with action recognition). We also hypothesised that imitator accuracy (actor-imitator correspondence) would be reduced following stimulation over the left pMTG. Contrary to our hypothesis, we found that stimulation over the pMTG, but not the vertex, during action observation reduced wrist velocity when participants later imitated meaningful, but not meaningless, hand gestures. These results provide causal evidence for a role of the left pMTG in the imitation of meaningful gestures, and may also be in keeping with proposals that left posterior temporal regions play a role in the production of postural components of gesture. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider a linear–quadratic stochastic two-person nonzero-sum differential game. Open-loop and closed-loop Nash equilibria are introduced. The existence of the former is characterized by the solvability of a system of forward–backward stochastic differential equations, and that of the latter is characterized by the solvability of a system of coupled symmetric Riccati differential equations. Sometimes, open-loop Nash equilibria admit a closed-loop representation, via the solution to a system of non-symmetric Riccati equations, which could be different from the outcome of the closed-loop Nash equilibria in general. However, it is found that for the case of zero-sum differential games, the Riccati equation system for the closed-loop representation of an open-loop saddle point coincides with that for the closed-loop saddle point, which leads to the conclusion that the closed-loop representation of an open-loop saddle point is the outcome of the corresponding closed-loop saddle point as long as both exist. In particular, for linear–quadratic optimal control problem, the closed-loop representation of an open-loop optimal control coincides with the outcome of the corresponding closed-loop optimal strategy, provided both exist. [ABSTRACT FROM AUTHOR]

Abstract: Apraxia (a disorder of complex movement) suggests that the left inferior parietal lobule (IPL) plays a role in kinematic or spatial aspects of imitation, which may be particularly important for meaningless (i.e. unfamiliar intransitive) actions. Mirror neuron theories indicate that the IPL is part of a frontoparietal system that can support imitation by linking observed and stored actions through visuomotor matching, and have less to say about different subregions of the left IPL, or how different types of action (i.e. meaningful or meaningless) are processed for imitation. We used repetitive transcranial magnetic stimulation (rTMS) to bridge this gap and better understand the roles of the left supramarginal gyrus (SMG) and left angular gyrus (AG) in imitation. We also examined whether these areas are differentially involved in meaningful and meaningless action imitation. We applied rTMS over the left SMG, over the left AG or during a no‐rTMS baseline condition, and then asked participants to imitate a confederate's actions whilst the arm and hand movements of both individuals were motion‐tracked. rTMS over both the left SMG and the left AG reduced the velocity of participants’ finger movements relative to the actor during imitation of finger gestures, regardless of action meaning. Our results support recent claims in apraxia and confirm a role for the left IPL in kinematic processing during gesture imitation, regardless of action meaning. [ABSTRACT FROM AUTHOR]

We consider Gillette's two-person zero-sum stochastic games with perfect information. For each $$k \in \mathbb {N}=\{0,1,\ldots \}$$ we introduce an effective reward function, called k-total. For $$k = 0$$ and 1 this function is known as mean payoff and total reward, respectively. We restrict our attention to the deterministic case. For all k, we prove the existence of a saddle point which can be realized by uniformly optimal pure stationary strategies. We also demonstrate that k-total reward games can be embedded into $$(k+1)$$ -total reward games. [ABSTRACT FROM AUTHOR]

Imitation is an important form of social behavior, and research has aimed to discover and explain the neural and kinematic aspects of imitation. However, much of this research has featured single participants imitating in response to pre-recorded video stimuli. This is in spite of findings that show reduced neural activation to video versus real life movement stimuli, particularly in the motor cortex. We investigated the degree to which video stimuli may affect the imitation process using a novel motion tracking paradigm with high spatial and temporal resolution. We recorded 14 positions on the hands, arms, and heads of two individuals in an imitation experiment. One individual freely moved within given parameters (moving balls across a series of pegs) and a second participant imitated. This task was performed with either simple (one ball) or complex (three balls) movement difficulty, and either face-to-face or via a live video projection. After an exploratory analysis, three dependent variables were chosen for examination: 3D grip position, joint angles in the arm, and grip aperture. A cross-correlation and multivariate analysis revealed that object-directed imitation task accuracy (as represented by grip position) was reduced in video compared to face-to-face feedback, and in complex compared to simple difficulty. This was most prevalent in the left-right and forward-back motions, relevant to the imitator sitting face-to-face with the actor or with a live projected video of the same actor. The results suggest that for tasks which require object-directed imitation, video stimuli may not be an ecologically valid way to present task materials. However, no similar effects were found in the joint angle and grip aperture variables, suggesting that there are limits to the influence of video stimuli on imitation. The implications of these results are discussed with regards to previous findings, and with suggestions for future experimentation.

This paper is concerned with a linear quadratic stochastic two-person zero-sum differential game with constant coefficients in an infinite time horizon. Open-loop and closed-loop saddle points are introduced. The existence of closed-loop saddle points is characterized by the solvability of an algebraic Riccati equation with a certain stabilizing condition. A crucial result makes our approach work is the unique solvability of a class of linear backward stochastic differential equations in an infinite horizon. [ABSTRACT FROM AUTHOR]

Imitation is an important form of social behavior, and research has aimed to discover and explain the neural and kinematic aspects of imitation. However, much of this research has featured single participants imitating in response to pre-recorded video stimuli. This is in spite of findings that show reduced neural activation to video vs. real life movement stimuli, particularly in the motor cortex. We investigated the degree to which video stimuli may affect the imitation process using a novel motion tracking paradigm with high spatial and temporal resolution. We recorded 14 positions on the hands, arms, and heads of two individuals in an imitation experiment. One individual freely moved within given parameters (moving balls across a series of pegs) and a second participant imitated. This task was performed with either simple (one ball) or complex (three balls) movement difficulty, and either face-to-face or via a live video projection. After an exploratory analysis, three dependent variables were chosen for examination: 3D grip position, joint angles in the arm, and grip aperture. A cross-correlation and multivariate analysis revealed that object-directed imitation task accuracy (as represented by grip position) was reduced in video compared to face-to-face feedback, and in complex compared to simple difficulty. This was most prevalent in the left-right and forward-back motions, relevant to the imitator sitting face-to-face with the actor or with a live projected video of the same actor. The results suggest that for tasks which require object-directed imitation, video stimuli may not be an ecologically valid way to present task materials. However, no similar effects were found in the joint angle and grip aperture variables, suggesting that there are limits to the influence of video stimuli on imitation. The implications of these results are discussed with regards to previous findings, and with suggestions for future experimentation. [ABSTRACT FROM AUTHOR]

In this paper, we consider a linear quadratic stochastic two-person zero-sum differential game. The controls for both players are allowed to appear in both drift and diffusion of the state equation. The weighting matrices in the performance functional are not assumed to be definite/nonsingular. The existence of an open-loop saddle point is characterized by the existence of an adapted solution to a linear forward-backward stochastic differential equation with constraints, together with a convexity-concavity condition, and the existence of a closed-loop saddle point is characterized by the existence of a regular solution to a Riccati differential equation. It turns out that there is a significant difference between open-loop and closed-loop saddle points. Also, it is found that there is an essential feature that prevents a linear quadratic optimal control problem from being a special case of linear quadratic two-person zero-sum differential games. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the ex post implementation of a social choice set with two agents. A social choice set F is ex post implementable with two agents if F satisfies the conditions of ex post incentive compatibility (EPIC) and ex post monotonicity (EM) in an environment that is economic and has a bad outcome. Furthermore, if F is a social choice function, (EPIC), (EM), and an economic environment are sufficient. [Copyright &y& Elsevier]

We study two-person, zero-sum recursive matrix games framing them in the more general context of nonleavable games. Our aim is to extend a result of Orkin (1972) by proving that a uniformly €-optimal stationary strategy is available to player I (player II) in any recursive game such that the set where the value of the game is strictly greater (less) than its utility is finite. The proof exploits some new connections between nonleavable and leavable games. In particular we find sufficient conditions for the existence of €-optimal stationary strategies for player I in a leavable game and we use these as a basis for constructing uniformly €-optimal stationary strategies for the recursive games with which we are concerned. [ABSTRACT FROM AUTHOR]

In this paper, we study repeated games with vector payoffs. Following Blackwell [2], we define weak approachability and its dual property, weak excludability. We use results from differential games with fixed duration to prove that every set is either weakly approachable or weakly excludable. [ABSTRACT FROM AUTHOR]