This paper investigates static games with unawareness, where players may be unaware of some of the choices that can be made. That is, different players may have different viewson the game. We propose ...an epistemic model that encodes players’ belief hierarchies on choices and views, and use it to formulate the basic reasoning concept of common belief in rationality . We do so for two scenarios: one in which we only limit the possible views that may enter the players’ belief hierarchies, and one in which we fix the players’ belief hierarchies on views. For both scenarios we design a recursive elimination procedure that yields for every possible view the choices that can rationally be made under common belief in rationality.
•I define common belief in rationality in games with unawareness.•I do so for two scenarios: with and without fixed beliefs on views.•For both scenarios, I provide elimination procedures that characterize the choices that can rationally be made under common belief in rationality.
Battigalli (1997) has shown that in dynamic games with perfect information and without relevant ties, the forward induction concept of extensive-form rationalizability yields the backward induction ...outcome. In this paper we provide a new proof for this remarkable result, based on four steps. We first show that extensive-form rationalizability can be characterized by the iterated application of a special reduction operator, the strong belief reduction operator. We next prove that this operator satisfies a mild version of monotonicity, which we call monotonicity on reachable histories. This property is used to show that for this operator, every possible order of elimination leads to the same set of outcomes. We finally show that backward induction yields a possible order of elimination for the strong belief reduction operator. These four properties together imply Battigalli's theorem.
•This paper gives a new proof of Battigalli's theorem, along the following steps.•Step 1: Extensive-form rationalizability is characterized by iterated application of strong belief reduction operator.•Step 2: Strong belief reduction operator is order independent with respect to outcomes.•Step 3: Backward induction is a possible elimination order for strong belief reduction operator.
For dynamic games we consider the idea that a player, at every stage of the game, will always believe that his opponents will choose rationally in the future. This is the basis for the concept of ...common belief in future rationality, which we formalize within an epistemic model. We present an iterative procedure, backward dominance, that proceeds by eliminating strategies from the game, based on strict dominance arguments. We show that the backward dominance procedure selects precisely those strategies that can rationally be chosen under common belief in future rationality if we would not impose (common belief in) Bayesian updating.
•We present the concept of common belief in future rationality for general dynamic games.•We present an algorithm that yields precisely those strategies you can rationally choose under common belief in future rationality.•We compare the concept and algorithm to other related concepts and algorithms in the literature.
This study explores the reported changes over time of the use of language learning strategies based on periodic self-reports of undergraduates that studied Spanish as a foreign language for three ...years. The purpose was to gain a better understanding of how the use of particular strategies evolved and consolidated or disappeared as students became progressively more proficient in Spanish. By using Oxford's taxonomy that differentiates and classifies language learning strategies according to their function, and employing a mixed-method approach that combined successive administrations of Oxford's Strategy Inventory of Language Learning with in-depth interviews, this study found that the most frequently used strategies as reported by students who started as absolute beginners and continued studying Spanish for three consecutive years were metacognitive strategies in the first year, social strategies in the second year and cognitive strategies in the third year. This study analysed and discussed these findings.
Animal welfare monitoring relies on sensor accuracy for detecting changes in animal well-being. We compared the distance calculations based on global positioning system (GPS) data alone or combined ...with motion data from triaxial accelerometers. The assessment involved static trackers placed outdoors or indoors vs. trackers mounted on cows grazing on pasture. Trackers communicated motion data at 1 min intervals and GPS positions at 15 min intervals for seven days. Daily distance walked was determined using the following: (1) raw GPS data (RawDist), (2) data with erroneous GPS locations removed (CorrectedDist), or (3) data with erroneous GPS locations removed, combined with the exclusion of GPS data associated with no motion reading (CorrectedDist_Act). Distances were analyzed via one-way ANOVA to compare the effects of tracker placement (Indoor, Outdoor, or Animal). No difference was detected between the tracker placement for RawDist. The computation of CorrectedDist differed between the tracker placements. However, due to the random error of GPS measurements, CorrectedDist for Indoor static trackers differed from zero. The walking distance calculated by CorrectedDist_Act differed between the tracker placements, with distances for static trackers not differing from zero. The fusion of GPS and accelerometer data better detected animal welfare implications related to immobility in grazing cattle.
All equilibrium concepts implicitly make a correct beliefs assumption, stating that a player believes that his opponents are correct about his first-order beliefs. In this paper we show that in many ...dynamic games of interest, this correct beliefs assumption may be incompatible with a very basic form of forward induction reasoning: the first two layers of extensive-form rationalizability (Pearce, 1984; Battigalli, 1997, epistemically characterized by Battigalli and Siniscalchi, 2002). Hence, forward induction reasoning naturally leads us away from equilibrium reasoning. In the second part we classify the games for which equilibrium reasoning is consistent with this type of forward induction reasoning, and find that this class is very small.
Virtual fencing systems have emerged as a promising technology for managing the distribution of livestock in extensive grazing environments. This study provides comprehensive documentation of the ...learning process involving two conditional behavioral mechanisms and the documentation of efficient, effective, and safe animal training for virtual fence applications on nursing Brangus cows. Two hypotheses were examined: (1) animals would learn to avoid restricted zones by increasing their use of containment zones within a virtual fence polygon, and (2) animals would progressively receive fewer audio-electric cues over time and increasingly rely on auditory cues for behavioral modification. Data from GPS coordinates, behavioral metrics derived from the collar data, and cueing events were analyzed to evaluate these hypotheses. The results supported hypothesis 1, revealing that virtual fence activation significantly increased the time spent in containment zones and reduced time in restricted zones compared to when the virtual fence was deactivated. Concurrently, behavioral metrics mirrored these findings, with cows adjusting their daily travel distances, exploration area, and cumulative activity counts in response to the allocation of areas with different virtual fence configurations. Hypothesis 2 was also supported by the results, with a decrease in cueing events over time and increased reliance with animals on audio cueing to avert receiving the mild electric pulse. These outcomes underscore the rapid learning capabilities of groups of nursing cows in responding to virtual fence boundaries.
