Acquisition of strategies depending on the opponents' competence level

The development of problem-solving skills from novices to advanced subjects in dependence of the competence level of the opponent is examined in a two-person zero-sum game (Othello). In a repeated-measurement design 18 Ss. (6 Ss in 3 groups) played 10 games against one of three opponent-strategies (implemented on a computer): one "expertlike" strategy, which uses domain specific knowledge and local heuristics (minimax-algorithm with alpha-beta pruning); one "novicelike" strategy, in which global, domain independent problem solving strategies (means-ends analysis, goal-reduction) are implemented; and one strategy, which contradicts the supposed heuristics of the novices, but which results in a "weak" performance (minimization in move-selection). Contrary to our assumptions no significant effects of experience could be verified (win versus loss during single runs). An experience dependent differentiation of global problem solving strategies could not be shown for any of the groups. Neither could a general improving effect of the model for acquiring local, task specific heuristics be proved.     

练习促进内隐策略生成：其发生过程及应用特点

本研究通过设置隐含算术策略的问题情境,比较不同顺序和设置条件的进程段行为反应和ERP数据差异,考察被试在不断练习条件下对隐含策略的习得过程及迁移应用特点。结果：被试在对隐含策略无意识的情况下,第1-4练习进程段的反应时、错误率显著低于第5进程段（探测段）。同时,不同进程段诱发的部分ERPs特征也呈现有规律的变化。结论：在存在隐含策略的算术策略任务情境中,通过练习人们可以在无意识情况下逐渐生成内隐策略,诱发的ERP成分P200、N400s可以部分地反映其生成过程。已生成的内隐策略,能部分地应用到相应的新情境中。     

Decisions of timing in bipolarized conflict situations with complete information

Games of timing constitute a sub-class of two-person, constant-sum, infinite games, where the problem facing each player is not what action to take, but rather when he should take action. The theoretical structure of games of timing with complete information and equal accuracy functions is described. An experimental paradigm of such games is presented by a computer-controlled, two-person, infinite game that simulates the Western-style duel.Ten pairs of male subjects participated in three sessions each in a duel experiment. Each pair played 420 duels in which both players had the same accuracy function, but the starting number of bullets available to each player in the dyad was varied systematically. The results of this experiment are analyzed and discussed in terms of variables that relate to predictions arising from the mathematical theory of duels.     

Subjective randomization in one-and two-person games

Following the study by Rapoport and Budescu (1992), two experiments are reported whose main purpose is to compare the generation of random sequences in one- and two-person games. The first experiment addresses the generation of trinary series in two-person zerosum games with asymmetric players. The second examines the generation of binary series using a between-subjects design, and compares the cognitive processes operating in one- and two-person games. Although both types of games result in similar deviations from randomness, they seem to induce qualitatively different cognitive processes.     

National security games

Issues that arise in using game theory to model national security problems are discussed, including positing nation-states as players, assuming that their decision makers act rationally and possess complete information, and modeling certain conflicts as two-person games. A generic two-person game called the Conflict Game, which captures strategic features of such variable-sum games as Chicken and Prisoners' Dilemma, is then analyzed. Unlike these classical games, however, the Conflict Game is a two-stage game in which each player can threaten to retaliate — and carry out this threat in the second stage — if its opponent chose noncooperation in the first stage.Conditions for the existence of different pure-strategy Nash equilibria, or stable outcomes, are found, and these results are extended to situations in which the players can select mixed strategies (i.e., make probabilistic threats or choices). Although the Conflict Game sheds light on the rational foundations underlying arms races, nuclear deterrence, and other strategic situations, more detailed assumptions are required to tie this generic game to specific conflicts.Steven J. Brams gratefully acknowledges the financial support of the National Science Foundation under Grant No. SES85-20154, the Sloan Foundation, and the Guggenheim Foundation.D. Marc Kilgour gratefully acknowledges the financial support of the Natural Sciences and Engineering Research Council of Canada under Grant No. A8974.     

A Modal Logic for Mixed Strategies

Modal logics have proven to be a very successful tool for reasoning about games. However, until now, although logics have been put forward for games in both normal form and games in extensive form, and for games with complete and incomplete information, the focus in the logic community has hitherto been on games with pure strategies. This paper is a first to widen the scope to logics for games that allow mixed strategies. We present a modal logic for games in normal form with mixed strategies, and demonstrate its soundness and strong completeness. Characteristic for our logic is a number of infinite rules.     

Effective choice in all the symmetric 2 × 2 games

Solution concepts for game play implicitly assume what information is relevant for choosing moves. Maximin and Eliminating Dominated Strategies use payoff order; mixed strategies and Harsanyi??s risk dominance use payoff values. ??Cooperative?? strategies use previous choices, ignoring payoffs altogether. We first define the 12 symmetric 2 × 2 games as a continuous payoff space then use this space to evaluate strategies based on different types of information. Strategic success is shown to be sensitive to actual payoffs and seldom consistent for all games of an ordinally defined category such as Chicken. A new hybrid strategy using both payoff and choice information is introduced and shown to produce efficient outcomes in all symmetric 2 × 2 games when employed by both players. It does well in evolutionary tournaments against strategies of other types, especially in the difficult distribution games including Battle-of-the-Sexes.     

Individual differences in game motivation as moderators of preprogrammed strategy effects in prisoner's dilemma.

The impact of three programmed strategies (tit-for-tat, 100% cooperation, and 100% defection) on cooperation level in the Prisoner's Dilemma game is examined as a function of the subject's motivational orientation (cooperative, competitive, or individualistic). Motivational orientation was assessed on the basis of each subject's choices across four classes of decomposed games. Following this assessment, subject's played 30 trials of Prisoner's dilemma in matrix form against one of the above-mentioned strategies. Results were wholly consistent with predictions, showing that (a) cooperatively oriented subjects cooperate with a tit-for-tat and a 100% cooperative strategy, but defect against a 100% defecting strategy, (b) competitive subjects defect against all three strategies; and (c) individualistic subjects defect against both 100% cooperative and 100% defective strategies, but they cooperate with a tit-for-tat strategy. It appears reasonable to conclude that the outcomes of a Prisoner's Dilemma have affectively different meaning (i.e., values) for subjects of differing orientations, and that subjects of all three orientations adopt strategies that effectively maximize their particular type of reward in the game.     

Analyzing a complex visuomotor tracking task with brain-electrical event related potentials

Non-invasive techniques such as neuroimaging and event-related potential (ERP) methods have dramatically enhanced our understanding of the human brain. According to the requirements of the applied method, it is useful to simplify tasks for methodological reasons. In the present study we tested whether ERP measures are also suitable for analyzing complex tasks. In order to do this, we developed an analysis strategy based on the post hoc analysis of the behavioural data. We applied this method to a pursuit-tracking task of 25 s trial duration, consisting of repeated and non-repeated waveforms, where subjects had to track a target cross with a mouse-controlled cursor cross. An EEG was recorded from 62 channels. Response-locked ERPs were computed for two types of error correction: the correction of errors induced externally by the change of target direction and of internal errors generated by the subject itself. We found several ERP components that could be assigned to different feedback and feedforward controlled processing steps in the frontoparietal circuitry underlying visuomotor control, such as movement planning, movement execution (motor potential), reafferent activity, visuospatial analysis, and attentional (P300) processes. Our results support newer models that propose a role for the posterior parietal cortex in integrating multimodal sensory information. In addition, fast (about 180 ms and probably facilitated by anticipation) and slow (about 230-260 ms) error corrections could be differentiated by the time course of ERP activity. Our results show that complex (motor) tasks can be investigated with ERPs. This opens fruitful perspectives for future research on motor control in an ecological setting.     

The use of electrophysiology in the study of early development

Electrophysiology is a timely and important tool in the study of early cognitive development. This commentary polishes the definition of event‐related potential (ERP) components; often interpreted as expressions of mental processes. Further, attention is drawn to time‐frequency analysis of the electroencephalogram (EEG) which conveys much more information than the exclusive use of traditional ERP methodology. Several studies have shown that frequency bands of the EEG undergo systematic development in early childhood. EEG frequency analysis has a potential in early risk assessment. 40 Hz gamma range oscillation bursts accompany stimulus feature binding both in infants and in adults, probably indexing grouping and selection of distributed neuronal populations. Methodological concerns are noted and the need for long‐term normative studies is stressed. Copyright © 2005 John Wiley & Sons, Ltd.     

Copying strategies and memory on the Complex Figure Test in psychiatric patients

We assessed three copying strategies on the Rey-Osterrieth Complex Figure Test among 50 psychiatric patients. The strategies were featural (detail-focused), contextual (framework-focused), and mixed. Reliable classification of each patient's copying strategy showed 7 patients used a featural and 7 patients used a contextual strategy. The remaining 36 used a mixed strategy involving both elements. Analysis indicated that patients who met DSM-III-R criteria for schizophrenia tended to use a mixed strategy. Nonschizophrenic patients also favoured the mixed approach. Moreover, when subjects were divided into groups based on their strategies, there were no differences in copying accuracy. However, the groups differed on immediate and delayed recall of the Complex Figure Test. Patients who adopted a featural strategy on the copy trial had the lowest recall scores. "Process" variables may be important in understanding neurocognitive functioning in schizophrenia; however, there is little evidence that schizophrenic patients use copying strategies consistent with lateralized impairment of brain function.     

短时接触双人电子游戏对幼儿同伴交往与亲社会行为的影响

电子游戏颇受儿童青睐,其用户日趋低龄化,它对幼儿的影响不容小觑。本实验以双人合作/竞技游戏为载体,考查了短时接触电子游戏对60名4~6岁幼儿的同伴交往与亲社会行为的影响,结果发现：1）幼儿与非好友玩伴共同接触双人电子游戏后会变得更喜欢自己的搭档,将其视为新好友并更希望未来与其交往;2）合作比竞技游戏更能促使幼儿喜爱玩伴,竞技游戏的获胜者比失败者更喜欢其搭档;3）年长比年少幼儿更喜欢与同伴交往;4）与其他非好友同伴相比,幼儿更愿意帮助自己的搭档。这表明短时接触内容适宜的双人电子游戏对幼儿的同伴交往和亲社会行为发展较为有益。     

Regional brain activity during face and word discrimination: simultaneous recording of event-related potentials and positron emission tomography

In order to clarify the brain mechanisms involved in the recognition of faces, words, and figures, spatiotemporal analyses were carried out with event-related potentials (ERPs) and positron emission tomography (PET) in normal subjects. In the first experiment, we analyzed the ERPs of eight normal subjects under a passive habituation paradigm using pictures of faces and letters. In the second experiment, regional cerebral blood flow (rCBF) measured using PET was obtained simultaneously with the ERP recordings during a continuous performance task (CPT) in 12 normal subjects. This required the active discrimination of famous people's faces, meaningful words consisting of two Japanese hiragana characters, and simple geometric figures. There were similar deflections in the global field power (GFP) in the first 200 ms of the passive and active tasks, regardless of type of stimuli. This suggests a common time course in the visual information processing mechanisms during the preattentive stage. Mesiotemporal activity, dominant on the right, was seen during the face discrimination task in both the PET results and the ERP topographies. In the word task, activity that was clearly dominant on the left was observed at around a 160 ms latency in the posteriotemporal region of the ERP topography and this again coincided well with the PET data. The spatiotemporal resolution of the analyses was improved by combining PET and topographic ERP studies, and this provided additional neurophysiological information concerning cognitive processing.     

Wavelet analysis of neuroelectric waveforms: a conceptual tutorial

This paper presents a nontechnical, conceptually oriented introduction to wavelet analysis and its application to neuroelectric waveforms such as the EEG and event related potentials (ERP). Wavelet analysis refers to a growing class of signal processing techniques and transforms that use wavelets and wavelet packets to decompose and manipulate time-varying, nonstationary signals. Neuroelectric waveforms fall into this category of signals because they typically have frequency content that varies as a function of time and recording site. Wavelet techniques can optimize the analysis of such signals by providing excellent joint time-frequency resolution. The ability of wavelet analysis to accurately resolve neuroelectric waveforms into specific time and frequency components leads to several analysis applications. Some of these applications are time-varying filtering for denoising single trial ERPs, EEG spike and spindle detection, ERP component separation and measurement, hearing-threshold estimation via auditory brainstem evoked response measurements, isolation of specific EEG and ERP rhythms, scale-specific topographic analysis, and dense-sensor array data compression. The present tutorial describes the basic concepts of wavelet analysis that underlie these and other applications. In addition, the application of a recently developed method of custom designing Meyer wavelets to match the waveshapes of particular neuroelectric waveforms is illustrated. Matched wavelets are physiologically sensible pattern analyzers for EEG and ERP waveforms and their superior performance is illustrated with real data examples.     

Ambiguous games: Evidence for strategic ambiguity aversion

The problem of ambiguity in games is discussed, and a class of ambiguous games is identified. A total of 195 participants played strategic-form games of various sizes with unidentified co-players. In each case, they first chose between a known-risk game involving a co-player indifferent between strategies and an equivalent ambiguous game involving one of several co-player types, each with a different dominant strategy, and then they chose a strategy for the preferred game. Half the players knew that the ambiguous co-player types were equally likely, and half did not. Half expected the outcomes to be known immediately, and half expected a week's delay. Known-risk games were generally preferred, confirming a significant strategic ambiguity aversion effect. In the delay conditions, players who knew that the ambiguous co-player types were equally likely were significantly less ambiguity averse than those who did not. Decision confidence was significantly higher in 2 × 2 than in larger games.     

Ambiguous games: evidence for strategic ambiguity aversion

The problem of ambiguity in games is discussed, and a class of ambiguous games is identified. A total of 195 participants played strategic-form games of various sizes with unidentified co-players. In each case, they first chose between a known-risk game involving a co-player indifferent between strategies and an equivalent ambiguous game involving one of several co-player types, each with a different dominant strategy, and then they chose a strategy for the preferred game. Half the players knew that the ambiguous co-player types were equally likely, and half did not. Half expected the outcomes to be known immediately, and half expected a week's delay. Known-risk games were generally preferred, confirming a significant strategic ambiguity aversion effect. In the delay conditions, players who knew that the ambiguous co-player types were equally likely were significantly less ambiguity averse than those who did not. Decision confidence was significantly higher in 2 × 2 than in larger games.     

Stimulus comparison strategies and task demands in successive discrimination

This research isolates two distinct strategies used to identify stimuli presented at different rates in successive discrimination tasks. The short-term strategy (used at rapid rates) compares current stimuli to immediately prior stimuli present in sensory or other short-term storage, whereas the long-term strategy (used at slow rates) compares current stimuli to a standard stimulus in long-term memory. In Experiment 1, subjects detected a medium-duration tone amid both long and short distractors. Analysis of false alarms indicated that strategy choice is strongly influenced by event rate, and therefore by the presence or absence of sensory traces of preceding stimuli. Experiment 2 was designed to force subjects to use the short-term strategy (to detect targets, present stimuli had to be compared to their immediate predecessors), and varied the event rate. Subjects were able to maintain a high level of performance throughout the task only at the fastest event rate. This pattern of results suggested that when the task demanded it, subjects could use a particular strategy, but if the event rate (and consequently the availability or otherwise of relevant memorial traces) was not favourable to that strategy, then performance was disadvantaged.     

“P300” and memory: Individual differences in the von Restorff effect

Event-related brain potentials (ERPs) were elicited by words in a free recall paradigm that included a novel item. The P300 component of the ERP is elicited by novel, task-relevant events, and we tested the hypothesis that P300 is a manifestation of the cognitive processing invoked during “context updating.” If the degree to which current representations in working memory need revision is related to P300 amplitude, then the P300 elicited by a given item should be related to the ability to recall that item on a subsequent test. Forty lists were presented to 12 subjects in each of two sessions. The lists were 15 words long, and 1 word, in position 6 through 10, was “isolated” by changing its size. Most subjects recalled these isolated words more often than other words in the same positions (von Restorff effect), and these words also elicited larger P300s than other words. Analysis of variance on the component scores from a principal components analysis revealed that words recalled had a larger amplitude P300 (on initial presentation) than words not recalled. Striking individual differences emerged, and there were strong relationships between the von Restorff effect, overall recall performance, mnemonic strategies, and the association between components of the ERP and recall performance. The overall recall performance of subjects who reported simple (rote) mnemonic strategies was low, but they showed a high von Restorff effect. For these subjects the amplitude of the P300 elicited by words during initial presentation predicted later recall. In contrast, subjects who reported complex mnemonic strategies remembered a high percentage of words and did not show a von Restorff effect. For these subjects P300 did not predict later recall, although a later “slow wave” component of the ERP did. The initial response to isolated items was the same for all subjects (a large P300), and all subjects recognized the isolates faster than other words in a recognition test given at the end of each session. The subjects in whom P300 did not predict recall reported mnemonic strategies that involved organizing the material. These strategies continue long after the time period reflected by P300 (600 msec). Because they were so effective they may have overshadowed the relationship between P300 and recall, which is based on the initial encoding of an event. Our interpretations were further confirmed and clarified from data obtained in a final grand recall and in the recognition test.     

Eye movements and brain electric potentials during reading

The development of theories and computational models of reading requires an understanding of processing constraints, in particular of timelines related to word recognition and oculomotor control. Timelines of word recognition are usually determined with event-related potentials (ERPs) recorded under conditions of serial visual presentation (SVP) of words; timelines of oculomotor control are derived from parameters of eye movements (EMs) during natural reading. We describe two strategies to integrate these approaches. One is to collect ERPs and EMs in separate SVP and natural reading experiments for the same experimental material (but different subjects). The other strategy is to co-register EMs and ERPs during natural reading from the same subjects. Both strategies yield data that allow us to determine how lexical properties influence ERPs (e.g., the N400 component) and EMs (e.g., fixation durations) across neighboring words. We review our recent research on the effects of frequency and predictability of words on both EM and ERP measures with reference to current models of eye-movement control during reading. Results are in support of the proposition that lexical access is distributed across several fixations and across brain-electric potentials measured on neighboring words.