Equivalence and Stooge Strategies in Zero-Sum Games

Classes of two-person zero-sum games termed "equivalent games" are defined. These are games with identical value and identical optimal mixed-strategies but with different matrix entries and thus different opportunities for exploiting a nonrational opponent. An experiment was conducted to investigate the strategy-choice behavior of subjects playing pairs of these "equivalent games." Also investigated was the extent to which subjects would exploit a programmed stooge as a function of the degree to which the stooge departed from his optimal strategy mix. The results indicated that subjects learned to exploit the nonrational play of the stooge opponent. The game factor, on the other hand, seemed to have no significant effect upon the strategy-choice behavior of the players. The implications of these results are discussed in light of questions raised by previous research on decision-making in 2 x 2 zero-sum games.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67183/2/10.1177_002200277301700306.pd

Extreme events and predictability of catastrophic failure in composite materials and in the Earth

Despite all attempts to isolate and predict extreme earthquakes, these nearly always occur without obvious warning in real time: fully deterministic earthquake prediction is very much a ‘black swan’. On the other hand engineering-scale samples of rocks and other composite materials often show clear precursors to dynamic failure under controlled conditions in the laboratory, and successful evacuations have occurred before several volcanic eruptions. This may be because extreme earthquakes are not statistically special, being an emergent property of the process of dynamic rupture. Nevertheless, probabilistic forecasting of event rate above a given size, based on the tendency of earthquakes to cluster in space and time, can have significant skill compared to say random failure, even in real-time mode. We address several questions in this debate, using examples from the Earth (earthquakes, volcanoes) and the laboratory, including the following. How can we identify ‘characteristic’ events, i.e. beyond the power law, in model selection (do dragon-kings exist)? How do we discriminate quantitatively between stationary and non-stationary hazard models (is a dragon likely to come soon)? Does the system size (the size of the dragon’s domain) matter? Are there localising signals of imminent catastrophic failure we may not be able to access (is the dragon effectively invisible on approach)? We focus on the effect of sampling effects and statistical uncertainty in the identification of extreme events and their predictability, and highlight the strong influence of scaling in space and time as an outstanding issue to be addressed by quantitative studies, experimentation and models