An Experimental Investigation of Colonel Blotto Games

"This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support all major theoretical predictions. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a 'guerilla warfare' strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players employ a 'stochastic complete coverage' strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields." (author's abstract)"Dieser Artikel untersucht das Verhalten von Individuen in einem 'constant-sum Colonel Blotto'-Spiel zwischen zwei Spielern, bei dem die Spieler mit unterschiedlichen Ressourcen ausgestattet sind und die erwartete Anzahl gewonnener Schlachtfelder maximieren. Die experimentellen Ergebnisse bestätigen alle wichtigen theoretischen Vorhersagen. Im Durchgang, in dem wie in einer Auktion der Sieg in einem Schlachtfeld deterministisch ist, wenden die Spieler, die sich im Nachteil befinden, eine 'Guerillataktik' an, und verteilen ihre Ressourcen stochastisch auf eine Teilmenge der Schlachtfelder. Spieler mit einem Vorteil verwenden eine Strategie der 'stochastischen vollständigen Abdeckung', indem sie zufällig eine positive Ressourcenmenge auf allen Schlachtfeldern positionieren. Im Durchgang, in dem sich der Gewinn eines Schlachtfeldes probabilistisch wie in einer Lotterie bestimmt, teilen beide Spieler ihre Ressourcen gleichmäßig auf alle Schlachtfelder auf." (Autorenreferat

Is it necessary to re-fuse a non-union of a hallux metatarsophalangeal joint arthrodesis?

BACKGROUND: The standard treatment for a non-union of the hallux metatarsophalangeal joint fusion has been to revise the fusion. Revision fusion is technically more demanding, often involving bone grafting, more substantial fixation and prolonged period of immobilization postoperatively. We present data to suggest that removal of hardware and debridement alone is an alternative treatment option. ---------- MATERIALS AND METHODS: A case note review identified patients with a symptomatic non-union after hallux metatarsophalangeal joint (MTPJ) fusion. It is our practice to offer these patients revision fusion or removal of hardware and debridement. For the seven patients that chose hardware removal and were left with a pseudarthrosis, a matched control group was selected from patients who had had successful fusions. Three outcome scores were used. Hallux valgus and dorsiflexion angles were recorded.---------- RESULTS: One hundred thirty-nine hallux MTPJ arthrodeses were carried out. Fourteen non-unions were identified. The rate of non-union in males and following previous hallux MTPJ surgery was 19% and 24%, respectively. In females undergoing a primary MTPJ fusion, the rate was 2.4%. Twelve non-union patients were reviewed at 27 months (mean). Eleven patients had elected to undergo removal of hardware and debridement. Four patients with pseudarthrosis were unhappy with the results and proceeded to either revision fusion or MTPJ replacement. Seven non-union patients, who had removal of hardware alone, had outcome scores marginally worse compared to those with successful fusions.---------- CONCLUSION: Removal of hardware alone is a reasonable option to offer as a relatively minor procedure following a failed arthrodesis of the first MTPJ. This must be accepted on the proviso that in this study four out of 11 (36%) patients proceeded to a revision first MTPJ fusion or first MTPJ replacement. We also found that the rate of non-union in primary first MTPJ fusion was significantly higher in males and those patients who had undergone previous surgery

Common value auctions with independent types

D44, Common values, Standard auctions, Rent extraction,