Using volume to prove Sperner’s Lemma

We provide a novel proof of Sperner’s Lemma that is intuitive and elementary if certain simple properties of Lebesgue measure are known. The research of A. McLennan is partly funded by the Australian Research Council grant DP0773324. This paper was partly written while he was a member of the Discipline of Economics, The University of Sydney. McLennan also gratefully acknowledges the hospitality of the Economic Theory Center of the University of Melbourne. The research of R. Tourky is partly funded by the Australian Research Council grant A00103450. This paper was partly written while he was a member of the Department of Economics, Purdue University.     

Asymptotic expected number of Nash equilibria of two-player normal form games

The formula given by McLennan [The mean number of real roots of a multihomogeneous system of polynomial equations, Amer. J. Math. 124 (2002) 49–73] is applied to the mean number of Nash equilibria of random two-player normal form games in which the two players have M and N pure strategies respectively. Holding M fixed while N→∞, the expected number of Nash equilibria is approximately . Letting M=N→∞, the expected number of Nash equilibria is , where is a constant, and almost all equilibria have each player assigning positive probability to approximately 31.5915 percent of her pure strategies.     

Community resilience to long-term tourism decline and rejuvenation: a literature review and conceptual model

Studied for decades in disciplines such as ecology, psychology, engineering and sociology ‘resilience’ can be defined as a system's ability to withstand and respond to change. The tourism literature has embraced the concept of community resilience by harnessing concepts of adaptive capacity and vulnerability. Many of these studies have focused on the tourism system's ability to respond to short-term disasters and hazards. With the growth of resilience studies in tourism, it is timely to take stock of the core premise of resilience as it is applied to tourism and to identify key gaps in current research. Consequently, this research aims to identify the core concepts of community resilience, with a focus on its application within tourism. The findings reveal that many studies have been conceptual, although there are an increasing number of empirical studies underpinned by resilience theory. Therefore, a conceptual model is presented to broaden existing resilience research and to guide future research into community resilience to tourism decline and rejuvenation.     

Have Australia's tourism strategies incorporated climate change?

Tourism is widely acknowledged as a key contributor to climate change, but it remains unclear how the tourism industry has been planning for climate change in practice. This paper conducts the most comprehensive critical review of Australia's tourism policy and planning documents to date. The paper explores the complex challenges posed by climate change to tourism and how tourism policy has been adapting over a 15-year period. Drawing on a longitudinal data-set of 477 Australian tourism policy and planning documents at the national, state, regional and local level, this research analyses the strategic discourse on climate change using content analysis and bibliometrics. The findings reveal opportunities, challenges and strategies for the tourism industry to contribute to the sustainable management of climate change. Opportunities include developing more “green” products, while strategies include establishing and/or participating in collaborative climate change schemes and strengthening dialogue surrounding climate change to aid the implementation of sustainable practices. Future research should consider the broader policy-making environment, such as the stakeholders, power and interest dynamics when analysing tourism strategies in relation to climate change.     

The next frontier in tourism emotion research

Emotion is emerging as a central concept in tourism research, critical for the delivery of memorable tourism experiences. However, existing approaches in tourism do not adequately explain the process by which emotions are elicited. Recent advances in cognitive and neuropsychology demonstrate that emotions are elicited through an appraisal process, which occurs in the cortex of the brain. These processes produce chemical monoamine neurotransmitters that lead to bodily feelings, which in turn enable our brain to recognise emotions. This research note draws on Lövheim’s Cube, a self-report scale that provides a proxy indicator of the likely presence of monoamine neurotransmitters of serotonin, dopamine and noradrenaline. Six images of the Great Barrier Reef were used as a stimuli in an online panel survey (n?=?1249). Results demonstrate that images used by tourism stakeholders are likely to produce stronger neurological reactions than images from an environmental non-governmental organisation. Combining recent advances in self-report methods with a neurocognitive approach has the propensity to offers additional insight into emotional reactions to visual stimuli. Further research should focus on the efficacy of utilising self-report measures with cutting edge psychophysiological techniques, such as ambulatory electroencephalography (EEG) to open the door to the next frontier in tourism emotion research.     

Intra-regional variation in land use and livelihood change during a forest transition in Costa Rica's dry North West

The work reported here examined intra-regional differences in land use and livelihood changes made by landholders during a forest transition in a dry region of North-West Costa Rica. It drew on the Sustainable Livelihoods Analysis framework to evaluate a qualitative, comparative study of landholders’ access to livelihood resources in two key landholder groups across five communities. Research findings show that while forest outcomes were similar across the two landholder groups and the five communities (net forest recovery), the livelihood dynamics leading to these outcomes varied. One important factor influencing this was small differences in the geographic location of the five communities, which shaped the effect of mediating institutions and policies on the accessibility and deployment of livelihood resources. The findings point to the importance of locally tailored interventions that reach beyond the field of forest conservation and management. These would include interventions to strengthen rural peoples’ access to resources needed to adapt livelihoods to changing socio-economic conditions. They would also include programs to reduce locally felt trade-offs between conservation and development. The findings also raise doubts that Costa Rica's payments for environmental services (PES) program, as it is currently structured, is an effective mechanisms for linking forest recovery and sustainable rural livelihoods in this particular region.     

Approximation of contractible valued correspondences by functions

Let X and Y be absolute neighborhood retracts (this is a large class of spaces) with X compact, and let F:X→Y be an upper hemicontinuous correspondence whose values are compact and contractible. It is shown that any neighborhood of the graph of F contains the graph of a continuous function f:X→Y. The relevance of this result to fixed point theory is indicated. It is also shown that if X is ‘locally infinite’, then F can be approximated in the stronger sense of the graph of f being close to the graph of F and every point in the graph of F being close to some point in the graph of f. A conjectured generalization of the main result is stated.     

The coexistence of tourism and mining: a strategic framework for cross-sectoral interaction

The tourism and resources sectors are often observed to come into conflict. Yet little research has examined the complex interactions between the two sectors, specifically the strategies for building resilient rural regions. Consequently, this research explores the coexistence of the tourism and resources sectors in the Gladstone and Roma regions in Queensland, Australia. A total of 78 in-depth interviews revealed a complex network of interactions between the tourism and resource sectors, outlining deficiencies in previous theoretical premises on sectoral interaction. Key findings revealed three key synergies including resources sector investment, resources sector multipliers and induced travel, and formal and informal partnerships. Strategies to enhance the coexistence also emerged focused on reducing the negative impacts of the co-evolution process, improving industrial tourism products and developing trust, partnerships and a joint vision between the two sectors. A theoretically informed management framework for future interaction is subsequently proposed for testing and application in other contexts.