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Game theory examines strategic decision-making in situations of conflict, cooperation, and coordination. It has become an established tool in economics, psychology and political science, and more recently has been applied to disease control. Used to examine vaccination uptake in human medicine, game theory shows that when vaccination is voluntary some individuals will choose to "free-ride" on the protection provided by others, resulting in insufficient coverage for control of a vaccine-preventable disease. Here, we use game theory to examine farmer uptake of a new diagnostic ELISA test for sheep scab-a highly infectious disease with an estimated cost exceeding £8M per year to the UK industry. The stochastic game models decisions made by neighboring farmers when deciding whether to adopt the newly available test, which can detect subclinical infestation. A key element of the stochastic game framework is that it allows multiple states. Depending on infestation status and test adoption decisions in the previous year, a farm may be at high, medium or low risk of infestation this year-a status which influences the decision the farmer makes and the farmer payoffs. Ultimately, each farmer's decision depends on the costs of using the diagnostic test vs. the benefits of enhanced disease control, which may only accrue in the longer term. The extent to which a farmer values short-term over long-term benefits reflects external factors such as inflation or individual characteristics such as patience. Our results show that when using realistic parameters and with a test cost around 50% more than the current clinical diagnosis, the test will be adopted in the high-risk state, but not in the low-risk state. For the medium risk state, test adoption will depend on whether the farmer takes a long-term or short-term view. We show that these outcomes are relatively robust to change in test costs and, moreover, that whilst the farmers adopting the test would not expect to see large gains in profitability, substantial reduction in sheep scab (and associated welfare implications) could be achieved in a cost-neutral way to the industry.

In this note oligopoly with iso‐elastic demand is analysed. Unlike previous studies we consider general iso‐elastic demand rather than the case of unit elasticity. An n‐firm Nash‐Cournot equilibrium for the case of heterogeneous constant marginal costs is derived. The main result is a closed‐form solution that shows the dependency of the equilibrium on the elasticity of demand and the share of industry costs. The result has applications to a wide range of areas in oligopoly theory by allowing comparisons across markets with different elasticities of demand.