Testing vocabulary is similar to testing in other areas of language knowledge and use. The same criteria of reliability, validity, practicality, and washback need to be considered when designing and evaluating vocabulary tests. In some ways testing vocabulary is easier than testing grammatical knowledge or control of discourse because the units to test are more obviously separate. It is not too difficult to identify what a word type is. However, there are problems and issues and we look at these in this chapter. This chapter has two major divisions. The first major division looks at the purposes of vocabulary tests, covering diagnostic, placement, achievement, and proficiency tests. The second major division looks at different test formats, answering questions like: Should choices be given? Should words be tested in context? How can I measure words that learners don’t know well? This section covers a wide range of vocabulary test formats, along with comments on their design and use.

Users may have multiple concurrent options regarding different objects/resources and their decisions usually negatively influence each other’s utility, which makes the sequential decision-making problem more challenging. In this chapter, we introduce an Indian buffet game to study how users in a dynamic system learn about the uncertain system state and make multiple concurrent decisions by not only considering their current myopic utility, but also the influence of subsequent users’ decisions. We analyze the Indian buffet game under two different scenarios: one of customers requesting multiple dishes without budget constraints and the other with budget constraints. In both cases, we design recursive best-response algorithms to find the subgame-perfect Nash equilibrium for customers and characterize special properties of the Nash equilibrium profile in a homogeneous setting. Moreover, we introduce a non-Bayesian social learning algorithm by which customers can learn the system state, and we theoretically prove its convergence. Finally, we conduct simulations to validate the effectiveness and efficiency of the Indian buffet game.