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This chapter compares conventional static measures of competitive balance with measures that take account of the mobility of teams into the upper ranks of professional leagues, which we call dynamic competitive balance. We use this measure to compare the open soccer leagues that permit entry by the process of promotion and relegation, to the closed leagues of North America where there is no automatic right of entry. We also identify the theoretical distribution of entrants to the top k ranks assuming that all teams have equal probabilities of winning. We find that the open leagues (OL) we study are less balanced, dynamically, than closed leagues (CL), and also that OL lie much further away from the theoretical distribution than CL.

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This paper considers price discrimination when competing firms do not observe a customer's type but only some other variable correlated to it. This is a typical situation in many insurance markets-such as motor insurancewhere it is also often the case that insurance is compulsory. We characterise the equilibria and their welfare properties under various price regimes. We show that discrimination based on immutable characteristics such as gender is a dominant strategy, either when firms offer policies at a fixed price or when they charge according to some consumption variable that is correlated to costs. In the latter case, gender discrimination can be an outcome of strategic interaction alone in situations where it would not be adopted by a monopolist. Strategic price discrimination may also increase cross subsidies between types, contrary to expectations.

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Penalty-kicks are analysed in the literature as 'real life experiments' for assessing the use of rational mixed strategies by professional players. However, each penalty kick cannot be considered a repetition of the same event because of the varying background conditions, in particular the heterogeneous ability of different players. Consequently, aggregate statistics over datasets composed of a large number of penalty kicks mediate the behaviour of the players in different games, and the properties of optimal mixed strategies cannot be tested directly because of aggregation bias. In this paper we model the heterogeneous ability of players. We then test the hypothesis that differently talented players randomise over different actions. To this aim, we study a dataset that collects penalties kicked during shootout series in the last editions of FIFA World-Cup and UEFA Euro-Cup (1994-2012 where kickers are categorized as specialists and non-specialists. The results support our theoretical predictions.

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