How should we make value judgments about wealth inequality? Harsanyi (1953) proposes

to take an individual who evaluates her well-being by expected utility and ask her to evaluate

the wealth possibilities ex-ante (i.e. before she finds her place in society, i.e., under the \veil

of ignorance" of Rawls (1971)) assuming that she will be allocated any one of the possible

wealth levels with equal probability. We propose a different notion of how wealth levels

are allocated, based on a competition or contest. We find that inequality can be captured

through the equilibrium properties of such a game. We connect the inequality measures

so derived to existing measures of inequality, and demonstrate the conditions under which

they satisfy the received key axioms of inequality measures (anonymity, homogeneity and

the Pigou-Dalton transfer principle). Our approach also provides a natural way to discuss

the tradeoff between greater total wealth and greater inequality.